ORIGINAL_ARTICLE
Cover for Volume.13, No.4
http://ijfs.usb.ac.ir/article_2622_62f46e0d5b4bbe46365d43f6b7ed13cd.pdf
2016-08-30T11:23:20
2018-08-18T11:23:20
0
10.22111/ijfs.2016.2622
ORIGINAL_ARTICLE
Hesitant Fuzzy Linguistic Arithmetic Aggregation Operators in Multiple Attribute Decision Making
In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with hesitant fuzzy linguistic information. Then, motivated by the idea of traditional arithmetic operation, we have developed some aggregation operators for aggregating hesitant fuzzy linguistic information: hesitant fuzzy linguistic weighted average (HFLWA) operator, hesitant fuzzy linguistic ordered weighted average (HFLOWA) operator and hesitant fuzzy linguistic hybrid average (HFLHA) operator. Furthermore, we propose the concept of the dual hesitant fuzzy linguistic set and develop some aggregation operators with dual hesitant fuzzy linguistic information. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy linguistic multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
http://ijfs.usb.ac.ir/article_2592_619f4e19e93b5824c3f4b46437720286.pdf
2016-08-30T11:23:20
2018-08-18T11:23:20
1
16
10.22111/ijfs.2016.2592
Multiple attribute decision making (MADM)
Hesitant fuzzy linguistic values
Hesitant fuzzy linguistic hybrid average (HFLHA) operator
Dual hesitant fuzzy linguistic set
Guiwu
Wei
weiguiwu@163.com
true
1
School of Business, Sichuan Normal University, Chengdu, 610101, P.R.
China; Communications Systems and Networks (CSN) Research Group, Department of
Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
School of Business, Sichuan Normal University, Chengdu, 610101, P.R.
China; Communications Systems and Networks (CSN) Research Group, Department of
Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
School of Business, Sichuan Normal University, Chengdu, 610101, P.R.
China; Communications Systems and Networks (CSN) Research Group, Department of
Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
LEAD_AUTHOR
Fuad E.
Alsaadi
true
2
Communications Systems and Networks (CSN) Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Communications Systems and Networks (CSN) Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Communications Systems and Networks (CSN) Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
AUTHOR
Tasawar
Hayat
true
3
Department of Mathematics, QuaidI-Azam University 45320, Islam-
abad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research
Group, Department of Mathematics, Faculty of Science, King Abdulaziz University,
Jeddah 21589, Saudi Arabia
Department of Mathematics, QuaidI-Azam University 45320, Islam-
abad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research
Group, Department of Mathematics, Faculty of Science, King Abdulaziz University,
Jeddah 21589, Saudi Arabia
Department of Mathematics, QuaidI-Azam University 45320, Islam-
abad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research
Group, Department of Mathematics, Faculty of Science, King Abdulaziz University,
Jeddah 21589, Saudi Arabia
AUTHOR
Ahmed
Alsaedi
true
4
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group,
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group,
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group,
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
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, Two theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 110
3
(2000), 267{269.
4
[4] S. M. Chen, S. H. Cheng and C. H. Chiou, Fuzzy multiattribute group decision making based
5
on intuitionistic fuzzy sets and evidential reasoning methodology, Information Fusion, 27
6
(2016), 215{227.
7
[5] T. Y. Chen, Bivariate models of optimism and pessimism in multi-criteria decision-making
8
based on intuitionistic fuzzy sets, Information Sciences, 181 (2011), 2139{2165.
9
[6] T. Y. Chen, The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy
10
sets for multiple criteria group decision making, Appl. Soft Comput., 26 (2015), 57{73.
11
[7] T. Y. Chen, An interval-valued intuitionistic fuzzy permutation method with likelihood-
12
based preference functions and its application to multiple criteria decision analysis, Appl.
13
Soft Comput., 42 (2016), 390-409.
14
[8] F. Chiclana, F. Herrera and E. Herrera-Viedma, The ordered weighted geometric opera-
15
tor: Properties and application, In: Proc of 8th Int Conf on Information Processing and
16
Management of Uncertainty in Knowledge-based Systems, Madrid, (2000), 985-991.
17
[9] M. Gabroveanu, I. Iancu and M. Cosulschi, An Atanassov's intuitionistic fuzzy reasoning
18
model, Journal of Intelligent and Fuzzy Systems, 30(1) (2016), 117{128.
19
[10] F. Herrera and E. Herrera-Viedma, Linguistic decision analysis: Steps for solving decision
20
problems under linguistic information, Fuzzy Sets and Systems, 115 (2000), 67{82.
21
[11] F. Herrera and L. Martnez, A 2-tuple fuzzy linguistic representation model for computing
22
with words, IEEE Transactions on Fuzzy Systems, 8 (2000), 746{752.
23
[12] J. Y. Huang, Intuitionistic fuzzy hamacher aggregation operators and their application
24
to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems, 27(1)
25
(2014), 505{513.
26
[13] X. P. Jiang and G. W. Wei, Some Bonferroni mean operators with 2-tuple linguistic infor-
27
mation and their application to multiple attribute decision making, Journal of Intelligent
28
and Fuzzy Systems, 27 (2014), 2153{2162.
29
[14] D. F. Li, TOPSIS-based nonlinear-programming methodology for multiattribute decision
30
making with interval-valued intuitionistic fuzzy sets, IEEE Transactions on Fuzzy Systems,
31
18 (2010), 299{311.
32
[15] D. F. Li and H. P. Ren, Multi-attribute decision making method considering the amount
33
and reliability of intuitionistic fuzzy information, Journal of Intelligent and Fuzzy Systems,
34
28(4) (2015), 1877{1883.
35
[16] R. Lin, G. W. Wei, H. J. Wang and X. F. Zhao, Choquet integrals of weighted triangular
36
fuzzy linguistic information and their applications to multiple attribute decision making,
37
Journal of Business Economics and Management, 15(5) (2014),795{809.
38
[17] L. Martinez and F. Herrera, An overview on the 2-tuple linguistic model for computing with
39
words in decision making: Extensions, applications and challenges, Information Sciences,
40
207(10) (2012), 1{18.
41
[18] J. M. Merigo, A unied model between the weighted average and the induced OWA operator,
42
Expert Systems with Applications, 38(9) (2011), 11560{11572.
43
[19] J. M. Merigo and M. Casanovas, Fuzzy generalized hybrid aggregation operators and its
44
application in decision making, International Journal of Fuzzy Systems, 12(1) (2010),
45
[20] J. M. Merigo and M. Casanovas, The fuzzy generalized OWA operator and its application
46
in strategic decision making, Cybernetics & Systems, 41(5) (2010), 359{370.
47
[21] J. M. Merigo, M. Casanovas and L. Martinez, Linguistic aggregation operators for linguistic
48
decision making based on the Dempster-Shafer theory of evidence, International Journal
49
of Uncertainty, Fuzziness and Knowledge-Based Systems, 18(3) (2010), 287{304.
50
[22] J. M. Merigo and A. M. Gil-Lafuente, Decision making techniques in business and econom-
51
ics based on the OWA operator, SORT-Statistics and Operations Research Transactions,
52
36(1) (2012), 81{102.
53
[23] J. M. Merigo and A. M. Gil-Lafuente, Induced 2-tuple linguistic generalized aggregation
54
operators and their application in decision-making, Information Sciences, 236(1) (2013),
55
[24] J. M. Merigo, A. M. Gil-Lafuente, L. G. Zhou and H. Y. Chen, Induced and linguistic
56
generalized aggregation operators and their application in linguistic group decision making,
57
Group Decision and Negotiation, 21(4) (2012), 531{549.
58
[25] L. D. Miguel, H. Bustince, J. Fernandez, E. Indurain, A. Kolesarova and R. Mesiar,
59
Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy
60
sets with an application to decision making, Information Fusion, 27 (2016), 189{197.
61
[26] V. Torra, The weighted OWA operator, International Journal of Intelligent Systems, 12
62
(1997), 153{166.
63
[27] V. Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems, 25 (2010),
64
[28] V. Torra and Y. Narukawa, On hesitant fuzzy sets and decision, In: The 18th IEEE
65
International Conference on Fuzzy Systems, Jeju Island, Korea, (2009), 1378{1382.
