ORIGINAL_ARTICLE
Cover vol. 12, no.4, August 2015-
http://ijfs.usb.ac.ir/article_2644_0b763cc2fad57051d99df4e9a72bcc60.pdf
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10.22111/ijfs.2016.2644
ORIGINAL_ARTICLE
Trapezoidal intuitionistic fuzzy prioritized aggregation operators and application to multi-attribute decision making
In some multi-attribute decision making (MADM) problems, various relationships among the decision attributes should be considered. This paper investigates the prioritization relationship of attributes in MADM with trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFNs are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. Firstly, the weighted possibility means of membership and non-membership functions for TrIFNs are defined. Hereby, a new lexicographic ranking method for TrIFNs is presented. Then, a series of trapezoidal intuitionistic fuzzy prioritized aggregation operators are developed, including the trapezoidal intuitionistic fuzzy prioritized score (TrIFPS) operator, trapezoidal intuitionistic fuzzy prioritized weighted average (TrIFPWA) operator, trapezoidal intuitionistic fuzzy prioritized “and” (TrIFP-AND) operator and trapezoidal intuitionistic fuzzy prioritized “or” (TrIFP-OR) operator. Some desirable properties of these operators are also discussed. By utilizing the TrIFPWA operator, the attribute values of alternatives are integrated into the overall ones, which are used to rank the alternatives. Thus, a new method is proposed for solving the prioritized MADM problems with TrIFNs. Finally, the applicability of the proposed method is illustrated with a supply chain collaboration example.
http://ijfs.usb.ac.ir/article_2083_b0bfd4eb1264f73143bcf1b0715c6d2f.pdf
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10.22111/ijfs.2015.2083
Multi-attribute decision making
Trapezoidal intuitionistic fuzzy number
Prioritized aggregation operators
Weighted possibility mean
Shuping
Wan
shupingwan@163.com
true
1
Jiangxi University of Finance and Economics
Jiangxi University of Finance and Economics
Jiangxi University of Finance and Economics
LEAD_AUTHOR
Jiuying
Dong
jiuyingdong@126.com
true
2
Jiangxi University of Finance and Economics
Jiangxi University of Finance and Economics
Jiangxi University of Finance and Economics
AUTHOR
Deyan
Yang
270632966@qq.com
true
3
Qingdao Technological University
Qingdao Technological University
Qingdao Technological University
AUTHOR
[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.
1
[2] K. Atanassov and G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and
2
Systems, 31(3) (1989), 343-349.
3
[3] C. Carlsson and R. Fullr, On possibilistic mean value and deviation of fuzzy numbers,
4
Fuzzy Sets and Systems, 122 (2001), 315-326.
5
[4] R. Fullr and P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers,
6
Fuzzy Sets and Systems, 136 (2003), 363-374.
7
[5] D. F. Li, A note on using intuitionistic fuzzy sets for fault-tree analysis on printed circuit
8
board assembly, Microelectronics Reliability, 48(10) (2008), 17-41.
9
[6] D. F. Li, A ratio ranking method of triangular intuitionistic fuzzy numbers and its appli-
10
cation to MADM problems, Computers and Mathematics with Applications, 60 (2010),
11
1557-1570.
12
[7] D. F. Li, J. X. Nan and M. J. Zhang, A ranking method of triangular intuitionistic fuzzy
13
numbers and application to decision making, International Journal of Computational In-
14
telligence Systems, 3(5) (2010), 522-530.
15
[8] B. Q. Li and W. He, Intuitionistic fuzzy PRI-AND and PRI-OR aggregation operators,
16
Information Fusion, 14 (2013), 450-459.
17
[9] R. Mansini, M. W. P. Savelsbergh and B. Tocchella, The supplier selection problem with
18
quantity discounts and truckload shipping, Omega, 40(4) (2012), 445-455.
