ORIGINAL_ARTICLE
Cover vol. 15, no. 1, February 2018
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10.22111/ijfs.2018.3585
ORIGINAL_ARTICLE
INVENTORY MODEL WITH DEMAND AS TYPE-2 FUZZY NUMBER: A FUZZY DIFFERENTIAL EQUATION APPROACH
An inventory model is formulated with type-2 fuzzy parameters under trade credit policy and solved by using Generalized Hukuhara derivative approach. Representing demand parameter of each expert's opinion is a membership function of type-1 and thus, this membership function again becomes fuzzy. The final opinion of all experts is expressed by a type-2 fuzzy variable. For this present problem, to get corresponding defuzzified values of the triangular type-2 fuzzy demand parameters, first critical value (CV)-based reduction methods are applied to reduce corresponding type-1 fuzzy variables which becomes pentagonal in form. After that $\alpha$- cut of a pentagonal fuzzy number is used to construct the upper $\alpha$- cut and lower $\alpha$- cut of the fuzzy differential equation. Different cases are considered for fuzzy differential equation: gH-(i) differentiable and gH-(ii) differentiable systems. The objective of this paper is to find out the optimal time so as to minimize the total inventory cost. The considered problem ultimately reduces to a multi-objective problem which is solved by weighted sum method and global criteria method. Finally the model is solved by generalised reduced gradient method using LINGO (13.0) software. The proposed model and technique are lastly illustrated by providing numerical examples. Results from two methods are compared and some sensitivity analyses both in tabular and graphical forms are presented and discussed. The effects of total cost with respect to the change of demand related parameter ($\beta$), holding cost parameter ($r$), unit purchasing cost parameter ($p$), interest earned $(i_e)$ and interest payable $(i_p)$ are discussed. We also find the solutions for type-1 and crisp demand as particular cases of type-2 fuzzy variable. This present study can be applicable in many aspects in many real life situations where type-1 fuzzy set is not sufficient to formulate the mathematical model. From the numerical studies, it is observed that under both gH-(i) and gH-(ii) cases, total cost of the system gradually reduces for the sub-cases - 1.1, 1.2 and 1.3 depending upon the positions of N(trade credit for customer) and M (trade credit for retailer) with respect to T (time period).
http://ijfs.usb.ac.ir/article_3576_1c33eb5cd6fc2e78a2fb684ac15ad700.pdf
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10.22111/ijfs.2018.3576
EOQ model
Delay in payment
Type-2 fuzzy demand
$alpha$-cut of pentagonal number
Bijoy Krishna
Debnath
true
1
Department of Mathematics, National Institute of Technology, Agartala, 799046, India
Department of Mathematics, National Institute of Technology, Agartala, 799046, India
Department of Mathematics, National Institute of Technology, Agartala, 799046, India
AUTHOR
Pinki
Majumder
pinki.mjmdr@redimail.com
true
2
Department of Mathematics, National Institute of Technology,
Agartala, 799046, India
Department of Mathematics, National Institute of Technology,
Agartala, 799046, India
Department of Mathematics, National Institute of Technology,
Agartala, 799046, India
AUTHOR
Uttam Kumar
Bera
berauttam@yahoo.co.in
true
3
Department of Mathematics, National Institute of Technology, Agartala, 799046, India
Department of Mathematics, National Institute of Technology, Agartala, 799046, India
Department of Mathematics, National Institute of Technology, Agartala, 799046, India
LEAD_AUTHOR
Manoranjan
Maiti
mmmaiti2005@yahoo.co.in
true
4
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India
AUTHOR
[1] T. Allahviranloo and M. Afshar Kermani, Numerical methods for fuzzy linear partial dif-
1
ferential equations under new definition for derivative, Iranian Journal Fuzzy Systems, 7(3)
2
(2010), 33{50.
3
[2] S. Arshed, On existence and uniqueness of solution of fuzzy fractional differential equations,
4
Iranian Journal Fuzzy Systems, 10(6) (2013), 137{151.
5
[3] B. Bede and S. G. Gal, Generalizations of the differentiability of fuzzy-number-valued func-
6
tions with applications to fuzzy differential equations, Fuzzy Sets Syst., 151(4) (2005), 581{
7
[4] B. Bede and L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy Sets
8
and Systems, 230(5) (2013), 119{141.
9
[5] K. J. Chung and L. E. Cardenas-Barron, The simplied solution procedure for deteriorating
10
items under stock-dependent demand and two-level trade credit in the supply chain manage-
11
ment, Appl. Math. Model., 37(7) (2013), 4653{4660.
12
[6] K. J. Chung, L. E. Cardenas-Barron and P. S. Ting, An inventory model with non-instan-
13
taneous receipt and exponentially deteriorating items for an integrated three layer supply
14
chain system under two levels of trade credit, Int. J. Prod. Eco., 155(5) (2014), 310{317.
15
[7] S. C. Chen, L. E. Cardenas-Barron and J. T. Teng, Retailer's economic order quantity when
16
the supplier offers conditionally permissible delay in payments link to order quantity, Int. J.
17
Prod. Econ., 155(3) (2014), 284{291.
18
[8] L. E. Cardenas-Barron, K. J. Chung and G. Trevio-Garza, Celebrating a century of the
19
economic order quantity model in honor of For Whitman Harris, Int. J. Prod. Econ., 155(7)
20
(2014), 1{7.
21
[9] B. Das, N. K. Mahapatra and M. Maiti, Initial-valued first order fuzzy differential equation
22
in Bi-level inventory model with fuzzy demand, Math. Model. Anal., 13(4) (2008), 493{512.
23
[10] D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press,
24
New York, 1980.
25
[11] D. Dubois and H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci., 9(6) (1978), 613{
26
[12] R. Ezzati, K. Maleknejad, S. Khezerloo and M. Khezerloo Convergence, Consistency and
27
stability in fuzzy differential equations, Iranian Journal Fuzzy Systems, 12(3) (2015), 95{
28
[13] S. K. Goyal, Economic order quantity under conditions of permissible delay in payments, J.
29
Oper. Res. Soc., 36(4) (1985), 335{338.
30
[14] P. Guchhait, M. K. Maiti and M. Maiti, A production inventory model with fuzzy produc-
31
tion and demand using fuzzy differential equation: An interval compared genetic algorithm
32
approach, Eng. Appl. Artif. Intel., 26(7) (2013), 766{778.
33
[15] Y. F. Huang, Supply chain model for the Retailer's ordering policy under two levels of delay
34
payments derived algebraically, Opsearch, 44(8) (2007), 366{377.
35
[16] N. N. Karnik and J. M. Mendel, Centroid of a type-2 fuzzy set, Information Sciences, 132(6)
36
(2001), 195{220.
37
[17] A. Kandel and W. J. Byatt, Fuzzy differential equations. In Proceedings of the International
38
Conference on Cybernetics and Society, Tokyo, November 1978, 1213{1216.
39
[18] F. Liu, An efficient centroid type-reduction strategy for general type-2 fuzzy logic system,
40
Information Sciences, 178(7) (2008), 2224{2236.
41
[19] P. Majumder, U. K. Bera and M. Maiti, An EPQ model for two-warehouse in unremitting
42
release pattern with two level trade credit period concerning both supplier and retailer, Appl.
43
Math. Comput., 274(6) (2016), 430{458.
44
[20] M. Mizumoto and K. Tanaka, Fuzzy sets of type-2 under algebraic product and algebraic sum,
45
Fuzzy Sets and Systems, 5(3) (1981), 277{280.
46
[21] J. S. Martnez, R. I. John, D. Hissel and M. C. Pera, A survey-based type-2 fuzzy logic system
47
for energy management in hybrid electrical vehicles, Information Sciences, 190(9) (2012),
48
[22] J. M. Mendel and R. I. John, Type-2 fuzzy sets made simple, IEEE Transactions on Fuzzy
49
Systems, 10(2) (2002), 307{315.
50
[23] M. K. Maiti and M. Maiti, Fuzzy inventory model with two warehouses under possibility
51
constraints, Fuzzy Sets Syst, 157(8) (2006), 52{73.
52
[24] S. M. Mousavi, S. Hajipour and N. N. Aalikar, A multi-product multi-period inventory
53
control problem under inflation and discount: a parameter-tuned particle swarm optimization
54
algorithm, Int. J. Adv. Manuf. Tech., 33(4) (2013), 1{18.
55
[25] S. M. Mousavi, J. Sadeghi, S. T. A. Niaki, N. Alikar, A. Bahreininejad and H. Metselaar,
56
Two parameter-tuned meta-heuristics for a discounted inventory control problem in a fuzzy
57
environment, Information Sciences, 276(8) (2014), 42{62.
58
[26] S. M. Mousavi, J. Sadeghi, S. T. A. Niaki and M. Tavana, A bi-objective inventory optimiza-
59
tion model under inflation and discount using tuned Pareto-based algorithms: NSGA-II,
60
NRGA, and MOPSO, Applied Soft Computing, 43(6) (2016), 57{72.
61
[27] S. M. Mousavi, A. Bahreininejad, N. Musa and F. Yusof, A modified particle swarm opti-
62
mization for solving the integrated location and inventory control problems in a two-echelon
63
supply chain network, J. intell. Manuf., 23(4) (2014), 1{16.
64
[28] L. Y. Ouyang, C. H. Hob and C. H. Su, An optimization approach for joint pricing and
65
ordering problem in an integrated inventory system with order-size dependent trade credit,
66
Comput. Indust. Eng., 57(7) (2009), 920{930.
67
[29] S. Pal, M. K. Maiti and M. Maiti, An EPQ model with price discounted promotional demand
68
in an imprecise planning horizon via Genetic Algorithm, Comput. Indust. Eng., 57(6) (2009),
69
[30] S. H. R. Pasandideh, S. T. A. Niaki and S. M. Mousavi, Two metaheuristics to solve a multi-
70
item multiperiod inventory control problem under storage constraint and discounts, Int. J.
71
Adv. Manuf. Technol., 69(7) (2013), 1{14.
72
[31] T. Pathinathan and K. Ponnivalavan, Pentagonal fuzzy numbers, Int. J. Comput. Algm.,
73
3(4) (2014), 1003{1005.
74
[32] R. Qin, Y. K. Liu and Z. Q. Liu, Methods of critical value reduction for type-2 fuzzy variables
75
and their applications, J. Comput. Appl. Math., 235(7) (2011), 1454{1481.