66
[29] H. J. Wang, X. F Zhao and G. W. Wei, Dual hesitant fuzzy aggregation operators in
67
multiple attribute decision making, Journal of Intelligent and Fuzzy Systems, 26(5) (2014),
68
2281{2290.
69
[30] X. R. Wang, Z. H. Gao, X. F. Zhao and G. W. Wei, Model for Evaluating the Government
70
Archives Websites Construction Based on the GHFHWD Measure with Hesitant Fuzzy
71
Information, International Journal of Digital Content Technology and its Applications,
72
5(12) (2011), 418{425.
73
[31] G. W. Wei, Some geometric aggregation functions and their application to dynamic mul-
74
tiple attribute decision making in intuitionistic fuzzy setting, International Journal of Un-
75
certainty, Fuzziness and Knowledge-Based Systems, 17(2) (2009), 179{196.
76
[32] G. W. Wei, Some induced geometric aggregation operators with intuitionistic fuzzy infor-
77
mation and their application to group decision making, Applied Soft Computing, 10(2)
78
(2010), 423{431.
79
[33] G. W. Wei, Gray relational analysis method for intuitionistic fuzzy multiple attribute
80
decision making, Expert Systems with Applications, 38 (2011), 11671{11677.
81
[34] G. W. Wei, Some harmonic averaging operators with 2-tuple linguistic assessment infor-
82
mation and their application to multiple attribute group decision making, International
83
Journal of Uncertainty, Fuzziness and Knowledge- Based Systems, 19(6) (2011), 977{998.
84
[35] G. W. Wei, Hesitant fuzzy prioritized operators and their application to multiple attribute
85
group decision making, Knowledge-Based Systems, 31 (2012), 176{182.
86
[36] G. W. Wei, Approaches to interval intuitionistic trapezoidal fuzzy multiple attribute deci-
87
sion making with incomplete weight information, International Journal of Fuzzy Systems,
88
17(3) (2015), 484{489.
89
[37] G. W. Wei, R. Lin, X. F. Zhao and H. J. Wang, An approach to multiple attribute deci-
90
sion making based on the induced Choquet integral with fuzzy number intuitionistic fuzzy
91
information, Journal of Business Economics and Management, 15(2) (2014), 277{298.
92
[38] G. W. Wei and N. Zhang, A multiple criteria hesitant fuzzy decision making with Shapley
93
value-based VIKOR method, Journal of Intelligent and Fuzzy Systems, 26(2) (2014), 1065{
94
[39] G. W. Wei and X. F. Zhao, Some induced correlated aggregating operators with intuition-
95
istic fuzzy information and their application to multiple attribute group decision making,
96
Expert Systems with Applications, 39(2) (2012), 2026{2034.
97
[40] G. W. Wei and X. F. Zhao, Some dependent aggregation operators with 2-tuple linguistic
98
information and their application to multiple attribute group decision making, Expert
99
Systems with Applications, 39 (2012), 5881{5886.
100
[41] G. W. Wei and X. F. Zhao, Induced hesitant interval-valued fuzzy einstein aggregation
101
operators and their application to multiple attribute decision making, Journal of Intelligent
102
and Fuzzy Systems, 24 (2013), 789{803.
103
[42] G. W. Wei, X. F. Zhao, H. J. Wang and R. Lin, Hesitant fuzzy choquet integral aggregation
104
operators and their applications to multiple attribute decision making, Information: An
105
International Interdisciplinary Journal, 15(2) (2012), 441{448.
106
[43] G. W. Wei, H. J. Wang, X. F. Zhao and R. Lin, Hesitant triangular fuzzy information ag-
107
gregation in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems,
108
26(3) (2014), 1201{1209.
109
[44] G. W. Wei, H. J. Wang, X. F. Zhao and R. Lin, Approaches to hesitant fuzzy multiple
110
attribute decision making with incomplete weight information, Journal of Intelligent and
111
Fuzzy Systems, 26(1) (2014), 259{266.
112
[45] M. Xia and Z. S. Xu, Hesitant fuzzy information aggregation in decision making, Interna-
113
tional Journal of Approximate Reasoning, 52(3) (2011), 395{407.
114
[46] Z. S. Xu, A method based on linguistic aggregation operators for group decision making
115
with linguistic preference relations, Information Sciences, 166(1) (2004), 19{30.
116
[47] Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transations on Fuzzy Systems,
117
15(6) (2007), 1179{1187.
118
[48] Z. S. Xu and Q. L. Da, An overview of operators for aggregating information, International
119
Journal of Intelligent System, 18 (2003), 953{969.
120
[49] Z. S. Xu and M. Xia, Distance and similarity measures for hesitant fuzzy sets, Information
121
Sciences, 181(11) (2011), 2128{2138.
122
[50] Z. S. Xu and M. Xia, On distance and correlation measures of hesitant fuzzy information,
123
International Journal of Intelligence Systems, 26(5) (2011), 410{425.
124
[51] Z. S. Xu, M. Xia and N. Chen, Some hesitant fuzzy aggregation operators with their
125
application in group decision making, Group Decision and Negotiation, 22(2) (2013),
126
[52] Z. S. Xu and R. R. Yager, Some geometric aggregation operators based on intuitionistic
127
fuzzy sets, International Journal of General System, 35 (2006), 417{433.
128
[53] R. R. Yager, Including importances in OWA aggregation using fuzzy systems modelling,
129
IEEE Transactions on Fuzzy Systems, 6 (1998), 286{294.
130
[54] R. R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision
131
making, IEEE Transactions on Systems Man and Cybernetics, 18 (1988), 183{190.
132
[55] R. R. Yager, K. J. Engemann and D. P. Filev, On the concept of immediate probabilities,
133
International Journal of Intelligent Systems, 10 (1995), 373{397.
134
[56] R. R. Yager and D. P. Filev, Induced ordered weighted averaging operators, IEEE Trans-
135
actions on Systems, Man, and Cybernetics- Part B, 29 (1999), 141{150.
136
[57] R. R. Yager, Prioritized aggregation operators, International Journal of Approximate Rea-
137
soning, 48 (2008), 263{274.
138
[58] O. Y. Yao and W. Pedrycz, A new model for intuitionistic fuzzy multi-attributes decision
139
making, European Journal of Operational Research, 249(2) (2016), 677{682.
140
[59] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{356.
141
[60] X. F. Zhao, Q. X. Li, G. W. Wei, Some prioritized aggregating operators with linguistic
142
information and their application to multiple attribute group decision making, Journal of
143
Intelligent and Fuzzy Systems, 26(4) (2014), 1619{1630.
144
[61] L. Y. Zhou, R. Lin, X. F. Zhao and G. W. Wei, Uncertain linguistic prioritized aggregation
145
operators and their application to multiple attribute group decision making, International
146
Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21(4) (2013), 603{627.
147
[62] B. Zhu, Z. S. Xu and M. M. Xia, Hesitant fuzzy geometric Bonferroni means, Information
148
Sciences, Information Sciences, 205(1) (2012), 72{85.
149
ORIGINAL_ARTICLE
A satisfactory strategy of multiobjective two person matrix games with fuzzy payoffs
The multiobjective two person matrix game problem with fuzzy payoffs is considered in this paper. It is assumed that fuzzy payoffs are triangular fuzzy numbers. The problem is converted to several multiobjective matrix game problems with interval payoffs by using the $alpha$-cuts of fuzzy payoffs. By solving these problems some $alpha$-Pareto optimal strategies with some interval outcomes are obtained. An interactive algorithm is presented to obtain a satisfactory strategy of players. Validity and applicability of the method is illustrated by a practical example.
http://ijfs.usb.ac.ir/article_2593_a3f6078e1878f648f551e48322f3dde9.pdf
2016-08-30T11:23:20
2018-08-18T11:23:20
17
33
10.22111/ijfs.2016.2593
Fuzzy multiobjective game
Interval multiobjective programming
Satisfactory strategy
Security level
Hamid
Bigdeli
true
1
Department of Mathematics, University of Birjand, Birjand, I.R. Iran
Department of Mathematics, University of Birjand, Birjand, I.R. Iran
Department of Mathematics, University of Birjand, Birjand, I.R. Iran
LEAD_AUTHOR
Hassan
Hassanpour
true
2
Department of Mathematics, University of Birjand, Birjand,
I.R. Iran
Department of Mathematics, University of Birjand, Birjand,
I.R. Iran
Department of Mathematics, University of Birjand, Birjand,
I.R. Iran
AUTHOR
[1] C. R. Bector and S. Chandra, Fuzzy mathematical programming and fuzzy matrix games,
1
Springer Verlag, Berlin, 2005.