19
[10] J. X. Nan, D. F. Li and M. J. Zhang, A lexicographic method for matrix games with
20
payos of triangular intuitionistic fuzzy numbers, International Journal of Computational
21
Intelligence Systems, 3(3) (2010), 280-289.
22
[11] M. H. Shu, C. H. Cheng and J. R. Chang, Using intuitionistic fuzzy sets for fault tree
23
analysis on printed circuit board assembly, Microelectronics Reliability, 46(12) (2006),
24
2139-2148.
25
[12] S. P. Wan, D. F. Li and Z. F. Rui, Possibility mean, variance and covariance of triangular
26
intuitionistic fuzzy numbers, Journal of Intelligent and Fuzzy Systems, 24(4) (2013), 847-
27
[13] S. P. Wan and D. F. Li, Possibility mean and variance based method for multi-attribute
28
decision making with triangular intuitionistic fuzzy numbers, Journal of Intelligent and
29
Fuzzy Systems, 24 (2013), 743-754.
30
[14] S. P. Wan, Q. Y. Wang and J. Y. Dong, The extended VIKOR method for multi-attribute
31
group decision making with triangular intuitionistic fuzzy numbers, Knowledge-Based Sys-
32
tems, 52 (2013), 65-77.
33
[15] S. P. Wan and J. Y. Dong, Possibility method for triangular intuitionistic fuzzy multi-
34
attribute group decision making with incomplete weight information, International Journal
35
of Computational Intelligence Systems, 7(1) (2014), 65-79.
36
[16] S. P. Wan and D. F. Li. Fuzzy LINMAP approach to heterogeneous MADM considering
37
comparisons of alternatives with hesitation degrees, Omega, 41(6)(2013), 925-940.
38
[17] S. P. Wan and D. F. Li. Atanassovs intuitionistic fuzzy programming method for hetero-
39
geneous multiattribute group decision making with Atanassovs intuitionistic fuzzy truth
40
degrees, IEEE Transaction on Fuzzy Systems, 22(2)(2014), 300-312.
41
[18] S. P. Wan and J. Y. Dong, Interval-valued intuitionistic fuzzy mathematical programming
42
method for hybrid multi-criteria group decision making with interval-valued intuitionistic
43
fuzzy truth degree, Information Fusion, 26 (2015), 49-65.
44
[19] S. P. Wan and J. Y. Dong, A possibility degree method for interval-valued intuitionistic
45
fuzzy multi-attribute group decision making, Journal of Computer and System Sciences,
46
80(1) (2014), 237-256.
47
[20] S. P. Wan and J. Y. Dong, Method of trapezoidal intuitionistic fuzzy number for multi-
48
attribute group decision, Control and Decision, 25(5) (2010), 773-776.
49
[21] S. P. Wan, Power average operators of trapezoidal intuitionistic fuzzy numbers and appli-
50
cation to multi-attribute group decision making, Applied Mathematical Modelling, 37(6)
51
(2013), 4112-4126.
52
[22] S. P. Wan and J. Y. Dong, Power geometric operators of trapezoidal intuitionistic fuzzy
53
numbers and application to multi-attribute group decision making, Applied Soft Comput-
54
ing, 29 (2015), 153-168.
55
[23] S. P.Wan, Method based on fractional programming for interval-valued intuitionistic trape-
56
zoidal fuzzy number multi-attribute decision making, Control and Decision, 27 (3) (2012),
57
[24] S. P. Wan, Multi-attribute decision making method based on interval-valued trapezoidal
58
intuitionistic fuzzy number, Control and Decision, 6 (2011), 857-866.
59
[25] J. Q. Wang, Overview on fuzzy multi-criteria decision-making approach, Control and De-
60
cision, 23(6) (2008), 601-607.
61
[26] J. Q. Wang and Z. Zhang, Aggregation operators on intuitionistic trapezoidal fuzzy num-
62
ber and its application to multi-criteria decision making problems, Journal of Systems
63
Engineering and Electronics, 20(2) (2009), 321-326.