76
[33] S. Sharan, S. P. Tiwary and V. K. Yadav, Interval type-2 fuzzy rough sets and interval type-2
77
fuzzy closure spaces, Iranian Journal of Fuzzy Systems, 12(3) (2015), 113{125.
78
[34] N. H. Shah and L. E. Cardenas-Barron, Retailer's decision for ordering and credit policies
79
for deteriorating items when a supplier offers order-linked credit period or cash discount,
80
Appl. Math. Comp., 259(5) (2015), 569{578.
81
[35] L. Stefanini and B. Bede, Generalized Hukuhara differentiability of interval-valued functions
82
and interval differential equations, Nonlinear Analysis, 71(4) (2009), 1311{1328.
83
[36] B. Sarkar, S. Saren and L. E. Cardenas-Barron, An inventory model with trade-credit policy
84
and variable deterioration for fixed lifetime products, Ann. Oper. Res., 229(1) (2015), 677{
85
[37] S. Tiwari, L. E. Cardenas-Barron, A. Khanna and C. K. Jaggi, Impact of trade credit and
86
inflation on retailer's ordering policies for non-instantaneous deteriorating items in a two-
87
warehouse environment, Int. J. Prod. Econ., 176(3) (2016), 154{169.
88
[38] J. Wu, F. B. Al-khateeb, J. T. Teng and L. E. Cardenas-Barron, Inventory models for dete-
89
riorating items with maximum lifetime under downstream partial trade credits to credit-risk
90
customers by discounted cash-flow analysis, Int. J. Prod. Eco., 171(1) (2016), 105{115.
91
[39] J. Wu, L. Y. Ouyang, L. E. Cardenas-Barron and S. K. Goyal, Optimal credit period and lot
92
size for deteriorating items with expiration dates under two-level trade credit financing, Eur.
93
J. Oper. Res., 237(3) (2014), 898{908.
94
[40] P. S. You, S. Ikuta and Y. C. Hsieh, Optimal ordering and pricing policy for an inventory
95
system with trial periods, Appl. Math. Model., 34(4) (2010), 3179{3188.
96
[41] L. A. Zadeh, The concept of a linguistic variable and its application to approximate resoning
97
I, Information Sciences, 8(2) (1975), 199{249.
98
[42] L. A. Zadeh, The concept of a linguistic variable and its application to approximate resoning
99
II, Information Sciences, 8(2) (1975), 301{357.
100
ORIGINAL_ARTICLE
SHAPLEY FUNCTION BASED INTERVAL-VALUED INTUITIONISTIC FUZZY VIKOR TECHNIQUE FOR CORRELATIVE MULTI-CRITERIA DECISION MAKING PROBLEMS
Interval-valued intuitionistic fuzzy set (IVIFS) has developed to cope with the uncertainty of imprecise human thinking. In the present communication, new entropy and similarity measures for IVIFSs based on exponential function are presented and compared with the existing measures. Numerical results reveal that the proposed information measures attain the higher association with the existing measures, which demonstrate their efficiency and reliability. To deal with the interactive characteristics among the elements in a set, Shapley weighted similarity measure based on proposed similarity measure for IVIFSs is discussed via Shapley function. Thereafter, the linear programming model for optimal fuzzy measure is originated for incomplete information about the weights of the criteria and thus, the optimal weight vector is obtained in terms of Shapley values. Further, the VIKOR technique is discussed for correlative multi-criteria decision making problems under interval-valued intuitionistic fuzzy environment. Finally, an example of investment problem is presented to exemplify the application of the proposed technique under incomplete and uncertain information situation.
http://ijfs.usb.ac.ir/article_3577_817d9d009ab46e0e1945d00b0cbbdef8.pdf
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10.22111/ijfs.2018.3577
Fuzzy set
Interval-valued intuitionistic fuzzy set
Entropy
Similarity measure
MCDM
VIKOR
Pratibha
Rani
pratibha138@gmail.com
true
1
Department of Mathematics, Jaypee University of Engineering and
Technology, Guna-473226, M. P., India
Department of Mathematics, Jaypee University of Engineering and
Technology, Guna-473226, M. P., India
Department of Mathematics, Jaypee University of Engineering and
Technology, Guna-473226, M. P., India
AUTHOR
Divya
Jain
divya.jain@juet.ac.in
true
2
Department of Mathematics, Jaypee University of Engineering and
Technology, Guna-473226, M. P., India
Department of Mathematics, Jaypee University of Engineering and
Technology, Guna-473226, M. P., India
Department of Mathematics, Jaypee University of Engineering and
Technology, Guna-473226, M. P., India
LEAD_AUTHOR
D. S.
Hooda
true
3
Guru Jambheshwar University of Science and Technology, Hisar-125001,
Haryana, India
Guru Jambheshwar University of Science and Technology, Hisar-125001,
Haryana, India
Guru Jambheshwar University of Science and Technology, Hisar-125001,
Haryana, India
AUTHOR
[1] M. D. Ansari, S. P. Ghrera and A. R. Mishra, Texture feature extraction using intuitionis-
1
tic fuzzy local binary pattern, Journal of Intelligent Systems, doi: 10.1515/jisys-2016-0155,
2
[2] K. T. Atanassov and G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and
3
Systems, 31 (1989), 343-349.
4
[3] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
5
[4] A. Awasthi and G. Kannan, Green supplier development program selection using NGT
6
and VIKOR under fuzzy environment, Computers and Industrial Engineering, 91 (2016),
7
[5] P. Burillo and H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy
8
sets, Fuzzy Sets and Systems, 78 (1996), 305-316.
9
[6] L. Chen and Z. S. Xu, A new prioritized multi-criteria outranking method: the prioritized
10
PROMETHEE, Journal of Intelligent and Fuzzy Systems, 29 (2015), 2099-2110.
11
[7] Q. Chen, Z. S. Xu, S. S. Liu and X. H. Yu, A method based on interval-valued intuitionistic
12
fuzzy entropy for multiple attribute decision making, Information, 13 (2010), 67-77.
13
[8] A. De Luca and S. Termini, A definition of a non-probabilistic entropy in the setting of fuzzy
14
sets theory, Information and Control, 20 (1972), 301-312.
15
[9] S. Ebrahimnejad, H. Hashemi, S. M. Mousavi and B. Vahdani, A new interval-valued in-
16
tuitionistic fuzzy model to group decision making for the selection of outsourcing providers,
17
Journal of Economic Computation and Economics Cybernetics Studies and Research, 49
18
(2015), 269-290.
19
[10] S. Ebrahimnejad, S. M. Mousavi, R. Tavakkoli-Moghaddam, H. Hashemi and B. Vahdani, A
20
novel two-phase group decision-making approach for construction project selection in a fuzzy
21
environment, Applied Mathematical Modelling, 36 (2012), 4197-4217.
22
[11] H. Gitinavard, S. M. Mousavi and B. Vahdani, A new multi-criteria weighting and rank-
23
ing model for group decision-making analysis based on interval-valued hesitant fuzzy sets to
24
selection problems, Neural Computing and Applications, 27 (2016), 1593-1605.
25
[12] H. Gitinavard, S. M. Mousavi, B. Vahdani and A. Siadat, A distance-based decision model
26
in interval-valued hesitant fuzzy setting for industrial selection problems, Scientia Iranica E,
27
23 (2016), 1928-1940.
28
[13] H. Hashemi, J. Bazargan and S. M. Mousavi, A compromise ratio method with an application
29
to water resources management: an intuitionistic fuzzy set, Water Resources Management,
30
27 (2013), 2029-2051.
31
[14] H. Hashemi, J. Bazargan, S. M. Mousavi and B. Vahdani, An extended compromise ratio
32
model with an application to reservoir flood control operation under an interval-valued intu-
33
itionistic fuzzy environment, Applied Mathematical Modelling, 38 (2014), 3495-3511.
34
[15] D. S. Hooda, A. R. Mishra and D. Jain, On generalized fuzzy mean code word lengths,
35
American Journal of Applied Mathematics, 2 (2014), 127-134.
36
[16] D. S. Hooda and A. R. Mishra, On trigonometric fuzzy information measures, ARPN Journal
37
of Science and Technology, 5 (2015), 145-152.
38
[17] W. L. Hung and M. S. Yang, Fuzzy entropy on intuitionistic fuzzy sets, International Journal
39
of Intelligent Systems, 21 (2006), 443-451.
40
[18] W. L. Hung and M. S. Yang, On similarity measures between intuitionistic fuzzy sets, Inter-
41
national Journal of Intelligent Systems, 23 (2008), 364-383.
42
[19] W. L. Hung and M. S. Yang, Similarity measures of intuitionistic fuzzy sets based on Haus-
43
dorff distance, Pattern Recognition Letters, 25 (2004), 1603-1611.
44
[20] R. A. Krohling and A. G. C. Pacheco, Interval-valued intuitionistic fuzzy TODIM, Procedia
45
Computer Science, 31 (2014), 236-244.
46
[21] D. Li and C. Cheng, New similarity measures of intuitionistic fuzzy sets and application to
47
pattern recognition, Pattern Recognition Letters, 23 (2002), 221225.
48
[22] Z. Liang and P. Shi, Similarity measures on intuitionistic fuzzy sets, Pattern Recognition
49
Letters, 24 (2003), 2687-2693.
50
[23] H. Liao, Z. S. Xu and X. J. Zeng, Hesitant fuzzy linguistic VIKOR method and its application
51
in qualitative multiple criteria decision making, IEEE Transactions on Fuzzy Systems, 23
52
(2015), 1343-1355.
53
[24] X. D. Liu, S. H. Zhang and F. L. Xiong, Entropy and subsethood for general interval-valued
54
intuitionistic fuzzy sets, In: L. Wang, Y. Jin (Eds.), FSKD, Springer-Verlag, Berlin Heidel-
55
berg LNAI, 3613 (2005), 42-52.
56
[25] P. Liu and L. Zhang, An extended multiple criteria decision making method based on
57
neutrosophic hesitant fuzzy information, Journal of Intelligent and Fuzzy Systems, doi:
58
10.3233/JIFS-16136, (2016).
59
[26] F. Meng and X. Chen, Entropy and similarity measure for Atannasov's interval-valued in-
60
tuitionistic fuzzy sets and their application, Fuzzy Optimization and Decision Making, 15
61
(2016), 75-101.