2
[2] S. M. Belenson and K. C. Kapur, An algorithm for solving multicriterion linear programming
3
problems with examples, Operational Research Quarterly, 24(1) (1973), 65{77.
4
[3] A. Billot, Economic theory of fuzzy equilibria, Springer-Verlag, 1992.
5
[4] J. J. Buckley, Multiple goal non-cooperative con
6
icts under uncertainty: a fuzzy set approach,
7
Fuzzy Sets and Systems, 13(2) (1984), 107{124.
8
[5] D. Butnariu, Fuzzy games; a description of the concept, Fuzzy Sets and Systems, 1(3) (1978),
9
[6] D. Butnariu, Stability and Shapley value for an n-persons fuzzy game, Fuzzy Sets and Systems,
10
4(1) (1980), 63{72.
11
[7] L. Campos, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets and
12
Systems, 32(3) (1989), 275{289.
13
[8] L. Chandra and A. Aggarwal, On solving matrix games with payos of triangular fuzzy num-
14
bers: Certain observations and generalizations, European Journal of Operational Research,
15
246 (2015), 575{581.
16
[9] M. Clemente and F. R. Fernandez, Pareto-optimal security strategies in matrix games with
17
fuzzy payos, Fuzzy Sets and Systems, 176(1) (2011), 36{45.
18
[10] W. D. Collins and C. Y. Hu, Studying interval valued matrix games with fuzzy logic, Soft
19
Computing, 12(2) (2008), 147{155.
20
[11] W. D. Cook, Zero-sum games with multiple goals, Naval Research Logistics Quarterly, 23(4)
21
(1976), 615{622.
22
[12] L. Cunlin and Z. Qiang, Nash equilibrium strategy for fuzzy noncooperative games, Fuzzy
23
Sets and Systems, 176(1) (2011), 46{55.
24
[13] B. Dutta and S. K. Gupta, On Nash equilibrium strategy of two person zero sum games with
25
trapezoidal fuzzy payos, Fuzzy Information and Engineering, 6(3) (2014), 299{314.
26
[14] K. Fahem and M. S. Radjef, Properly ecient nash equilibrium in multicriteria noncooper-
27
ative games, Mathematical Methods of Operations Research, 82(2) (2015), 175{193.
28
[15] F. R. Fernandez and J. Puerto, Vector linear programming in zero-sum multicriteria matrix
29
games, Journal of Optimization Theory and Application, 89(1) (1996), 115{127.
30
[16] D. Fudenberg and J. Tirole, Game theory, The MIT Press, 1991.
31
[17] C. L. Hwang and K. Yoon, Multiple attribute decision making: methods and applications, a
32
state of the art survey, Springer-Verlag, Berlin, 1981.
33
[18] S. Kumar, Max-min solution approach for multiobjective matrix game with fuzzy goals, Yugoslav
34
Journal of Operations Research, 2015.
35
[19] M. Larbani, Non cooperative fuzzy games in normal form: a survey, Fuzzy Sets and Systems,
36
160(22) (2009), 3184{3210.
37
[20] D. F. Li, A fuzzy multiobjective programming approach to solve fuzzy matrix games, The
38
Journal of Fuzzy Mathematics, 7(4) (1999), 907{912.
39
[21] D. F. Li, Lexicographic method for matrix games with payos of triangular fuzzy numbers,
40
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16(3) (2008),
41
[22] D. F. Li, A fast approach to compute fuzzy values of matrix games with payos of triangular
42
fuzzy numbers, European Journal of Operational Research, 223(2) (2012), 421{429.
43
[23] D. F. Li and J. X. Nan, An interval-valued programming approach to matrix games with
44
payos of triangular intuitionistic fuzzy numbers, Iranian Journal of Fuzzy Systems, 11(2)
45
(2014), 45{57.
46
[24] T. Maeda, On characterization of equilibrium strategy of two-person zero sum games with
47
fuzzy payos, Fuzzy Sets and Systems, 139(2) (2003), 283{296.
48
[25] P. K. Nayak and M. Pal, Linear programming technique to solve two-person matrix games
49
with interval pay-os, Asia-Pacic Journal of Oprational Research, 26(2) (2009), 285{305.
50
[26] J. V. Neumann and O. Morgenstern, Theory of games and economic behavior, Wiley, New
51
York, 1944.
52
[27] I. Nishizaki and M. Sakawa, Fuzzy and multiobjective games for con
53
ict resolution, Springer
54
Verlag, Berlin, 2001.
55
[28] G . Owen, Game theory, Academic Press, San Diego, Third Edition, 1995.
56
[29] M. Sakawa, Fuzzy sets and interactive multiobjective optimization, Plenum press, New York
57
and london, 1993.
58
[30] M. R. Seikh, P. K. Nayak and M. Pal, An alternative approach for solving fuzzy matrix
59
games, International Journal of Mathematics and Soft Computing, 5(1) (2015), 79{92.
60
[31] M. R. Seikh, P. K. Nayak and M. Pal, Matrix games with intuitionistic fuzzy pay-os, Journal
61
of Information & Optimization Sciences, 36(1-2) (2015), 159{181.
62
[32] M. R. Seikh, P. K. Nayak and M. Pal, Application of intuitionistic fuzzy mathematical pro-
63
gramming with exponential membership and quadratic non-membership functions in matrix
64
games, Annals of Fuzzy Mathematics and Informatics, 9(2) (2015), 183{195.
65
[33] M. Zeleny, Games with multiple payos, International Journal of Game Theory, 4(4) (1975),
66
[34] X. Zhou, Y. Song, Q. Zhang and X. Gao, Multiobjective matrix game with vague payos,
67
Fuzzy Information and Engineering, 40 (2007), 543{550.
68
ORIGINAL_ARTICLE
Bisimulation for BL-general fuzzy automata
In this note, we define bisimulation for BL-general fuzzy automata and show that if there is a bisimulation between two BL-general fuzzy automata, then they have the same behavior.For a given BL-general fuzzy automata, we obtain the greatest bisimulation for the BL-general fuzzy automata. Thereafter, if we use the greatest bisimulation, then we obtain a quotient BL-general fuzzy automata and this quotient is minimal, furthermore there is a morphism from the first one to its quotient.Also, for two given BL-general fuzzy automata we present an algorithm, which determines bisimulation between them.Finally, we present some examples to clarify these new notions.
http://ijfs.usb.ac.ir/article_2594_42b1b8528d5cf9d63d89ed191424c188.pdf
2016-08-30T11:23:20
2018-08-18T11:23:20
35
50
10.22111/ijfs.2016.2594
BL-general fuzzy automata
Bisimulation
Reduction
General fuzzy automata
Quotient automata
M.
Shamsizadeh
true
1
Department of Mathematics, Graduate University of Advanced
Technology, Kerman, Iran
Department of Mathematics, Graduate University of Advanced
Technology, Kerman, Iran
Department of Mathematics, Graduate University of Advanced
Technology, Kerman, Iran
LEAD_AUTHOR
M. M.
Zahedi
zahedi_mm@ mail.uk.ac.ir
true
2
Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran
Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran
Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran
AUTHOR
K.
Abolpour
true
3
Department of Mathematics, Kazerun Branch, Islamic Azad University,
Kazerun, Iran
Department of Mathematics, Kazerun Branch, Islamic Azad University,
Kazerun, Iran
Department of Mathematics, Kazerun Branch, Islamic Azad University,
Kazerun, Iran
AUTHOR
[1] K. Abolpour and M. M. Zahedi, BL-general fuzzy automata and accept behavior, Journal
1
Applied Mathematics and Computing, 38 (2012), 103-118.
2
[2] K. Abolpour and M. M. Zahedi, Isomorphism between two BL-general fuzzy automata, Soft
3
Computing, 16 (2012), 729-736.
4
[3] C. Baier, B. Engelen and M. Majster Cederbaum, Deciding bisimilarity and similarity for
5
probabilistic processes, Journal of Computer and System Sciences, 60 (2000), 187-231.