62
[27] A. R. Mishra, Intuitionistic fuzzy information measures with application in rating of township
63
development, Iranian Journal of Fuzzy Systems, 13(3) (2016), 49-70.
64
[28] A. R. Mishra, D. Jain and D. S. Hooda, On fuzzy distance and induced fuzzy information
65
measures, Journal of Information and Optimization Sciences, 37 (2016), 193211.
66
[29] A. R. Mishra, D. Jain and D. S. Hooda, On logarithmic fuzzy measures of information and
67
discrimination, Journal of Information and Optimization Sciences, 37 (2016), 213231.
68
[30] A. R. Mishra, D. S. Hooda and D. Jain, Weighted trigonometric and hyperbolic fuzzy infor-
69
mation measures and their applications in optimization principles, International Journal of
70
Computer and Mathematical Sciences, 3 (2014), 6268.
71
[31] A. R. Mishra, D. S. Hooda and Divya Jain, On exponential fuzzy measures of information
72
and discrimination, International Journal of Computer Applications, 119 (2015), 17.
73
[32] A. R. Mishra, D. Jain and D. S. Hooda, Intuitionistic fuzzy similarity and information mea-
74
sures with physical education teaching quality assessment, proceeding of IC3T-2015, Springer-
75
Advances in intelligent systems and computing series-11156, 379 (2016), 387-399.
76
[33] A. R. Mishra, D. Jain and D. S. Hooda, Exponential intuitionistic fuzzy information measure
77
with assessment of service quality, International Journal of Fuzzy Systems, 19(3) (2017),
78
[34] A. R. Mishra, P. Rani and D. Jain, Information measures based TOPSIS method for mul-
79
ticriteria decision making problem in intuitionistic fuzzy environment, Iranian Journal of
80
Fuzzy Systems, 14(6) (2017), 41-63.
81
[35] S. M. Mousavi, F. Jolai, R. Tavakkoli-Moghaddam and B. Vahdani, A fuzzy grey model based
82
on the compromise ranking for multi-criteria group decision making problems in manufac-
83
turing systems, Journal of Intelligent and Fuzzy Systems, 24 (2013), 819-827.
84
[36] S. M. Mousavi, S. A. Torabi and R. Tavakkoli-Moghaddam, A hierarchical group decision-
85
making approach for new product selection in a fuzzy environment, Arabian Journal of Science
86
and Engineering, 38 (2013), 3233-3248.
87
[37] S. M. Mousavi, B. Vahdani, R. Tavakkoli-Moghaddam and N. Tajik, Soft computing based
88
on a fuzzy grey compromise solution approach with an application to the selection problem of
89
material handling equipment, International Journal of Computer Integrated Manufacturing,
90
27 (2014), 547-569.
91
[38] S. M. Mousavi, H. Gitinavard and B. Vahdani, Evaluating construction projects by a new
92
group decision-making model based on intuitionistic fuzzy logic concepts, International Jour-
93
nal of Engineering, Transactions C: Aspects, 28 (2015), 1312-1319.
94
[39] S. M. Mousavi, B. Vahdani, H. Gitinavard and H. Hashemi, Solving robot selection problem
95
by a new interval-valued hesitant fuzzy multi-attributes group decision method, International
96
Journal of Industrial Mathematics, 8 (2016), 231240.
97
[40] S. M. Mousavi and B. Vahdani, Cross-docking location selection in distribution systems: a
98
new intuitionistic fuzzy hierarchical decision model, International Journal of Computational
99
Intelligence Systems, 9 (2016), 91-109.
100
[41] T. Murofushi, A technique for reading fuzzy measures (I): The shapley value with respect to
101
a fuzzy measure, In 2nd Fuzzy Workshop, Nagoaka, Japan, (1992), 39-48.
102
[42] S. Opricovic, Multicriteria optimization of civil engineering systems, University of Belgrade,
103
Belgrade, Serbia, 2 (1998), 5-21.
104
[43] N. R. Pal and S. K. Pal, Object background segmentation using new definitions of entropy,
105
IEEE Proceedings, 136 (1989), 284-295.
106
[44] C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal, 27
107
(1948), 379-423.
108
[45] L. S. Shapley, A Value for n-person game. In H. Kuhn & A. Tucker (Eds.), Contributions to
109
the theory of games, Princeton, Princeton University Press, II (1953), 307-317.
110
[46] S. Singh, O. Ezutah Udoncy. M. Siti Nurmaya, M. Abu Mahat and K. Y. Wong, Strategy
111
selection for sustainable manufacturing with integrated ahp-vikor method under interval-
112
valued fuzzy environment, The International Journal of Advanced Manufacturing Technology,
113
84 (2016), 547563.
114
[47] M. Sugeno, Theory of fuzzy integral and its application, Doctorial Dissertation, Tokyo Insti-
115
tute of Technology, (1974), 30-55.
116
[48] E. Szmidt and J. Kacprzyk, A concept of similarity for intuitionistic fuzzy sets and its
117
application in group decision making, In: Proceedings of International Joint Conference on
118
Neural Networks & IEEE International Conference on Fuzzy Systems, Budapest, Hungary,
119
(2004), 25-29.
120
[49] E. Szmidt and J. Kacprzyk, Analysis of similarity measures for Atanassov's intuitionistic
121
fuzzy sets, In:Proceedings IFSA/EUSFLAT, (2009), 14161421.
122
[50] E. Szmidt and J. Kacprzyk, Entropy for intuitionistic fuzzy sets, Fuzzy Sets and Systems,
123
118 (2001), 467-477.
124
[51] B. Vahdani, S. M. Mousavi, H. Hashemi, M. Mousakhani and R. Tavakkoli-Moghaddam, A
125
new compromise solution method for fuzzy group decision-making problems with an applica-
126
tion to the contractor selection, Engineering Applications of Artificial Intelligence, 26 (2013),
127
[52] B. Vahdani, S. M. Mousavi, R. Tavakkoli-Moghaddam and H. Hashemi, A new design of
128
the elimination and choice translating reality method for multiple-criteria group decision-
129
making in an intuitionistic fuzzy environment, Applied Mathematical Modelling, 37 (2013),
130
1781-1799.
131
[53] R. Vetschera and A. Teixeira De Almeida, A PROMETHEE-based approach to portfolio
132
selection problems, Computers and Operations Research, 39 (2012), 1010-1020.
133
[54] R. Verma and B. D. Sharma, Exponential entropy on intuitionistic fuzzy sets, Kybernetika,
134
49 (2013), 114-127.
135
[55] C. P. Wei, P. Wang and Y. Z. Zhang, Entropy, similarity measure of interval-valued intu-
136
itionistic fuzzy sets and their applications, Information Sciences, 181 (2011), 42734286.
137
[56] C. P. Wei and Y. Z. Zhang, Entropy measures for interval-valued intuitionistic fuzzy sets and
138
their applications in group decision-making, Mathematical Problems in Engineering, 2015
139
(2015), 1-13.
140
[57] K. L. Wu and M. S. Yang, Alternative C-means clustering algorithms, Pattern Recognition
141
Letters, 32 (2002), 2267-2278.
142
[58] Y. Wu, K. Chen, B. Zeng H. Xu and Y. Yang, Supplier selection in nuclear power industry
143
with extended VIKOR method under linguistic information, Applied Soft Computing, 48
144
(2016), 444-457.
145
[59] Z. S. Xu, An overview of distance and similarity measures of intuitionistic measures, Interna-
146
tional Journal of Uncertainty, Fuzziness and Knowledge-Based systems, 16 (2008), 529555.
147
[60] Z. S. Xu, On similarity measures of interval-valued intuitionistic fuzzy sets and their appli-
148
cation to pattern recognitions, Journal of Southeast University, 23 (2007), 139-143.
149
[61] J. Ye, Fuzzy cross entropy of interval-valued intuitionistic fuzzy sets and its optimal decision-
150
making method based on the weights of alternatives, Experts Systems with Applications, 38
151
(2011), 6179-6183.
152
[62] J. Ye, Multicriteria decision-making method using the dice similarity measure based on the
153
rreduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets, Applied Mathe-
154
matical Modelling, 36 (2012), 4466-4472.
155
[63] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338356.
156
[64] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-
157
I, Information Sciences, 8 (1975), 199-249.
158
[65] X. Zhao, T. Zou, S. Yang and M. Yang, Extended VIKOR method with fuzzy cross-entropy
159
of interval-valued intuitionistic fuzzy sets, Proceedings of the 2nd International Conference
160
on Computer and Information Application, (2012), 1093-1096.
161
ORIGINAL_ARTICLE
ITERATIVE METHOD FOR SOLVING TWO-DIMENSIONAL NONLINEAR FUZZY INTEGRAL EQUATIONS USING FUZZY BIVARIATE BLOCK-PULSE FUNCTIONS WITH ERROR ESTIMATION
In this paper, we propose an iterative procedure based on two dimensionalfuzzy block-pulse functions for solving nonlinear fuzzy Fredholm integralequations of the second kind. The error estimation and numerical stabilityof the proposed method are given in terms of supplementary Lipschitz condition.Finally, illustrative examples are included in order to demonstrate the accuracyand convergence of the proposed method.
http://ijfs.usb.ac.ir/article_3578_dadf16bc5320d88699ca38f16ea27e14.pdf
2018-03-01T11:23:20
2018-02-25T11:23:20
55
76
10.22111/ijfs.2018.3578
Two dimensional nonlinear fuzzy Fredholm integral equations of the second kind
Two dimensional fuzzy block-pulse functions
Supplementary Lipschitz condition
Shokrollah
Ziari
shok_ziari@yahoo.com
true
1
Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran
LEAD_AUTHOR
[1] S. Abbasbandy, E. Babolian and M. Alavi, Numerical method for solving linear Fredholm
1
fuzzy integral equations of the second kind, Chaos Solitons Fractals, 31(1) (2007), 138-146.
2
[2] R. P. Agrawal, D. Oregan and V. Lakshmikantham, Fuzzy Volterra Integral Equations: A
3
Stacking Theorem Approach, Applicable Analysis: An International Journal, 83(5) (2004),
4
[3] G. A. Anastassiou, Fuzzy Mathematics: Approximation Theory, Springer, Berlin (2010).
5
[4] E. Babolian, H. Sadeghi Goghary and S. Abbasbandy, Numerical solution of linear Fredholm
6
fuzzy integral equations of the second kind by Adomian method, Applied Mathematics and
7
Computation, 161 (2005), 733-744.
8
[5] M. Baghmisheh and R. Ezzati, Numerical solution of nonlinear fuzzy Fredholm integral equa-
9
tions of the second kind using hybrid of block-pulse functions and Taylor series, Advances in
10
Difference Equations, DOI 10.1186/s13662-015-0389-7, 51 (2015), 1-15.
11
[6] K. Balachandran and P. Prakash, Existence of solutions of nonlinear fuzzy Volterra- Fredholm
12
integral equations, Indian Journal of Pure and Applied Mathematics, 33 (2002), 329-343.
13
[7] K. Balachandran and K. Kanagarajan, Existence of solutions of general nonlinear fuzzy
14
Volterra-Fredholm integral equations, Journal of Applied Mathematics and Stochastic Anal-
15
ysis, 3 (2005), 333-343.
16
[8] B. Bede and S. G. Gal, Quadrature rules for integrals of fuzzy-number-valued functions, Fuzzy
17
Sets and Systems, 145 (2004), 359-380.
18
[9] A. M. Bica, Error estimation in the approximation of the solution of nonlinear fuzzy Fredholm
19
integral equations, Information Science, 178 (2008), 1279-1292.
20
[10] A. M. Bica and C. Popescu, Approximating the solution of nonlinear Hammerstein fuzzy
21
integral equations, Fuzzy Sets and Systems, 245 (2014), 1-17.
22
[11] A. M. Bica and C. Popescu, Fuzzy trapezoidal cubature rule and application to two-
23
dimensional fuzzy Fredholm integral equations, Soft Computing, 21(5) (2017), 1229-1243.
24
[12] A. M. Bica, S. Ziari, Iterative numerical method for solving fuzzy Volterra linear integral
25
equations in two dimensions, Soft Computing, 21(5) (2017), 1097-1108.
26
[13] P. Diamond, Theory and applications of fuzzy Volterra integral equations, IEEE Transactions
27
on Fuzzy Systems, 10(1) (2002), 97-102.
28
[14] D. Dubois and H. Prade, Fuzzy numbers: an overview, In: Analysis of Fuzzy Information,
29
CRC Press, BocaRaton, (1) (1987), 3-39.
30
[15] R. Ezzati and S. Ziari, Numerical solution and error estimation of fuzzy Fredholm integral
31
equation using fuzzy Bernstein polynomials, Aust. J. Basic Appl. Sci., 5(9) (2011), 2072-2082.
32
[16] R. Ezzati and S. Ziari, Numerical solution of nonlinear fuzzy Fredholm integral equations
33
using iterative method, Applied Mathematics and Computation, 225 (2013), 33-42.
34
[17] R. Ezzati and S. Ziari, Numerical solution of two-dimensional fuzzy Fredholm integral equa-
35
tions of the second kind using fuzzy bivariate Bernstein polynomials, Int. J. Fuzzy Systems,
36
15(1) (2013), 84-89.
37
[18] R. Ezzati and S. M. Sadatrasoul, Application of bivariate fuzzy Bernstein polynomials to
38
solve two-dimensional fuzzy integral equations, Soft Computing, 21(14) (2017), 3879-3889.
39
[19] J. X. Fang and Q. Y. Xue, Some properties of the space fuzzy-valued continuous functions
40
on a compact set, Fuzzy Sets Systems, 160 (2009), 1620-1631.
41
[20] M. A. Fariborzi Araghi and N. Parandin, Numerical solution of fuzzy Fredholm integral
42
equations by the Lagrange interpolation based on the extension principle, Soft Computing,
43
15 (2011), 2449-2456.
44
[21] M. Friedman, M. Ma and A. Kandel, Numerical solutions of fuzzy differential and integral
45
equations, Fuzzy Sets and Systems, 106 (1999), 35-48.
46
[22] M. Friedman, M. Ma and A. Kandel, Solutions to fuzzy integral equations with arbitrary
47
kernels, International Journal of Approximate Reasoning, 20 (1999), 249-262.
48
[23] S. G. Gal, Approximation theory in fuzzy setting, In: Anastassiou, GA (ed.) Handbook of
49
Analytic-Computational Methods in Applied Mathematics, Chapman & Hall/CRC Press,
50
Boca Raton, (2000), 617-666.
51
[24] R. Goetschel and W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986),
52
[25] L. T. Gomes, L. C. Barros and B. Bede, Fuzzy Differential Equations in Various Approaches,
53
Springer (2015).
54
[26] Z. H. Jiang and W. Schanfelberger, Block-Pulse Functions and Their Applications in Control
55
Systems, Springer, Berlin (1992).
56
[27] C. V. Negoita and D. A. Ralescu, Applications of Fuzzy Sets to Systems Analysis, Wiley,
57
New York (1975).
58
[28] J. Y. Park and H. K. Han, Existence and uniqueness theorem for a solution of fuzzy Volterra
59
integral equations, Fuzzy Sets and Systems, 105 (1999), 481-488.
60
[29] J. Y. Park and J. U. Jeong, On the existence and uniqueness of solutions of fuzzy Volttera-
61
Fredholm integral equations, Fuzzy Sets and Systems, 115 (2000), 425-431.
62
[30] S. M. Sadatrasoul and R. Ezzati, Iterative method for numerical solution of two-dimensional
63
nonlinear fuzzy integral equations, Fuzzy Sets and Systems, 280 (2015), 91-106.
64
[31] S. M. Sadatrasoul and R. Ezzati, Numerical solution of two-dimensional nonlinear Hammer-
65
stein fuzzy integral equations based on optimal fuzzy quadrature formula, Journal of Compu-
66
tational and Applied Mathematics, 292 (2016), 430-446.
67
[32] P. V. Subrahmanyam and S. K. Sudarsanam, A note on fuzzy Volterra integral equations,
68
Fuzzy Sets and Systems, 81 (1996), 237-240.
69
[33] C.Wu, S. Song and H.Wang, On the basic solutions to the generalized fuzzy integral equation,
70
Fuzzy Sets and Systems, 95 (1998), 255-260.
71
[34] C. Wu and Z. Gong, On Henstock integral of fuzzy-number-valued functions (I), Fuzzy Sets
72
and Systems, 120 (2001), 523-532.
73
[35] S. Ziari, R. Ezzati and S. Abbasbandy, Numerical solution of linear fuzzy Fredholm inte-
74
gral equations of the second kind using fuzzy Haar wavelet, In: Advances in Computational
75
Intelligence. Communications in Computer and Information Science, 299 (2012), 79-89.
76
[36] S. Ziari and A. M. Bica, New error estimate in the iterative numerical method for nonlinear
77
fuzzy Hammerstein-Fredholm integral equations, Fuzzy Sets and Systems, 295 (2016), 136-
78
ORIGINAL_ARTICLE
SOME SIMILARITY MEASURES FOR PICTURE FUZZY SETS AND THEIR APPLICATIONS
In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similarity measure, weighted set-theoretic cosine similarity measure, grey similarity measure and weighted grey similarity measure. Then, we apply these similarity measures between picture fuzzy sets to building material recognition and minerals field recognition. Finally, two illustrative examples are given to demonstrate the efficiency of the similarity measures for building material recognition and minerals field recognition.
http://ijfs.usb.ac.ir/article_3579_78359250002654fac62dee60be8e46ac.pdf
2018-03-01T11:23:20
2018-02-25T11:23:20
77
89
10.22111/ijfs.2018.3579
Picture fuzzy set
Cosine similarity measure
Set-theoretic similarity measure
Grey similarity measure
Building material recognition
Minerals field recognition
Guiwu
Wei
weiguiwu@163.com
true
1
School of Business, Sichuan Normal University, Chengdu, 610101, P.R.
China
School of Business, Sichuan Normal University, Chengdu, 610101, P.R.
China
School of Business, Sichuan Normal University, Chengdu, 610101, P.R.
China
LEAD_AUTHOR
[1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
1
[2] K. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33 (1989), 37-46.
2
[3] K. Atanassov and G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Sys-
3
tems, 31 (1989), 343-349.
4
[4] K. Atanassov, Operators over interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Sys-
5
tems, 64(2) (1994), 159-174.
6
[5] A. Bhattacharya, On a measure of divergence of two multinomial populations, Sankhya, 7
7
(1946), 401-406.
8
[6] H. Bustince, and P. Burillo, Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy
9
Sets and Systems, 74(2) (1995), 237-244.
10
[7] S. M. Chen, S. H. Cheng and C. H. Chiou, Fuzzy multiattribute group decision making based
11
on intuitionistic fuzzy sets and evidential reasoning methodology, Information Fusion, 27
12
(2016), 215-227.
13
[8] T. Y. Chen,The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets
14
for multiple criteria group decision making, Applied Soft Computing, 26 (2015), 57-73.
15
[9] T. Y. Chen, An interval-valued intuitionistic fuzzy permutation method with likelihood-based
16
preference functions and its application to multiple criteria decision analysis, Applied Soft
17
Computing, 42 (2016), 390-409.
18
[10] B. Cuong, Picture fuzzy sets-first results. part 1, In: Seminar "Neuro-Fuzzy Systems with
19
Applications", Institute of Mathematics, Hanoi, 2013.
20
[11] X. P. Jiang and G. W. Wei, Some Bonferroni mean operators with 2-tuple linguistic infor-
21
mation and their application to multiple attribute decision making, Journal of Intelligent and
22
Fuzzy Systems, 27 (2014), 2153-2162.
23
[12] D. F. Li and C. Cheng, New similarity measures of intuitionistic fuzzy sets and application
24
to pattern recognition, Pattern Recognition Letters, 23 (1-3) (2002), 221-225.
25
[13] D. F. Li, TOPSIS-Based nonlinear-programming methodology for multiattribute decision
26
making with interval-valued intuitionistic fuzzy sets, IEEE Transactions on Fuzzy Systems,
27
18 (2010), 299-311.
28
[14] D. F. Li and H. P. Ren, Multi-attribute decision making method considering the amount and
29
reliability of intuitionistic fuzzy information, Journal of Intelligent and Fuzzy Systems, 28(4)
30
(2015), 1877-1883.
31
[15] R. Lin, G. W. Wei, H. J. Wang and X. F. Zhao, Choquet integrals of weighted triangular fuzzy
32
linguistic information and their applications to multiple attribute decision making, Journal
33
of Business Economics and Management, 15(5)(2014), 795-809.