6
[4] P. Buchholz, Bisimulation relations for weighted automata, Theoretical Computer Science,
7
393 (2008), 109-123.
8
[5] Y. Cao, G. Chen and E. Kerre, Bisimulations for fuzzy transition systems, IEEE Transactions
9
on Fuzzy Systems, 19 (2011), 540-552.
10
[6] Y. Cao, H. Wang, S. X. Sun and G. Chen, A behavioral distance for fuzzy-transition systems,
11
IEEE Transactions on Fuzzy Systems, 21 (2012), 735-747.
12
[7] M. Ciric, J. Ignjatovic, M. Basic and I. Jancic, Nondeterministic automata: equivalence,
13
bisimulations, and uniform relations, Information Sciences, 261 (2013), 185-218.
14
[8] M. Ciric, J. Ignjatovic, N. Damljanovic and M. Basic, Bisimulations for fuzzy automata,
15
Fuzzy Sets and Systems, 186 (2012) 100-139.
16
[9] M. Ciric, J. Ignjatovic, I. Jancic and N. Damljanovic, Computation of the greatest simulations
17
and bisimulations between fuzzy automata, Fuzzy Sets and Systems, 208 (2012), 22-42.
18
[10] N. Damljanovic, M. Ciric and J. Ignjatovic, Bisimulations for weighted automata over an
19
additively idempotent semiring, Theoretical Computer Science, 534 (2014), 86-100.
20
[11] W. Deng and D. W. Qiu, Supervisory control of fuzzy discrete event systems for simulation
21
equivalence, IEEE Transactions on Fuzzy Systems, 23 (2015), 178-192.
22
[12] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal
23
of Approximate Reasoning, 38 (2005), 175-214.
24
[13] C. L. Giles, C. W. Omlin and K. K. Thornber, Equivalence in knowledge representation:
25
automata, recurrent neural networks, and dynamical fuzzy systems, Proceedings of IEEE, 87
26
(1999), 1623-1640.
27
[14] M. M. Gupta, G. N. Saridis and B. R. Gaines, Fuzzy Automata and Decision Processes,
28
North Holland, New York, (1977), 111-175.
29
[15] P. Hajek, Metamathematics of fuzzy logic, Trends in Logic, Kluwer, Dordercht, 4 (1998).
30
[16] J. Hgberg, A. Maletti and J. May, Backward and forward bisimulation minimisation of tree
31
automata, In: J. Holub, J. drek (Eds.), IAA07, in: Lecture Notes in Computer Science, 4783
32
(2007), 109-121.
33
[17] J. Hgberg, A. Maletti and J. May, Backward and forward bisimulation minimisation of tree
34
automata, Theoretical Computer Science, 410 (2009) 3539-3552.
35
[18] D. C. Kozen, Automata and computability, Springer, USA, 1997.
36
[19] E. T. Lee and L. A. Zadeh, Note on fuzzy languages, Information Sciences, 1 (1969), 421-434.
37
[20] L. Li and D. Qiu, On the state minimization of fuzzy automata, IEEE Transactions on Fuzzy
38
Systems, 23 (2015), 434-443.
39
[21] N. Lynch and F. Vaandrager, Forward and backward simulations, Information and Computation,
40
121 (1995), 214-233.
41
[22] D. S. Malik and J. N. Mordeson, Fuzzy Automata and Languages: Theory and Applications,
42
Chapman Hall, CRC Boca Raton, London, New York, Washington DC, 2002.
43
[23] D. S. Malik and J. N. Mordeson, Fuzzy discrete structures, Physica-Verlag, New York, (2000),
44
London, 2002.
45
[24] R. Milner, Acalculus of communicating systems, In: G. Goos, J. Hartmanis (Eds.), Lecture
46
Notes in Computer Science, Springer, 92 (1980).
47
[25] C. W. Omlin, K. K. Thornber and C. L. Giles, Fuzzy nite-state automata can be deter-
48
ministically encoded in recurrent neural networks, IEEE Transactions on Fuzzy Systems, 5
49
(1998), 76-89.
50
[26] D. Park, Concurrency and automata on innite sequences, In: P.Deussen(Ed.), Proceedings
51
of the 5th GI Conference, Karlsruhe, Germany, Lecture Notesin Computer Science, Springer-
52
Verlag, 104, (1981), 167-183.
53
[27] W. Pedrycz and A. Gacek, Learning of fuzzy automata, International Journal of Computational
54
Intelligence and Applications, 1 (2001), 19-33.
55
[28] K. Peeva, Behavior, reduction and minimization of nite L-automata, Fuzzy Sets and Systems,
56
28 (1988), 171-181.
57
[29] K. Peeva, Equivalence, reduction and minimization of nite automata over semirings, Theoretical
58
Computer Science, 88 (1991), 269-285.
59
[30] D. Qiu, Automata theory based on complete residuated lattice-valued logic, Science in China
60
Series: Information Sciences, 44 (2001), 419-429.
61
[31] D. Qiu, Automata theory based on complete residuated lattice-valued logic (II), Science in
62
China Series F: Information Sciences, 45 (2002), 442-452.
63
[32] D. Qiu, Characterizations of fuzzy nite automata, Fuzzy Sets and Systems, 141 (2004),
64
[33] D. Qiu, Pumping lemma in automata theory based on complete residuated lattice-valued logic:
65
A not, Fuzzy Sets and Systems, 157 (2006), 2128-2138.
66
[34] D. Qiu, Supervisory control of fuzzy discrete event systems: a formal approach, IEEE Transactions
67
on Systems, Man and CyberneticsPart B, 35 (2005), 72-88.
68
[35] E. S. Santos, Maxmin automata, Information Control, 13 (1968), 363-377.
69
[36] V. Topencharov and K. Peeva, Equivalence, reduction and minimization of nite fuzzy au-
70
tomata, Journal of Mathematical Analysis and Applications, 84 (1981), 270-281.
71
[37] E. Turunen, Boolean deductive systems of BL-algebras, Archive for Mathematical Logic, 40
72
(2001), 467-473.
73
[38] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept
74
to pattern classication, Ph.D. Thesis, Purdue University, Lafayette, IN, 1967.
75
[39] W. G. Wee and K. S. Fu, A formulation of fuzzy automata and its application as a model of
76
learning systems, IEEE Transactions on Systems, Man and Cybernetics, 5 (1969), 215-223.
77
[40] L. Wu and D. Qiu, Automata theory based on complete residuated lattice-valued logic: Re-
78
duction and minimization, Fuzzy Sets and Systems, 161 (2010), 1635-1656.
79
[41] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965,) 338-353.
80
ORIGINAL_ARTICLE
Characterizations of $L$-convex spaces
In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it is proved that these categories are all isomorphic to the category of $L$-convex spaces whenever $L$ is a completely distributive lattice with an order-reversing involution operator.
http://ijfs.usb.ac.ir/article_2595_892a5985091b412961eb99fb84c5bfbe.pdf
2016-08-30T11:23:20
2018-08-18T11:23:20
51
61
10.22111/ijfs.2016.2595
$L$-convex structure
$L$-concave structure
Convex $L$-closure operator
Concave $L$-interior operator
Concave $L$-neighborhood system
Bin
Pang
pangbin1205@163.com
true
1
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
AUTHOR
Yi
Zhao
zhaoyisz420@sohu.com
true
2
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
LEAD_AUTHOR
[1] S. Abramsky and A. Jung, Domain theory, S. Abramsky, D. Gabbay, T.S.E. Mailbaum (Eds.),
1
Handbook of Logic in Computer Science, Oxford University Press, Oxford (1994), 1{168.
2
[2] V. Chepoi, Separation of two convex sets in convexity structures, J. Geom., 50 (1994), 30{51.
3
[3] E. Ellis, A general set-separation theorem, Duke Math. J., 19 (1952), 417{421.
4
[4] J. Eckho, Radon's theorem in convex product structures I, Monatsh. Math., 72 (1968),
5
[5] J. Eckho, Radon's theorem in convex product structures II, Monatsh. Math., 73 (1969),
6
[6] R. E. Jamison, A general theory of convexity, Dissertation, University ofWashington, Seattle,
7
Washington, 1974.