34
[16] R. Lin, X. F. Zhao, H. J.Wang and G. W.Wei, Hesitant fuzzy linguistic aggregation operators
35
and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy
36
Systems, 27 (2014), 49-63.
37
[17] R. Lin, X. F. Zhao and G. W. Wei, Models for selecting an ERP system with hesitant fuzzy
38
linguistic information, Journal of Intelligent and Fuzzy Systems, 26(5) (2014), 2155-2165.
39
[18] M. Lu and G. W. Wei, Models for multiple attribute decision making with dual hesitant fuzzy
40
uncertain linguistic information, International Journal of Knowledge-based and Intelligent
41
Engineering Systems, 20(4) (2016), 217-227.
42
[19] L. D. Miguel, H. Bustince, J. Fernndez, E. Indurin, A. Kolesrov and R. Mesiar, Construction
43
of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an
44
application to decision making, Information Fusion, 27 (2016), 189-197.
45
[20] G. Salton and M. J. McGill, Introduction to Modern Information Retrieval, McGraw-Hill
46
Book Company, New York, 1983.
47
[21] P. Singh, Correlation coefficients for picture fuzzy sets, Journal of Intelligent & Fuzzy Sys-
48
tems, 27 (2014), 2857-2868.
49
[22] L. Son, DPFCM: A novel distributed picture fuzzy clustering method on picture fuzzy sets,
50
Expert System with Applications, 2 (2015), 51-66.
51
[23] Y. Tang, L. L. Wen and G. W. Wei, Approaches to multiple attribute group decision making
52
based on the generalized Dice similarity measures with intuitionistic fuzzy information, In-
53
ternational Journal of Knowledge-based and Intelligent Engineering Systems, 21(2) (2017),
54
[24] P. H. Thong and L. H. Son, A new approach to multi-variables fuzzy forecasting using picture
55
fuzzy clustering and picture fuzzy rules interpolation method, in: 6th International Conference
56
on Knowledge and Systems Engineering, Hanoi, Vietnam, (2015), 679-690.
57
[25] N. T. Thong, HIFCF: An effective hybrid model between picture fuzzy clustering and intu-
58
itionistic fuzzy recommender systems for medical diagnosis expert systems with applications,
59
Expert Systems with Applications, 42(7) (2015), 3682-3701.
60
[26] H. J. Wang, X. F. Zhao and G. W. Wei, Dual Hesitant Fuzzy Aggregation Operators in
61
Multiple Attribute Decision Making, Journal of Intelligent and Fuzzy Systems, 26(5) (2014),
62
2281-2290.
63
[27] G. W. Wei, Some geometric aggregation functions and their application to dynamic multiple
64
attribute decision making in intuitionistic fuzzy setting, International Journal of Uncertainty,
65
Fuzziness and Knowledge- Based Systems, 17(2) (2009), 179-196.
66
[28] G. W. Wei, Some induced geometric aggregation operators with intuitionistic fuzzy informa-
67
tion and their application to group decision making, Applied Soft Computing, 10(2) (2010),
68
[29] G. W. Wei, GRA method for multiple attribute decision making with incomplete weight
69
information in intuitionistic fuzzy setting, Knowledge-based Systems, 23(3) (2010), 243-247.
70
[30] G. W.Wei, Gray relational analysis method for intuitionistic fuzzy multiple attribute decision
71
making, Expert Systems with Applications, 38 (2011), 11671-11677.
72
[31] G. W. Wei and X. F. Zhao, Some induced correlated aggregating operators with intuitionistic
73
fuzzy information and their application to multiple attribute group decision making, Expert
74
Systems with Applications, 39 (2) (2012), 2026-2034.
75
[32] G. W. Wei, H. J. Wang and R. Lin, Application of correlation coefficient to interval-valued
76
intuitionistic fuzzy multiple attribute decision making with incomplete weight information,
77
Knowledge and Information Systems, 26(2) (2011), 337-349.
78
[33] G. W. Wei, Approaches to interval intuitionistic trapezoidal fuzzy multiple attribute decision
79
making with incomplete weight information, International Journal of Fuzzy Systems, 17(3)
80
(2015), 484-489.
81
[34] G. W. Wei, Interval valued hesitant fuzzy uncertain linguistic aggregation operators in mul-
82
tiple attribute decision making, International Journal of Machine Learning and Cybernetics,
83
7(6) (2016), 1093-1114.
84
[35] G. W. Wei, Picture fuzzy cross-entropy for multiple attribute decision making problems,
85
Journal of Business Economics and Management, 17(4) (2016), 491-502.
86
[36] G. W. Wei, Picture 2-tuple linguistic Bonferroni mean operators and their application to
87
multiple attribute decision making, International Journal of Fuzzy System, 19(4) (2017),
88
[37] G. W. Wei, F. E. Alsaadi, T. Hayat and A. Alsaedi, Hesitant fuzzy linguistic arithmetic ag-
89
gregation operators in multiple attribute decision making, Iranian Journal of Fuzzy Systems,
90
13(4) (2016), 1-16.
91
[38] G. W. Wei, F. E. Alsaadi, T. Hayat and A. Alsaedi, A linear assignment method for multi-
92
ple criteria decision analysis with hesitant fuzzy sets based on fuzzy measure, International
93
Journal of Fuzzy Systems, 19(3) (2017), 607-614.
94
[39] G. W. Wei, F. E. Alsaadi, T. Hayat and A. Alsaedi, Projection models for multiple attribute
95
decision making with picture fuzzy information, International Journal of Machine Learning
96
and Cybernetics, DOI: 10.1007/s13042-016-0604-1, 2016.
97
[40] G. W. Wei, F. E. Alsaadi, T. Hayat and A. Alsaedi, Picture 2-tuple linguistic aggregation
98
operators in multiple attribute decision making, Soft Computing, 22(3) (2018), 989-1002.
99
[41] G. W. Wei, R. Lin, X. F. Zhao and H. J. Wang, An approach to multiple attribute deci-
100
sion making based on the induced Choquet integral with fuzzy number intuitionistic fuzzy
101
information, Journal of Business Economics and Management, 15(2) (2014), 277-298.
102
[42] G. W. Wei, R. Lin and H. J. Wang, Distance and similarity measures for hesitant interval-
103
valued fuzzy sets, Journal of Intelligent and Fuzzy Systems, 27(1) (2014), 19-36.
104
[43] G. W. Wei, X. R. Xu and D. X. Deng, Interval-valued dual hesitant fuzzy linguistic geo-
105
metric aggregation operators in multiple attribute decision making, International Journal of
106
Knowledge-based and Intelligent Engineering Systems, 20(4) (2016), 189-196
107
[44] G. W. Wei, H. J. Wang, X. F. Zhao and R. Lin, Hesitant triangular fuzzy information
108
aggregation in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems,
109
26(3) (2014), 1201-1209.
110
[45] G. W. Wei and X. F. Zhao, Some induced correlated aggregating operators with intuitionistic
111
fuzzy information and their application to multiple attribute group decision making, Expert
112
Systems with Applications, 39(2) (2012), 2026-2034.
113
[46] Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transations on Fuzzy Systems,
114
15(6) (2007), 1179-1187.
115
[47] Z. S. Xu, On correlation measures of intuitionistic fuzzy sets, Lecture Notes in Computer
116
Science, 4224 (2006), 16-24.
117
[48] Z. S. Xu and R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy
118
sets, International Journal of General System, 35 (2006), 417-433.
119
[49] Z. S. Xu and X. Q. Cai, Intuitionistic Fuzzy Information Aggregation: Theory and Applica-
120
tions, Science Press, 2008.
121
[50] Z. S. Xu and J. Chen, An overview of distance and similarity measures of intuitionistic fuzzy
122
sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16(4)
123
(2008), 529-555.
124
[51] J. Ye, Cosine similarity measures for intuitionistic fuzzy sets and their applications, Math-
125
ematical and Computer Modelling, 53(1) (2011), 91-97.
126
[52] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-356.
127
[53] X. F. Zhao, Q. X. Li and G. W. Wei, Some prioritized aggregating operators with linguistic
128
information and their application to multiple attribute group decision making, Journal of
129
Intelligent and Fuzzy Systems, 26(4) (2014), 1619-1630.
130
[54] X. F. Zhao, R. Lin and G. W. Wei, Hesitant triangular fuzzy information aggregation based
131
on einstein operations and their application to multiple attribute decision making, Expert
132
Systems with Applications, 41(4) (2014), 1086-1094.
133
[55] X. F. Zhao and G. W. Wei, Some intuitionistic fuzzy einstein hybrid aggregation operators
134
and their application to multiple attribute decision making, Knowledge-Based Systems, 37
135
(2013), 472-479.
136
[56] L. Y. Zhou, R. Lin, X. F. Zhao and G. W. Wei, Uncertain linguistic prioritized aggregation
137
operators and their application to multiple attribute group decision making, International
138
Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21(4) (2013), 603-627.
139
[57] B. Zhu, Z. S. Xu and M. M. Xia, Hesitant fuzzy geometric Bonferroni means, Information
140
Sciences, 205(1) (2012), 72-85.
141
ORIGINAL_ARTICLE
A NEW APPROACH FOR PARAMETER ESTIMATION IN FUZZY LOGISTIC REGRESSION
Logistic regression analysis is used to model categorical dependent variable. It is usually used in social sciences and clinical research. Human thoughts and disease diagnosis in clinical research contain vagueness. This situation leads researchers to combine fuzzy set and statistical theories. Fuzzy logistic regression analysis is one of the outcomes of this combination and it is used in situations where the classical logistic regression assumptions' are not satisfied. Also it can be used if the observations or their relations are vague. In this study, a model called “Fuzzy Logistic Regression Based on Revised Tanaka's Fuzzy Linear Regression Model” is proposed. In this regard, the methodology and formulation of the proposed model is explained in detail and the revised Tanaka's regression model is used to estimate the parameters. The Revised Tanaka's Regression model is an extension of Tanaka's Regression Model in which the objection function is developed. An application is performed on birth weight data set. Also, an application of diabetes data set used in Pourahmad et al.'s study was conducted via our proposed data set. The validity of the model is shown by the help of goodness – of –fit criteria called Mean Degree Memberships (MDM).
http://ijfs.usb.ac.ir/article_3580_f9f590713068e42b84d5b7b1b97954c4.pdf
2018-03-01T11:23:20
2018-02-25T11:23:20
91
102
10.22111/ijfs.2018.3580
Fuzzy logistic regression
Revised Tanaka regression model
MDM criteria
GULTEKIN
ATALIK
gultekinatalik@anadolu.edu.tr
true
1
Department of Statistics, Anadolu University, Eskisehir, Turkey and Department of Statistics, Amasya University, Amasya,Turkey
Department of Statistics, Anadolu University, Eskisehir, Turkey and Department of Statistics, Amasya University, Amasya,Turkey
Department of Statistics, Anadolu University, Eskisehir, Turkey and Department of Statistics, Amasya University, Amasya,Turkey
LEAD_AUTHOR
Sevil
Senturk
true
2
Department of Statistics, Anadolu University, Eskisehir, Turkey
Department of Statistics, Anadolu University, Eskisehir, Turkey
Department of Statistics, Anadolu University, Eskisehir, Turkey
AUTHOR
[1] G. Atalik, A New Approach for Parameter Estimation in Fuzzy Logistic Regression and
1
an Application, Master of Science Thesis, Anadolu University, Graduate School of Sciences,
2
Eskisehir (2014).
3
[2] H. Bircan, Lojistik Regresyon Analizi: Tp Verileri zerine Bir Uygulama, Kocaeli niversitesi
4
Sosyal Bilimler Enstits Dergisi, 8(1) (2004), 185-208.
5
[3] R. M. Dom, S. A. Kareem, A. Razak and B. Abidin, A learning system prediction method
6
using fuzzy regression, In Proceedings of the International MultiConference of Engineers and
7
Computer Scientists, Hong Kong, China, (2008), 19-21.
8
[4] Y. Q. He, L. K. Chan and M. L. Wu, Balancing productivity and consumer satisfaction
9
for profitability: statistical and fuzzy regression analysis, European Journal of Operational
10
Resarch, 176(1) (2007), 252-263.
11
[5] S. S. Hirve and B. R. Ganatra, Determinants of low birth weight: a commun,ty based prospec-
12
tive cohort study, Indian Pediatrics, 31(10) (1994), 1221-1225.
13
[6] D. W. Hosmer and S. Lemeshow, Applied Logistic Regression, John Wiley and Sons, New
14
York, 2000.
15
[7] D. G. Kleinbaum and M. Klein, Logistic Regression, A Self-Learning Text (Second Edition
16
ed.), Springer - Verlag , New York, 2002.
17
[8] E. Kirimi and S. Pence, The affects of smoking during pregnancy to fetus and plasental
18
development, Van Medical Journal, 6(1) (1999), 28-30.
19
[9] D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to Linear Regression Analysis,
20
John Wiley and Sons, New York, 2001.
21
[10] P. Nagar and S. Srivastava, Adaptive fuzzy regression model for the prediction of dichotomous
22
response variables using cancer data: a case study, Journal of Applied Mathematics, Statistics
23
and Informatics, 4(2) (2008), 183-191.
24
[11] M. Namdari, A. Abadi, S. M. Taheri, M. Rezaei, M. Kalantari and N. Omidvar, Effect of
25
folic acid on appetite in children: Ordinal logistic and fuzzy logistic regressions, Nutrition,
26
30(3) (2014), 274-278.
27
[12] M. Namdari, J. H. Yoon, A. Abadi, S. M. Taheri and S. H. Choi, Fuzzy Logistic Regression
28
with Least Absolute Deviations Estimators, Soft Computing, 19(4) (2015), 909-917.
29
[13] S. Pourahmad, S. M. T. Ayatollahi and S. M. Taheri, Fuzzy logistic regression: a new possi-
30
bilistic model and its application in clinical vague status, Iranian Journal of Fuzzy Systems,
31
8(1) (2011), 1-17.
32
[14] S. Pourahmad, S. M. Ayatollahi and S. M. Taheri, Fuzzy logistic regression based on the
33
least squares approach with application in clinical studies, Computers and Mathematics with
34
Applications, 62(9) (2011), 3353-3365.
35
[15] H. Tanaka, S. Uejima and K. Asai, Lineer regression analysis with fuzzy model, IEEE Transactions
36
On Systems, Man, and Cybernetics, 12(6) (1982), 903-907.
37
[16] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
38
[17] L. A. Zadeh, Discussion: probability theory and fuzzy logic are complementary rather than
39
competitive, Technometrics, 37(3) (1995), 271-276.
40
ORIGINAL_ARTICLE
QUANTALE-VALUED GAUGE SPACES
We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the quantale, is even isomorphic to our category. Finally, the category of quantale-valued metric spaces is shown to be coreflectively embedded in our category.
http://ijfs.usb.ac.ir/article_3581_e2cdd171cdf1a1b1c5932b122c4123ba.pdf
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103
122
10.22111/ijfs.2018.3581
$L$-gauge space
$L$-approach space
$L$-metric space
Continuity space
Gunther
Jager
g.jager@ru.ac.za, gunther.jaeger@fh-stralsund.de
true
1
University of Applied Sciences Stralsund, D-18435 Stralsund, Germany
University of Applied Sciences Stralsund, D-18435 Stralsund, Germany
University of Applied Sciences Stralsund, D-18435 Stralsund, Germany
LEAD_AUTHOR
Wei
Yao
yaowei0516@163.com
true
2
Hebei University of Science and Technology, 050054 Shijiazhuang, P.R.China
Hebei University of Science and Technology, 050054 Shijiazhuang, P.R.China
Hebei University of Science and Technology, 050054 Shijiazhuang, P.R.China
AUTHOR
[1] S. Abramsky and A. Jung, Domain Theory, in: S. Abramsky, D.M. Gabby, T.S.E. Maibaum
1
(Eds.), Handbook of Logic and Computer Science, Vol. 3, Claredon Press, Oxford, 1994.
2
[2] J. Adamek., H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley, New
3
York, 1989.
4
[3] R. C. Flagg, Quantales and continuity spaces, Algebra Univers., 37 (1997), 257 { 276.
5
[4] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, Continuous
6
Lattices and Domains, Cambridge University Press, Cambridge, 2003.
7
[5] J. Gutierrez Garca, On stratfiied L-valued filters induced by >-filters, Fuzzy Sets and Systems
8
157 (2006), 813 { 819.
9
[6] D. Hofmann, G. J. Seal and W. Tholen, Monoidal Topology - A Categorical Approach to
10
Order, Metric and Topology, Cambridge University Press, Cambridge, 2014.
11
[7] U. Hohle, Commutative, residuated l-monoids, in: Non-classical logics and their applications
12
to fuzzy subsets (U. Hohle, E.P. Klement, eds.), Kluwer, Dordrecht (1995), 53 { 106.
13
[8] G. Jager, A convergence theory for probabilistic metric spaces, Quaestiones Math., 38 (2015),
14
[9] G. Jager, Probabilistic approach spaces, Math. Bohemica, 142(3) (2017), 277-298.
15
[10] H. Lai and W. Tholen, Quantale-valued topological spaces via closure and convergence, Topology
16
Appl., 230 (2017), 599-620.
17
[11] R. Lowen, Approach spaces: A common supercategory of TOP and MET, Math. Nachr., 141
18
(1989), 183 { 226.
19
[12] R. Lowen, Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad,
20
Clarendon Press, Oxford, 1997.
21
[13] R. Lowen, Index Analysis, Springer-Verlag, London, 2015.
22
[14] G. Preuss, Foundations of Topology. An Approach to Convenient Topology, Kluwer Academic
23
Publishers, Dordrecht, 2002.
24
[15] S. Saminger-Platz and C. Sempi, A primer on triangle functions I, Aequationes Math., 76
25
(2008), 201 { 240.
26
[16] S. Saminger-Platz and C. Sempi, A primer on triangle functions II, Aequationes Math., 80
27
(2010), 239 { 261.
28
[17] B. Schweizer and A. Sklar, Probabilistic metric spaces, North Holland, New York, 1983.
29
[18] W. Yao and B. Zhao, Kernel systems on L-ordered sets, Fuzzy Sets and Systems 182 (2011),
30
101 { 109.
31
[19] W. Yao, A duality between -categories and algebraic -categories, Electronic Notes in Theoretical
32
Computer Science, 301 (2014), 153 { 168.
33
ORIGINAL_ARTICLE
ON TRUNCATED MEASURES OF INCOME INEQUALITY FROM A FUZZY PERSPECTIVE
In most statistical analysis, inequality or extent of variation in income isrepresented in terms of certain summary measures. But some authors arguedthat the concept of inequality is vague and thus cannot be measured as anexact concept. Therefore, fuzzy set theory provides naturally a useful toolfor such circumstances. In this paper we have introduced a real-valued fuzzymethod of illustrating the measures of income inequality in truncated randomvariables based on the case where the conditional events are vague. Toguarantee certain relevant properties of these measures, we first selectedthree main families of measures and obtained their closed formulas, thenused two simulated and real data set to illustrate the usefulness of derivedresults.
http://ijfs.usb.ac.ir/article_3582_8a116cc7c46a92b83fb40a6372c29f51.pdf
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123
137
10.22111/ijfs.2018.3582
Measures of income inequality
Gini index
Fuzzy event
Membership function
Truncated distribution
Reza
Pourmousa
pourm@uk.ac.ir
true
1
Department of Statistics, Faculty of Mathematics ~and Computer
Shahid Bahonar University of Kerman
Kerman, Iran
Department of Statistics, Faculty of Mathematics ~and Computer
Shahid Bahonar University of Kerman
Kerman, Iran
Department of Statistics, Faculty of Mathematics ~and Computer
Shahid Bahonar University of Kerman
Kerman, Iran
LEAD_AUTHOR
[1] B. C. Arnold, Majorization and the Lorenz order, Lecture notes in statistics 43, Springer,
1
Berlin and New York, 1987.
2
[2] F. Belzunce, J. Candel and J. M. Ruiz, Ordering of truncated distributions through concen-
3
tration curves, Sankhya A, 57 (1995), 375-383.
4
[3] N. Bhattacharya, A property of the Pareto distribution, Sankhya B, 25 (1963), 195-196.
5
[4] M. Bonetti, C. Gigliarano and P. Muliere, The Gini concentration test for survival data,
6
Lifetime Data Analysis, 15 (2009), 493-518.
7
[5] G. M. Cordeiro, The Kumaraswamy generalized half-normal distribution for skewed positive
8
data, Journal of Data Science, 10 (2012), 195-224.
9
[6] Y. Dodge, The Oxford Dictionary of Statistical Terms, OUP, 2003.