8
[7] D. C. Kay and E. W. Womble, Axiomatic convexity theory and the relationship between the
9
Caratheodory, Helly and Radon numbers, Pacic J. Math., 38 (1971), 471{485.
10
[8] M. Lassak, On metric B-convexity for which diameters of any set and its hull are equal, Bull.
11
Acad. Polon. Sci., 25 (1977), 969{975.
12
[9] F. W. Levi, On Helly's theorem and the axioms of convexity, J. Indian Math. Soc., 15 Part
13
A (1951), 65{76.
14
[10] Y. Maruyama, Lattice-valued fuzzy convex geometry, RIMS Kokyuroku, 164 (2009), 22{37.
15
[11] K. Menger, Untersuchungen uber allgemeine Metrik, Math. Ann., 100(1928), 75{163.
16
[12] B. Pang and F. G. Shi, Subcategories of the category of L-convex spaces, Fuzzy Sets Syst.,
17
(2016), http://dx.doi.org/10.1016/j.fss.2016.02.014.
18
[13] B. Pang and F. G. Shi, L-hull operators and L-interval operators in L-convex spaces, Sub-
19
[14] M. V. Rosa, On fuzzy topology fuzzy convexity spaces and fuzzy local convexity, Fuzzy Sets
20
Syst., 62 (1994), 97{100.
21
[15] F. G. Shi and Z. Y. Xiu, A new approach to the fuzzication of convex structures, J. Appl.
22
Math., 2014 (2014), 12 pages.
23
[16] G. Sierkama, Caratheodory and Helly-numbers of convex-product-structures, Pacic J. Math.,
24
61 (1975), 272{282.
25
[17] G. Sierkama, Relationships between Caratheodory, Helly, Radon and Exchange numbers of
26
convex spaces, Nieuw Archief Wisk, 25 (1977), 115{132.
27
[18] V. P. Soltan, Some questions in the abstract theory of convexity, Soviet Math. Dokl., 17
28
(1976), 730{733.
29
[19] V. P. Soltan, D-convexity in graphs, Soviet Math. Dokl., 28 (1983), 419{421.
30
[20] V. P. Soltan, Introduction to the axiomatic theory of convexity, (Russian) Shtiinca, Kishinev
31
[21] M. Van De Vel, Finite dimensional convex structures II: the invariants, Topology Appl., 16
32
(1983), 81{105.
33
[22] M. Van De Vel, Binary convexities and distributive lattices, Proc. London Math. Soc., 48
34
(1984), 1{33.
35
[23] M. Van De Vel, Theory of convex structures, North-Holland, Amsterdam 1993.
36
[24] J. C. Varlet, Remarks on distributive lattices, Bull. Acad. Polon. Sci., 23 (1975), 1143{1147.
37
ORIGINAL_ARTICLE
Multiple Fuzzy Regression Model for Fuzzy Input-Output Data
A novel approach to the problem of regression modeling for fuzzy input-output data is introduced.In order to estimate the parameters of the model, a distance on the space of interval-valued quantities is employed.By minimizing the sum of squared errors, a class of regression models is derived based on the interval-valued data obtained from the $\alpha$-level sets of fuzzy input-output data.Then, by integrating the obtained parameters of the interval-valued regression models, the optimal values of parameters for the main fuzzy regression model are estimated.Numerical examples and comparison studies are given to clarify the proposed procedure, and to show the performance of the proposed procedure with respect to some common methods.
http://ijfs.usb.ac.ir/article_2596_c5d1e02ec07e74c58799b657496f0c39.pdf
2016-08-30T11:23:20
2018-08-18T11:23:20
63
78
10.22111/ijfs.2016.2596
Fuzzy regression
Interval-valued regression
Least squares method
$LR$-Fuzzy number
Multiple regression
Predictive ability
Jalal
Chachi
taheri.chachi@gmail.com
true
1
Department of Mathematics, Statistics and Computer Sciences, Sem-
nan University, Semnan, Semnan 35195-363, Iran
Department of Mathematics, Statistics and Computer Sciences, Sem-
nan University, Semnan, Semnan 35195-363, Iran
Department of Mathematics, Statistics and Computer Sciences, Sem-
nan University, Semnan, Semnan 35195-363, Iran
LEAD_AUTHOR
S. Mahmoud
Taheri
taher@cc.iut.ac.ir;sm_taheri@ut.ac.ir
true
2
Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, P.O. Box 11365-4563, Iran
Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, P.O. Box 11365-4563, Iran
Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, P.O. Box 11365-4563, Iran
AUTHOR
[1] A. R. Arabpour and M. Tata, Estimating the parameters of a fuzzy linear regression model,
1
Iranian Journal of Fuzzy Systms, 5(2) (2008), 1-19.
2
[2] M. Are and S. M. Taheri, Least-squares regression based on Atanassov's intuitionistic fuzzy
3
inputs-outputs and Atanassov's intuitionistic fuzzy parameters, IEEE Trans. on Fuzzy Syst.,
4
23 (2015), 1142-1154.
5
[3] A. Bargiela, W. Pedrycz and T. Nakashima, Multiple regression with fuzzy data, Fuzzy Sets
6
Syst., 158 (2007), 2169-2188.
7
[4] A. Bisserier, R. Boukezzoula and S. Galichet, A revisited approach to linear fuzzy regression
8
using trapezoidal fuzzy intervals, Inf. Sci., 180 (2010), 3653-3673.
9
[5] J. Chachi and M. Roozbeh, A fuzzy robust regression approach applied to bed-
10
load transport data, Communications in Statistics-Simulation and Computation, DOI:
11
10.1080/03610918.2015.1010002, 2015.
12
[6] J. Chachi and S. M. Taheri, A least-absolutes approach to multiple fuzzy regression, in: Proc.
13
58th ISI Congress, Dublin, Ireland, CPS077-01, 2011.
14
[7] J. Chachi and S. M. Taheri, A least-absolutes regression model for imprecise response based
15
on the generalized Hausdor-metric, J. Uncertain Syst., 7 (2013), 265-276.
16
[8] J. Chachi, S. M. Taheri and N. R. Arghami, A hybrid fuzzy regression model and its appli-
17
cation in hydrology engineering, Applied Soft Comput., 25 (2014), 149{158.
18
[9] J. Chachi, S. M. Taheri and H. Rezaei Pazhand, Suspended load estimation using L1-Fuzzy
19
regression, L2-Fuzzy regression and MARS-Fuzzy regression models, Hydrological Sciences
20
J., 61(8) (2016), 1489-1502.
21
[10] J. Chachi, S. M. Taheri and R. H. Rezaei Pazhand, An interval-based approach to fuzzy
22
regression for fuzzy input-output data, in: Proc. IEEE Int. Conf. Fuzzy Syst., Taipei, Taiwan,
23
(2011), 2859-2863.
24
[11] S. P. Chen and J. F. Dang, A variable spread fuzzy linear regression model with higher
25
explanatory power and forecasting accuracy, Inf. Sci., 178 (2008), 3973-3988.
26
[12] R. Coppi, P. D'Urso, P. Giordani and A. Santoro, Least squares estimation of a linear re-
27
gression model with LR fuzzy response, Comp. Stat. Data Anal., 51 (2006), 267-286.
28
[13] P. D'Urso, Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data,
29
Comp. Stat. Data Anal., 42 (2003), 47-72.
30
[14] P. D'Urso and Gastaldi T., An orderwise polynomial regression procedure for fuzzy data,
31
Fuzzy Set Syst., 130 (2002), 1-19.
32
[15] P. D'Urso, R. Massari and A. Santoro, A class of fuzzy clusterwise regression models, Inf.
33
Sci., 180 (2010), 4737-4762.
34
[16] P. D'Urso, R. Massari and A. Santoro, Robust fuzzy regression analysis, Inf. Sci., 181 (2011),
35
4154-4174.
36
[17] P. D'Urso and A. Santoro, Fuzzy clusterwise regression analysis with symmetrical fuzzy output
37
variable, Comp. Stat. Data Anal., 51 (2006), 287-313.
38
[18] M. B. Ferraro, R. Coppi, G. Gonzalez Rodrguez and A. Colubi, A linear regression model
39
for imprecise response, Int. J. Approx. Reason., 51 (2010), 759-770.