10
[7] O. Elteto, E. Frigyes, New income inequality measures as efficient tools for causal analysis
11
and planning, Econometrica, 36 (1968), 383-396.
12
[8] C. Gini, On the measure of concentration with special reference to incom and statistics,
13
Colorado College Publication, General Series, 208 (1936), 73-79.
14
[9] K. Hanada, A Formula of Gini's concentration ratio and its applications to life tables, Journal
15
of Japanese Statistical Society, 19 (1983), 293-325.
16
[10] N. Kakwani, On a class of poverty measures, Econometrica, 48 (1980), 437-446.
17
[11] C. Kleiber and S. Kotz, Statistical Size Distributions in Economics and Actuarial Sciences,
18
Wiley, Hoboken, 2003.
19
[12] D. Kundu and H. Howlader, Bayesian Inference and prediction of the inverse Weibull dis-
20
tribution for Type-II censored data, Computational Statistics and Data Analysis, 54 (2010),
21
1547-1558.
22
[13] J. Kupka and S. Loo, The hazard and vitality measures of aging, Journal of Applied Proba-
23
bility, 26 (1989), 532-542.
24
[14] J. Lawry, Modelling and Reasoning with Vague Concepts, Springer, 2006.
25
[15] M.O. Lorenz, Methods of measuring the moncentration of wealth, Journal of the american
26
statistical association, 70(9) (1905), 209-217.
27
[16] T. S. K. Moothathu, A characterization of power function distribution through a property of
28
the Lorenz curve. Sankhya, The Indian Journal of Statistics, Series B, 48 (1986), 262-265.
29
[17] J. K. Ord, G. P. Patil and C. Taillie, Truncated distributions and measures of income in-
30
equality. Sankhya, The Indian Journal of Statistics, Series B, 45 (1983), 413-430.
31
[18] T. J. Ross, J. M. Booker and W. J. Parkinson, Fuzzy Logic and Probability Applications,
32
SIAM, Philadelphia, 2002.
33
[19] V. M. Shkolnikov, E. E. Andreev and A. Z. Begun, Gini coeffcient as a life table func-
34
tion: Computation from discrete data, decomposition of differences and empirical examples,
35
Demographic Research, 8 (2003), 305-358.
36
[20] L. M. Surhone, M. T. Timpledon and S. F. Marseken, Truncated Distribution, Betascript
37
Publishing, 2010.
38
[21] S. Yitzhaki, On an extension of the Gini inequality index, International economic review, 24
39
(1983), 617-628.
40
[22] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338-353.
41
[23] L.A. Zadeh, Probability measures of fuzzy events, Journal of Mathematical Analysis and
42
Applications, 23(1968), 421-427
43
ORIGINAL_ARTICLE
A NEW APPROACH IN FAILURE MODES AND EFFECTS ANALYSIS BASED ON COMPROMISE SOLUTION BY CONSIDERING OBJECTIVE AND SUBJECTIVE WEIGHTS WITH INTERVAL-VALUED INTUITIONISTIC FUZZY SETS
Failure modes and effects analysis (FMEA) is a well-known risk analysis approach that has been conducted to distinguish, analyze and mitigate serious failure modes. It demonstrates the effectiveness and the ability of understanding and documenting in a clear manner; however, the FMEA has weak points and it has been criticized by some authors. For example, it does not consider relative importance among three risk factors (i.e., $ O, S $ and $ D $). Different sequences of $ O $, $ S $ and $ D $ may result in exactly the same value of risk priority number (RPN), but their semantic risk implications may be totally different and these three risk factors are difficult to be precisely expressed. This study introduces a new interval-valued intuitionistic fuzzy (IVIF)-decision approach based on compromise solution concept that defeats the above weak points and improves the traditional FMEA's results. This study firstly employs both subjective and objective weights in the decision process simultaneously. Secondly, there are two kinds of subjective weights performed in the study: aggregated weights obtained by experts' assessments as well as entropy measure. Thirdly, this approach is defined under an IVIF-environment to ensure that the evaluation information would be preserved, and the uncertainties could be handled during the computations. Hence, it considers uncertainty in experts' judgments as well as reduces the probability of obtaining two ranking orders with the same value. Finally, the alternatives are ranked with a new collective index according to the compromise solution concept. To show the effectiveness of the proposed approach, two practical examples are solved from the recent literature in engineering applications. The proposed decision approach has an acceptable performance. Also, its advantages have been mentioned in comparison with other decision approaches.
http://ijfs.usb.ac.ir/article_3583_a1e482e0977b7d1891e80c27fcf0934e.pdf
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139
161
10.22111/ijfs.2018.3583
Failure modes and effects analysis (FMEA)
Compromise solution concept
Interval-valued intuitionistic fuzzy sets (IVIFSs)
Subjective and objective weights
Horizontal directional drilling (HDD) machine
Tanker equipment
Z.
Hajighasemi
z.hajighasemi99@gmail.com
true
1
Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran
Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran
Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran
LEAD_AUTHOR
S. Meysam
Mousavi
true
2
Department of Industrial Engineering, Faculty of Engineering,
Shahed University, Tehran, Iran
Department of Industrial Engineering, Faculty of Engineering,
Shahed University, Tehran, Iran
Department of Industrial Engineering, Faculty of Engineering,
Shahed University, Tehran, Iran
AUTHOR
[1] K. Atanassov and G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Sys-
1
tems, 31 (1989), 343{349.
2
[2] K. T. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and
3
Systems, 64 (1994), 159{174.
4
[3] G. Baek, S. Kim, S. Cheon, H. Suh and D. Lee, Prioritizing for failure modes of dynamic
5
positioning system using fuzzy-FMEA, Journal of Korean Institute of Intelligent Systems, 25
6
(2015), 174{179.
7
[4] F. E. Boran, S. Genc M. Kurt and D. Akay, A multi-criteria intuitionistic fuzzy group decision
8
making for supplier selection with topsis method, Expert Systems with Applications, 36
9
(2009), 11363{11368.
10
[5] M. Braglia, Mafma: multi-attribute failure mode analysis, International Journal of Quality
11
& Reliability Management, 17 (2000), 1017{1033.
12
[6] N. Chanamool and T. Naenna, Fuzzy FMEA application to improve decision-making process
13
in an emergency department, Applied Soft Computing, 43 (2016), 441{453.
14
[7] C. L. Chang, C. C. Wei and Y. H. Lee, Failure mode and effects analysis using fuzzy method
15
and grey theory, Kybernetes, 28 (1999), 1072{1080.
16
[8] K. H. Chang and C. H. Cheng, A risk assessment methodology using intuitionistic fuzzy set
17
in FMEA, International Journal of Systems Science, 41 (2010), 1457{1471.
18
[9] K. H. Chang, C. H., Cheng and Y. C. Chang, Reprioritization of failures in a silane supply
19
system using an intuitionistic fuzzy set ranking technique, Soft Computing, 14 (2010), 285{
20
[10] T. Y. Chen, A prioritized aggregation operator-based approach to multiple criteria decision
21
making using interval-valued intuitionistic fuzzy sets: a comparative perspective, Information
22
Sciences, 281 (2014), 97{112.
23
[11] T. Y. Chen, The inclusion-based topsis method with interval-valued intuitionistic fuzzy sets
24
for multiple criteria group decision making, Applied Soft Computing, 26 (2015), 57{73.
25
[12] K. S. Chin, Y. M. Wang, G. K. K. Poon and J. B. Yang, Failure mode and effects analysis
26
by data envelopment analysis, Decision Support Systems, 48 (2009), 246{256.
27
[13] Y. Du, H. Mo, X. Deng, R. Sadiq and Y. Deng, A new method in failure mode and eects
28
analysis based on evidential reasoning, International Journal of System Assurance Engineer-
29
ing and Management, 5 (2014), 1{10.
30
[14] H.R. Feili, N. Akar, H. Lotfizadeh, M. Bairampour and S. Nasiri, Risk analysis of geothermal
31
power plants using failure modes and effects analysis (FMEA) technique, Energy Conversion
32
and Management, 72 (2013), 69{76.
33
[15] H. Hashemi, J. Bazargan, S. M. Mousavi and B. Vahdani, An extended compromise ratio
34
model with an application to reservoir ood control operation under an interval-valued intu-
35
itionistic fuzzy environment, Applied Mathematical Modelling, 38 (2014), 3495{3511.
36
[16] M. S. Kirkire, S. B. Rane and J. R. Jadhav, Risk management in medical product development
37
process using traditional FMEA and fuzzy linguistic approach: a case study, Journal of
38
Industrial Engineering International, 11 (2015), 595{611.
39
[17] M. Kumru and P. Y. Kumru, Fuzzy FMEA application to improve purchasing process in a
40
public hospital, Applied Soft Computing, 13 (2013), 721{733.
41
[18] R. J. Kuo, Y. H. Wu and T. S. Hsu, Integration of fuzzy set theory and TOPSIS into HFMEA
42
to improve outpatient service for elderly patients in taiwan, Journal of the Chinese Medical
43
Association, 75 (2012), 341{348.
44
[19] Z. Li and K. C. Kapur, Some perspectives to define and model reliability using fuzzy sets,
45
Quality Engineering, 25 (2013), 136{150.
46
[20] H. C. Liu, L. Liu, Q. H. Bian, Q. L. Lin, N. Dong and P. C. Xu, Failure mode and effects
47
analysis using fuzzy evidential reasoning approach and grey theory, Expert Systems with
48
Applications, 38 (2011), 4403{4415.
49
[21] H. C. Liu, L. Liu and P. Li, Failure mode and effects analysis using intuitionistic fuzzy hybrid
50
weighted euclidean distance operator, International Journal of Systems Science, 45 (2014),
51
2012{2030.
52
[22] H. C. Liu, J. X. You, M. M. Shan and L. N. Shao, Failure mode and effects analysis using
53
intuitionistic fuzzy hybrid TOPSIS approach, Soft Computing, 19 (2015), 1085{1098.
54
[23] P. Liu, L. He and X. Yu, Generalized hybrid aggregation operators based on the 2-dimension
55
uncertain linguistic information for multiple attribute group decision making, Group Decision
56
and Negotiation, 25 (2016), 103{126.
57
[24] P. Liu and F. Jin, A multi-attribute group decision-making method based on weighted geomet-
58
ric aggregation operators of interval-valued trapezoidal fuzzy numbers, Applied Mathematical
59
Modelling, 36 (2012), 2498{2509.