40
[19] H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, Fuzzy linear regression model with crisp
41
coecients: A programming approach, Iranian J. Fuzzy Syst., 7 (2010), 19-39.
42
[20] H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, A goal programming approach to fuzzy
43
linear regression with fuzzy input-output data, Soft Comput., 15 (2011), 1569-1580.
44
[21] Y. C. Hu, Functional-link nets with genetic-algorithm-based learning for robust nonlinear
45
interval regression analysis, Neurocomputin, 72 (2009), 1808-1816.
46
[22] C. Kao and C. L. Chyu, A fuzzy linear regression model with better explanatory power, Fuzzy
47
Sets Syst., 126 (2002), 401-409.
48
[23] C. Kao and C. L. Chyu, Least-squares estimates in fuzzy regression analysis, European J.
49
Oper. Res., 148 (2003), 426-435.
50
[24] M. Kelkinnama and S. M. Taheri, Fuzzy least-absolutes regression using shape preserving
51
operations, Inf. Sci., 214 (2012), 105-120.
52
[25] B. Kim and R. R. Bishu, Evaluation of fuzzy linear regression models by comparison mem-
53
bership function, Fuzzy Sets Syst., 100 (1998), 343-352.
54
[26] K. S. Kula and A. Apaydin, Fuzzy robust regression analysis based on the ranking of fuzzy
55
sets, Int. J. Uncertain., Fuzziness Knowledge-Based Syst., 16 (2008), 663-681.
56
[27] J. Lu and R. Wang, An enhanced fuzzy linear regression model with more
57
exible spreads,
58
Fuzzy Sets Syst., 160 (2009), 2505-2523.
59
[28] M. H. Mashinchi, M. A. Orgun, M. Mashinchi and W. Pedrycz, A tabu-harmony search-based
60
approach to fuzzy linear regression, IEEE Trans. Fuzzy Syst., 19 (2011), 432-448.
61
[29] MATLAB, The Language of Technical Computing, The MathWorks Inc., MA, 2009.
62
[30] M. Modarres, E. Nasrabadi and M. M. Nasrabadi, Fuzzy linear regression analysis from the
63
point of view risk, Int. J. Uncertain., Fuzziness Knowledge-Based Syst., 12 (2004), 635-649.
64
[31] M. Modarres, E. Nasrabadi and M. M. Nasrabadi, Fuzzy linear regression with least squares
65
errors, Appl. Math. Comput., 163 (2005), 977-989.
66
[32] R. E. Moore, R. B. Kearfott and M. J. Cloud, Introduction to Interval Analysis, Society for
67
Industrial and Applied Mathematics, Philadelphia, PA, 2009.
68
[33] M. Namdari, J. H. Yoon, A. Abadi, S. M. Taheri and S. H. Choi, Fuzzy logistic regression
69
with least absolute deviations estimators, Soft Comput., 19 (2015), 909-917.
70
[34] E. Nasrabadi and S. M. Hashemi, Robust fuzzy regression analysis using neural networks,
71
Int. J. Uncertain., Fuzziness Knowledge-Based Syst., 16 (2008), 579-598.
72
[35] E. Nasrabadi, S. M. Hashemi and M. Ghatee, An LP-based approach to outliers detection
73
in fuzzy regression analysis, Int. J. Uncertain., Fuzziness Knowledge-Based Syst., 15 (2007),
74
[36] M. M. Nasrabadi and E. Nasrabadi, A mathematical-programming approach to fuzzy linear
75
regression analysis, Appl. Math. Comput., 155 (2004), 873-881.
76
[37] M. M. Nasrabadi, E. Nasrabadi and A. R. Nasrabadi, Fuzzy linear regression analysis: a
77
multi-objective programming approach, Appl. Math. Comput., 163 (2005), 245-251.
78
[38] S. Pourahmad, S. M. T. Ayatollahi and S. M. Taheri, Fuzzy logistic regression: A new
79
possibilistic model and its application in clinical vague status, Iranian J. Fuzzy Syst., 8
80
(2011), 1-17.
81
[39] S. Pourahmad, S. M. T. Ayatollahi, S. M. Taheri and Z. Habib Agahi, Fuzzy logistic regression
82
based on the least squares approach with application in clinical studies, Comput. Math. Appl.,
83
62 (2011), 3353-3365.
84
[40] M. R. Rabiei, N. R. Arghami, S. M. Taheri and B. Sadeghpour Gildeh, Least-squares approach
85
to regression modeling in full interval-valued fuzzy environment, Soft Comput., 18 (2014),
86
2043-2059.
87
[41] M. Sakawa and H. Yano, Multiobjective fuzzy linear regression analysis for fuzzy input-output
88
data, Fuzzy Sets Syst., 157 (1992), 173-181.
89
[42] H. Shakouri and R. Nadimi, A novel fuzzy linear regression model based on a non-equality
90
possibility index and optimum uncertainty, Appl. Soft Comput., 9 (2009), 590-598.
91
[43] S. M. Taheri and M. Kelkinnama, Fuzzy linear regression based on least absolute deviations,
92
Irannian Journal of Fuzzy Systems, 9(1) (2012), 121-140.
93
[44] H. Tanaka, I. Hayashi and J. Watada, Possibilistic linear regression analysis for fuzzy data,
94
European J. Oper. Res., 40 (1989), 389-396.
95
[45] H. Tanaka, S. Vejima and K. Asai, Linear regression analysis with fuzzy model, IEEE Trans.
96
Syst., Man, Cybernetics, 12 (1982), 903-907.
97
[46] H. J. Zimmermann, Fuzzy set theory and its applications, 4th ed., Kluwer Niho, Boston,
98
ORIGINAL_ARTICLE
On impulsive fuzzy functional differential equations
In this paper, we prove the existence and uniqueness of solution to the impulsive fuzzy functional differential equations under generalized Hukuhara differentiability via the principle of contraction mappings. Some examples are provided to illustrate the result.
http://ijfs.usb.ac.ir/article_2597_14b4ee49034a4c88aca9d65fbe0dcb9b.pdf
2016-08-30T11:23:20
2018-08-18T11:23:20
79
94
10.22111/ijfs.2016.2597
Impulsive fuzzy functional differential equations
impulsive functional differential equations
impulsive differential equations
Ho
Vu
hovumath@gmail.com
true
1
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
AUTHOR
Ngo
VanHoa
true
2
Division of Computational Mathematics and Engineering, Institute
for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Division of Computational Mathematics and Engineering, Institute
for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Division of Computational Mathematics and Engineering, Institute
for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
LEAD_AUTHOR
[1] T. Allahviranloo, S. Abbasbandy, S. Salahshour and A. Hakimzadeh, A new method for
1
solving fuzzy linear dierential equations, Computing, 92 (2010), 181{197.
2
[2] T. Allahviranloo, S. Salahshour and S. Abbasbandy, Explicit solutions of fractional dieren-
3
tial equations with uncertainty, Soft Computing, 16 (2011), 297{302.
4
[3] T. Allahviranloo, S. Abbasbandy, O. Sedaghgatfar and P. Darabi, A new method for solving
5
fuzzy integro-dierential equation under generalized dierentiability, Neural Computing and
6
Applications, 21 (2011), 191{196.
7
[4] L. C. Barros, R. C. Bassanezi and P. A. Tonelli, Fuzzy modelling in population dynamics,
8
Ecological Modelling, 128 (2000), 27{33.
9
[5] M. Benchohra, J. Henderson and S. Ntouyas, Impulsive dierential equations and inclusions,
10
Hindawi Publishing Corporation, USA, 2006.
11
[6] M. Benchohra, J. J. Nieto and A. Ouahab, Fuzzy solutions for impulsive dierential equations,
12
Communications in Applied Analysis, 11 (2007), 379{394.
13
[7] J. J. Buckley and T. Feuring, Fuzzy dierential equations, Fuzzy Sets and Systems, 110
14
(2000), 43 { 54.
15
[8] V. J. Devi and A. S. Vatsala, Method of vector lyapunov functions for impulsive fuzzy systems,
16
Dynamic Systems and Applications, 13 (2004), 521{531.
17
[9] L. S. Dong, H. Vu and N. V. Hoa, The formulas of the solution for linear-order random fuzzy
18
dierential equations, Journal of Intelligent & Fuzzy Systems, 28 (2015), 795{807.
19
[10] M. Guo, X. Xue and R. Li, Impulsive functional dierential inclusions and fuzzy population
20
models, Fuzzy Sets and Systems, 138 (2003), 601{615.
21
[11] N. V. Hoa, Fuzzy fractional functional dierential equations under Caputo gH-
22
dierentiability, Communications in Nonlinear Science and Numerical Simulation, 22 (2015),
23
1134-1157.
24
[12] N. V. Hoa, Fuzzy fractional functional integral and dierential equations, Fuzzy Sets and
25
Systems, 280 (2015), 58-90.
26
[13] N. V. Hoa and N. D. Phu, Fuzzy functional integro-dierential equations under generalized
27
H-dierentiability, Journal of Intelligent & Fuzzy Systems, 26 (2014), 2073{2085.
28
[14] N. V. Hoa, N. D. Phu, T. T. Tung and L. T. Quang, Interval-valued functional integro-
29
dierential equations, Advance in Dierence Equations, (2014), 2014:177.
30
[15] N. V. Hoa, P. V. Tri, T. T. Dao and I. Zelinka, Some global existence results and stability
31
theorem for fuzzy functional dierential equations, Journal of Intelligent & Fuzzy Systems,
32
28 (2015), 393{409.
33
[16] O. Kaleva, Fuzzy dierential equations, Fuzzy Sets and Systems, 24 (1987), 301{317.
34
[17] V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of impulsive dierential
35
equations, World Scientic, 1989.
36
[18] V. Lakshmikantham, T. Gnana Bhaskar and Devi J. Vasundhara, Theory of set dierential
37
equations in a metric space, Cambridge Scientic Publishing, UK, 2006.
38
[19] V. Lakshmikantham and F. A. McRae, Basic results for fuzzy impulsive dierential equations,
39
Mathematical Inequalities & Applications, 4 (2001), 239{246.
40
[20] V. Lupulescu, On a class of fuzzy functional dierential equations, Fuzzy Sets and Systems,
41
160 (2009), 1547{1562.
42
[21] R. N. Mohapatra and V. Lakshmikantham, Theory of fuzzy dierential equations and inclu-
43
sions, CRC Press, Singapore, 2003.
44
[22] J. J. Nieto, A. Khastan and K. Ivaz, Numerical solution of fuzzy dierential equations under
45
generalized dierentiability, Nonlinear Analysis: Hybrid Systems, 3 (2009), 700{707.
46
[23] J. J. Nieto and R. Rodrguez-Lopez, Periodic boundary value problem for non-Lipschitzian
47
impulsive functional dierential equations, Journal of Mathematical Analysis and Applica-
48
tions, 318 (2006), 593-610.
49
[24] R. Rodrguez-Lopez, Periodic boundary value problems for impulsive fuzzy dierential equa-
50
tions, Fuzzy Sets and Systems, 159 (2008), 1384{1409.
51
[25] A. M. Samoilenko and N. A. Perestyuk, Impulsive dierential equations, World Scientic,
52
Singapore, 1995.
53
[26] P. V. Tri, N. V. Hoa and N. D. Phu, Sheaf fuzzy problems for functional dierential equations,
54
Advance in Dierence Equation, 2014 2014:156
55
[27] A. S. Vatsala, Impulsive hybrid fuzzy dierential equations, Facta Univ. Ser Mech, Automatic
56
Control Robot, 3 (2003), 851{859.
57
[28] H. Vu, L. S. Dong and N. V. Hoa, Random fuzzy functional integro-dierential equations
58
under generalized Hukuhara dierentiability , Journal of Intelligent & Fuzzy Systems, 27
59
(2014), 1491-1506.
60
[29] H. Vu and L. S. Dong, Random set-valued functional dierential equations with the second
61
type hukuhara derivative, Dierential Equations & Applications, 5 (2013), 501{518.
62
[30] H. Vu and L. S. Dong, Initial value problem for second-order random fuzzy dierential equa-
63
tions, Advances in Dierence Equations, 2015 2015:373
64
ORIGINAL_ARTICLE
Stratified $(L,M)$-fuzzy Q-convergence spaces
This paper presents the concepts of $(L,M)$-fuzzy Q-convergence spaces and stratified $(L,M)$-fuzzy Q-convergence spaces. It is shown that the category of stratified $(L,M)$-fuzzy Q-convergence spaces is a bireflective subcategory of the category of $(L,M)$-fuzzy Q-convergence spaces, and the former is a Cartesian-closed topological category. Also, it is proved that the category of stratified $(L,M)$-fuzzy topological spaces can be embedded in the category of stratified $(L,M)$-fuzzy Q-convergence spaces as a reflective subcategory, and the former is isomorphic to the category of topological stratified $(L,M)$-fuzzy Q-convergence spaces.
http://ijfs.usb.ac.ir/article_2598_1c939cd4dac89ee78894504a9620668f.pdf
2016-08-30T11:23:20
2018-08-18T11:23:20
95
111
10.22111/ijfs.2016.2598
(Stratified) $(L
M)$-fuzzy topology
M)$-fuzzy Q-convergence structure
Topological category
Cartesian-closedness
Bin
Pang
pangbin1205@163.com
true
1
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
AUTHOR
Yi
Zhao
zhaoyisz420@sohu.com
true
2
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
LEAD_AUTHOR
[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New
1
York, 1990.
2
[2] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182{190.
3
[3] J. M. Fang, Categories isomorphic to L-FTOP, Fuzzy Sets Syst., 157 (2006), 820{831.
4
[4] J. M. Fang, Stratied L-ordered convergence structures, Fuzzy Sets Syst., 161 (2010), 2130{
5
[5] J. M. Fang, Relationships between L-ordered convergence structures and strong L-topologies,
6
Fuzzy Sets Syst., 161 (2010), 2923{2944.
7
[6] M. Guloglu and D. Coker, Convergence in I-fuzzy topological spaces, Fuzzy Sets Syst., 151
8
(2005), 615{623.
9
[7] U. Hohle and A. P. Sostak, Axiomatic foudations of xed-basis fuzzy topology, In: U. Hohle,
10
S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory,
11
Handbook Series, vol.3, Kluwer Academic Publishers, Boston, Dordrecht, London, (1999),
12
[8] G. Jager, A category of L-fuzzy convergence spaces, Quaest. Math., 24 (2001), 501{517.
13
[9] G. Jager, Subcategories of lattice-valued convergence spaces, Fuzzy Sets Syst., 156 (2005),
14
[10] G. Jager, Pretopological and topological lattice-valued convergence spaces, Fuzzy Sets Syst.,
15
158 (2007), 424{435.
16
[11] G. Jager, Lattice-valued convergence spaces and regularity, Fuzzy Sets Syst., 159 (2008),
17
2488{2502.
18
[12] G. Jager, Fischer's diagonal condition for lattice-valued convergence spaces, Quaest. Math.,
19
31 (2008), 11{25.
20
[13] G. Jager, Stratied LMN-convergence tower spaces, Fuzzy Sets Syst., 282 (2016), 62{73.
21
[14] T. Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, 1985.
22
[15] L. Q. Li and Q. Jin, On adjunctions between Lim, SL-Top, and SL-Lim, Fuzzy Sets Syst.,
23
182 (2011), 66{78.
24
[16] L. Q. Li and Q. Jin, On stratied L-convergence spaces: Pretopological axioms and diagonal
25
axioms, Fuzzy Sets Syst., 204 (2012), 40{52.
26
[17] R. Lowen, Convergence in fuzzy topological spaces, Gen. Topl. Appl., 10 (1979),147{160.
27
[18] K. C. Min, Fuzzy limit spaces, Fuzzy Sets Syst., 32 (1989), 343{357.
28
[19] B. Pang and J.M. Fang, L-fuzzy Q-convergence structures, Fuzzy Sets Syst., 182 (2011),
29
[20] B. Pang, Futher study on L-fuzzy Q-convergence structures, Iranian Journal of Fuzzy Systems,
30
10(5) (2013), 147{164.
31
[21] B. Pang, On (L;M)-fuzzy convergence spaces, Fuzzy Sets Syst., 238 (2014), 46{70.