60
[25] P. Liu and Y. Liu, An approach to multiple attribute group decision making based on intu-
61
itionistic trapezoidal fuzzy power generalized aggregation operator, International Journal of
62
Computational Intelligence Systems, 7 (2014), 291{304.
63
[26] P. Liu and Y. Wang, Multiple attribute decision-making method based on single-valued neu-
64
trosophic normalized weighted bonferroni mean, Neural Computing and Applications, 25
65
(2014), 2001{2010.
66
[27] P. Liu and X. Yu, 2-dimension uncertain linguistic power generalized weighted aggregation
67
operator and its application in multiple attribute group decision making, Knowledge-Based
68
Systems, 57 (2014), 69{80.
69
[28] P. Liu, X. Zhang and F. Jin, A multi-attribute group decision-making method based on
70
interval-valued trapezoidal fuzzy numbers hybrid harmonic averaging operators, Journal of
71
Intelligent & Fuzzy Systems, 23 (2012), 159{168.
72
[29] N. Rachieru, N. Belu and D. C. Anghel, Evaluating the risk of failure on injection pump
73
using fuzzy FMEA method, Applied Mechanics and Materials, 657 (2014), 976{980.
74
[30] S.-M. Seyed-Hosseini N. Safaei and M. Asgharpour, Reprioritization of failures in a system
75
failure mode and effects analysis by decision making trial and evaluation laboratory technique,
76
Reliability Engineering & System Safety, 91 (2006), 872{881.
77
[31] F. Smarandache, Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis
78
& synthetic analysis, American Research Press, USA, ISBN(s): 1879585634, 28(1) (1998),
79
[32] B. Vahdani, M. Salimi and M. Charkhchian, A new FMEA method by integrating fuzzy belief
80
structure and TOPSIS to improve risk evaluation process, International Journal of Advanced
81
Manufacturing Technology, 77 (2015), 357{368.
82
[33] Z. Wang, K. W. Li and W. Wang, An approach to multiattribute decision making with
83
interval-valued intuitionistic fuzzy assessments and incomplete weights, Information Sciences,
84
179 (2009), 3026{3040.
85
[34] D.Woods, A failure mode and effects analysis (FMEA) from operating room setup to incision
86
for living donor liver transplantation, In 2015 Apha Annual Meeting & Expo, 5(2) (2015),
87
[35] N. Xiao, H. Z. Huang, Y. Li, L. He and T. Jin, Multiple failure modes analysis and weighted
88
risk priority number evaluation in FMEA, Engineering Failure Analysis, 18 (2011), 1162{
89
[36] Z. Xu, An overview of methods for determining OWA weights, International Journal of In-
90
telligent Systems, 20 (2005), 843-865.
91
[37] Z. Xu, Methods for aggregating interval-valued intuitionistic fuzzy information and their
92
application to decision making, Control and Decision, 22 (2007), 215{225.
93
[38] R. R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision-
94
making, IEEE Transactions on Systems, Man, and Cybernetics, 18 (1988), 183{190.
95
[39] J. Ye, Multicriteria fuzzy decision-making method based on a novel accuracy function un-
96
der interval-valued intuitionistic fuzzy environment, Expert Systems with Applications, 36
97
(2009), 6899{6902.
98
[40] J. Ye, Multicriteria fuzzy decision-making method using entropy weights-based correlation
99
coefficients of interval-valued intuitionistic fuzzy sets, Applied Mathematical Modelling, 34
100
(2010), 3864{3870.
101
[41] T. M. Yeh and L. Y. Chen, Fuzzy-based risk priority number in fmea for semiconductor wafer
102
processes, International Journal of Production Research, 52 (2014), 539{549.
103
[42] D. Yu, Y. Wu and T. Lu, Interval-valued intuitionistic fuzzy prioritized operators and their
104
application in group decision making Knowledge-Based Systems, 30 (2012), 57{66.
105
[43] S. X. Zeng, C. M. Tam and V. W. Tam, Integrating safety, environmental and quality risks
106
for project management using a fmea method, Engineering Economics, 66 (2015), 44{52.
107
[44] X. Zhang and Z. Xu, Soft computing based on maximizing consensus and fuzzy topsis ap-
108
proach to interval-valued intuitionistic fuzzy group decision making, Applied Soft Computing,
109
26 (2015), 42-56.
110
[45] Q. Zhou and V. V. Thai, Fuzzy and grey theories in failure mode and effect analysis for
111
tanker equipment failure prediction, Safety Science, 83 (2016), 74{79.
112
ORIGINAL_ARTICLE
ON SOMEWHAT FUZZY AUTOMATA CONTINUOUS FUNCTIONS IN FUZZY AUTOMATA TOPOLOGICAL SPACES
In this paper, the concepts of somewhat fuzzy automata continuous functions and somewhat fuzzy automata open functions in fuzzy automata topological spaces are introduced and some interesting properties of these functions are studied. In this connection, the concepts of fuzzy automata resolvable spaces and fuzzy automata irresolvable spaces are also introduced and their properties are studied.
http://ijfs.usb.ac.ir/article_3584_8690026e4194f60da8e7e75afe0a7c27.pdf
2018-03-01T11:23:20
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163
178
10.22111/ijfs.2018.3584
Somewhat fuzzy automata continuous function
Somewhat fuzzy automata open function
Fuzzy automata resolvable and fuzzy automata irresolvable space
N.
Krithika
true
1
Department of Mathematics, Sri Sarada College for Women, Salem,
Tamilnadu, India
Department of Mathematics, Sri Sarada College for Women, Salem,
Tamilnadu, India
Department of Mathematics, Sri Sarada College for Women, Salem,
Tamilnadu, India
LEAD_AUTHOR
B.
Amudhambigai
true
2
Department of Mathematics, Sri Sarada College forWomen, Salem,
Tamilnadu, India
Department of Mathematics, Sri Sarada College forWomen, Salem,
Tamilnadu, India
Department of Mathematics, Sri Sarada College forWomen, Salem,
Tamilnadu, India
AUTHOR
[1] K. K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity,
1
J. Math. Anal. Appl., 82 (1981), 14{32.
2
[2] K. K. Azad, Fuzzy Hausdroff spaces and fuzzy perfect mappings, J. Math. Anal. Appl., 82
3
(1981), 297{305.
4
[3] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182{190.
5
[4] P. Das, A fuzzy topology associated with a fuzzy finite state machine, Fuzzy Sets and Systems,
6
105(3) (1999), 469{479.
7
[5] D. H. Foster, Fuzzy topological groups, J. Math. Anal. Appl., 67 (1979), 549{564.
8
[6] K. R. Gentry and H. B. Hoyle III, Somewhat continuous functions, Czech. Math. J., 21 (96)
9
(1971), 5{12.
10
[7] M. Ghorani and M. M. Zahedi, Characterizations of complete residuated lattice-valued finite
11
tree automata, Fuzzy Sets and Systems, 199 (2012) 28{46.
12
[8] E. Hewitt, A problem in set theoretic topology, Duke Math. J., 10 (1943), 309{333.
13
[9] J. Ignjatovic, M. Ciric and S. Bogdanovic, Determinization of fuzzy automata with member-
14
ship values in complete residuated lattices, Information Sciences, 178 (2008), 164{180.
15
[10] J. Ignjatovic, M. Ciric and V. Simovic, Fuzzy relation equations and subsystems of fuzzy
16
transition systems, Knowledge-Based Systems, 38 (2013), 48{61.
17
[11] Y. M. Li, A categorical approach to lattice-valued fuzzy automata, Fuzzy Sets and Systems,
18
157 (2006), 855{864.
19
[12] Y. M. Li, Finite automata theory with membership values in lattices, Information Sciences,
20
181 (2011), 1003{1017.
21
[13] P. Li and Y. M. Li, Algebraic properties of LA-languages, Information Sciences, 176 (2006),
22
3232{3255.
23
[14] Z. H. Li, P. Li and Y. M. Li, The relationships among several types of fuzzy automata,
24
Information Sciences, 176 (2006), 2208{2226.
25
[15] D. S. Malik and J. N. Mordeson, Algebraic fuzzy automata theory, Arabian J. Sci, Eng., 25
26
(2000), 23{50.
27
[16] D. S. Malik, J. N. Mordeson and M. K. Sen, On subsystems of fuzzy finite state machines,
28
Fuzzy Sets and Systems, 68 (1994), 83{92.
29
[17] P. V. Ramakrishnan and V. Lakshmana Gomathi Nayagam, Nearly fuzzy Hausdor spaces,
30
Indian J. Pure Appl. Math., 31(5) (2000), 695{712.
31
[18] A. K. Srivastava and S. P. Tiwari, A topology for fuzzy automata, Proc. AFSS International
32
Conference on Fuzzy Systems, Lecture Notes in Artificial Intelligence, Springer-Verlag, 2275
33
(2002), 485{491.
34
[19] A. K. Srivastava and S. P. Tiwari, On relationships among fuzzy approximation operators,
35
fuzzy topology, and fuzzy automata, Fuzzy sets and systems, 138 (2003), 197{204.
36
[20] G. Thangaraj and G. Balasubramanian, On somewhat fuzzy continuous functions, J. Fuzzy
37
Math., 11(2) (2003), 725{736.
38
[21] S. P. Tiwari and S. Sharan, Fuzzy automata based on lattice-ordered monoids with algebraic
39
and topological aspects, Fuzzy Information and Engineering, 2 (2012), 155{164.
40
[22] S. P. Tiwari, A. K. Singh and S. Sharan, Fuzzy automata based on lattice-ordered monoid
41
and associated topology, Journal of Uncertain Systems, 6(1) (2012), 51{55.
42
[23] S. P. Tiwari, A. K. Singh, S. Sharan and V. K. Yadav, Bifuzzy core of fuzzy automata, Iranian
43
Journal of Fuzzy Systems, 12(2) (2015), 63{73.
44
[24] W. G.Wee, On generalizations of adaptive algorithm and application of the fuzzy sets concept
45
to pattern classification , Ph. D. Thesis, Purdue University, 1967.
46
[25] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338{353.
47
ORIGINAL_ARTICLE
Persian-translation vol. 15, no. 1, February 2018
http://ijfs.usb.ac.ir/article_3586_f7966fa359aeecc41fd2a80aeb092aba.pdf
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10.22111/ijfs.2018.3586