32
[22] B. Pang and F. G. Shi, Degrees of compactness of (L;M)-fuzzy convergence spaces and its
33
applications, Fuzzy Sets Syst., 251 (2014), 1{22.
34
[23] B. Pang, Enriched (L;M)-fuzzy convergence spaces, J. Intell. Fuzzy Syst., 27 (2014), 93{103.
35
[24] G. Preuss, Foundations of topology{an approach to convenient topology, Kluwer Academic
36
Publisher, Dordrecht, Boston, London, 2002.
37
[25] A. P. Sostak, On a fuzzy topological structure, Suppl. Rend. Circ. Mat. Palermo Ser. II, 11
38
(1985), 89{103.
39
[26] L. S. Xu, Characterizations of fuzzifying topologies by some limit structures, Fuzzy Sets Syst.,
40
123 (2001), 169{176.
41
[27] W. Yao, On many-valued stratied L-fuzzy convergence spaces, Fuzzy Sets Syst., 159 (2008),
42
2503{2519.
43
[28] W. Yao, On L-fuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6(1) (2009),
44
[29] W. Yao, Moore-Smith convergence in (L;M)-fuzzy topology, Fuzzy Sets Syst., 190 (2012),
45
ORIGINAL_ARTICLE
Fuzzy Topology Generated by Fuzzy Norm
In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuzzy topologies.
http://ijfs.usb.ac.ir/article_2599_80e905324f5d0d9df4942f664b21aabb.pdf
2016-08-30T11:23:20
2018-08-18T11:23:20
113
123
10.22111/ijfs.2016.2599
Fuzzy norm
Fuzzy topology
locally convex topological vector space
M.
Saheli
true
1
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
LEAD_AUTHOR
[1] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math.,
1
11(3) (2003), 687-705.
2
[2] T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151
3
(2005), 513-547.
4
[3] S. C. Cheng and J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces,
5
Bull. Cal. Math. Soc., 86 (1994), 429-436.
6
[4] N. F. Das and P. Das, Fuzzy topology generated by fuzzy norm, Fuzzy Sets and Systems, 107
7
(1999), 349-354.
8
[5] J. X. Fang, On I-topology generated by fuzzy norm, Fuzzy Sets and Systems, 157 (2006),
9
2739-2750.
10
[6] C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48 (1992),
11
[7] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
12
[8] I. Karmosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11
13
(1975), 326-334.
14
[9] A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), 143-
15
[10] M. Saheli, On fuzzy topology and fuzzy norm, Annals of Fuzzy Mathematics and Informatics,
16
10(4) (2015), 639647.
17
[11] J. Xiao and X. Zhu, Fuzzy normed space of operators and its completeness, Fuzzy Sets and
18
Systems, 133 (2003) 389-399.
19
[12] G. H. Xu and J. X. Fang, A new I-vector topology generated by a fuzzy norm, Fuzzy Sets and
20
Systems, 158 (2007), 2375-2385.
21
ORIGINAL_ARTICLE
Extended Fuzzy $BCK$-subalgebras
This paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study considers a type of fuzzy hyper $BCK$-ideals in this hyperstructure and describes the relationship between hyper $BCK$-ideals and fuzzy hyper $BCK$-ideals. In fact, it tries to introduce a strongly regular relation on hyper $BCK$-algebras. Moreover, by using the fuzzy hyper $BCK$-ideals, it defines a congruence relation on (weak commutative) hyper $BCK$-algebras that under some conditions is strongly regular and the quotient of any hyper $BCK$-algebra via this relation is a $($hyper $BCK$-algebra$)$ $BCK$-algebra.
http://ijfs.usb.ac.ir/article_2600_ec5ab1057962c6beff342819cbfc8af5.pdf
2016-08-30T11:23:20
2018-08-18T11:23:20
125
144
10.22111/ijfs.2016.2600
Extended fuzzy $BCK$-subalgebra
(Strongly) Fuzzy hyper $BCK$-ideal
Fundamental relation $beta^*$
Jianming
Zhan
zhanjianming@ hotmail.com
true
1
Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China
Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China
Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China
AUTHOR
Mohammad
Hamidi
m.hamidi20@gmail.com
true
2
Department of Mathematics, Payame Noor University, Tehran,
Iran
Department of Mathematics, Payame Noor University, Tehran,
Iran
Department of Mathematics, Payame Noor University, Tehran,
Iran
AUTHOR
Arsham
Borumand Saeid
arsham@iauk.ac.ir
true
3
Department of Pure Mathematics, Faculty of Mathematics
and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Pure Mathematics, Faculty of Mathematics
and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Pure Mathematics, Faculty of Mathematics
and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
LEAD_AUTHOR
[1] M. Bakhshi, M. M. Zahdi and R. A. Borzooei, Fuzzy (positive, weak) implicative hyper BCK-
1
ideals, Iranian Journal of Fuzzy Systems, 1(2) (2004), 63-79.
2
[2] R. A. Borzooei, R. Ameri and M. Hamidi, Fundamental relation on hyper BCK-algebras, An.
3
Univ. oradea, fasc. Mat., 21(1) (2014), 123{136.
4
[3] G. R. Biyogmam, O. A. Heubo-Kwegna and J. B. Nganou, Super implicative hyper BCK-
5
algebras, Int. J. Pure Appl. Math., 76(2) (2012), 267-275.
6
[4] J. Chvalina, S. Hoskova-Mayerova and A. D. Nezhad, General actions of hyperstructures and
7
some applications, An. St. Univ. Ovidius Constanta, 21(1) (2013), 59{82.
8
[5] P. Corsini, Prolegomena of hypergroup theory, Second Edition, Aviani Editor, 1993.
9
[6] P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Klwer Academic Pub-
10
lishers, 2002.
11
[7] J. Dongho, Category of fuzzy hyper BCK-algebras, arXiv:1101.2471.
12
[8] P. F. He and X. L. Xin, Fuzzy hyperlattices, Comput. Math. Appl., 62 (2011), 4682{4690.
13
[9] S. Hoskova, Topological hypergroupoids, Comput. Math. Appl., 64 (2012), 2845{2849.
14
[10] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV, Proc. Japan Acad.
15
Ser. A Math. Sci., 42 (1966), 19{22.
16
[11] Y. B. Jun, M. M. Zahedi, X. L. Xin and R. A. Borzooei, On hyper BCK-algebras, Ital. J.
17
Pure Appl. Math., 10 (2000), 127{136.
18
[12] Y. B. Jun and X. L. Xin, Fuzzy hyper BCK-ideals of hyper BCK-algebras, Sci. Math. Jpn.,
19
53(2) (2001), 353{360.
20
[13] Y. B. Jun, M. S. Kang and S. Z. Song, Several types of bipolar fuzzy hyper BCK-ideals in
21
hyper BCK-algebras, Honam Math. J., 34(2) (2012), 145{159.
22
[14] V. Leoreanu-Fotea, Fuzzy hypermodules, Comput. Math. Appl., 57 (2009), 466{475.
23
[15] F. Marty, Sur une Generalization de la notion de groupe, 8th Congres Math. Scandinaves,
24
Stockholm., (1934), 45{49.
25
[16] J. Meng and Y. B. Jun, BCK-algebra, Kyung Moonsa, Seoul, 1994.
26
[17] H. T. Nguyen and E. A. Walker, A First Course in Fuzzy Logic, (Third Edition), Chapman
27
and Hall/CRC. Boca Raton, 2005.
28
[18] M. K. Sen, R. Ameri and G. Chowdhury, Fuzzy hypersemigroups, Soft Comput., 12 (2008),
29
[19] X. Xie, Fuzzy ideals extensions in semigroups, Kyungpook Math. J., 42(1) (2002), 39{49.
30
[20] X. L. Xin and P. Wang, States and measures on hyper BCK-algebras, J. Appl. Math., (2014),
31
[21] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338{353.
32
[22] J. Zhan, Fuzzy regular relations on hyperquasigroups, J. Math. Res. Exposition, Nov., 30(6)
33
(2010), 1083{1090.
34
ORIGINAL_ARTICLE
Persian Translation of Abstracts
http://ijfs.usb.ac.ir/article_2623_142703c45c95558598fdf7e2eb9c6fb3.pdf
2016-08-01T11:23:20
2018-08-18T11:23:20
145
158
10.22111/ijfs.2016.2623