64
[27] J. Q.Wang, R. R. Nie, H. Y. Zhang and X. H. Chen, New operators on triangular intuition-
65
istic fuzzy numbers and their applications in system fault analysis, Information Sciences,
66
251 (2013), 79-95.
67
[28] H. M.Wang, Y. J. Xu and J. M. Merig, Prioritized aggregation for non-homogeneous group
68
decision making in water resource management, Economic Computation and Economic
69
Cybernetics Studies and Research, 48(1) (2014), 247-258.
70
[29] G. W. Wei, Some arithmetic aggregation operators with trapezoidal intuitionistic fuzzy
71
numbers and their application to group decision making, Journal of Computers, 3(2010),
72
[30] G. W. Wei, Hesitant fuzzy prioritized operators and their application to multiple attribute
73
decision making, Knowledge-Based Systems, 31(7) (2012), 176-182.
74
[31] G. W. Wei and J. M. Merig, Methods for strategic decision making problems with immedi-
75
ate probabilities in intuitionistic fuzzy setting, Scientia Iranica, 19(6) (2012), 1936-1946.
76
[32] J. Wu and Q. W. Cao, Some families of geometric aggregation operators with intuitionistic
77
trapezoidal fuzzy numbers, Applied mathematical modeling, 37 (1/2) (2013), 318-327.
78
[33] J. Wu and Y. J. Liu, An approach for multiple attribute group decision making problems
79
with interval-valued intuitionistic trapezoidal fuzzy numbers, Computers and Industrial
80
Engineering, 66 (2013), 311-324.
81
[34] Y. J. Xu, T. Sun and D. F. Li, Intuitionistic fuzzy Prioritized OWA aggregation operator
82
and its application to multi-criteria decision making, Control and Decision, 26(1) (2011),
83
[35] R. R. Yager, Modeling prioritized multi-criteria decision making, IEEE Transactions on
84
Systems, Man and Cybernetics, Part B. Cybernetics, 34 (2004), 2396-2404.
85
[36] R. R. Yager, Prioritized aggregation operators, International Journal of Approximate Rea-
86
soning, 48 (2008), 263-274.
87
[37] R. R. Yager, Prioritized OWA aggregation, Fuzzy Optimization and Decision Making, 8
88
(2009), 245-262.
89
[38] H. B. Yan, V. N. Huynh, Y. Nakamori and T. Murai, On prioritized weighted aggregation
90
in multi-criteria decision making, Expert Systems with Applications, 38 (2011), 812-823.
91
[39] X. H. Yu and Z. S. Xu, Prioritized intuitionistic fuzzy aggregation operators, Information
92
Fusion, 14(1) (2013), 108-116.
93
[40] D. Yu, J. M. Merig and L. G. Zhou, Interval-valued multiplicative intuitionistic fuzzy
94
preference relations, International Journal of Fuzzy Systems, 15(4) (2013), 412-422.
95
[41] D. J. Yu, Intuitionistic fuzzy prioritized operators and their application in multi-criteria
96
group decision making, Technological and Economic Development of Economy, 19(1)
97
(2013), 1-21.
98
[42] D. J. Yu, Y. Y.Wu and T. Lu, Interval-valued intuitionistic fuzzy prioritized operators and
99
their application in group decision making, Knowledge-Based Systems, 30 (2012), 57-66.
100
[43] L. A. Zadeh, Fuzzy sets., Information and Control, 18 (1965), 338-353.
101
[44] X. Zhang, F. Jian and P. D. Liu, A grey relational projection method for multi-attribute
102
decision making based on intuitionistic trapezoidal fuzzy number, Applied Mathematical
103
Modelling, 37(5) (2013), 3467-3477.
104
ORIGINAL_ARTICLE
An Optimization Model for Multi-objective Closed-loop Supply Chain Network under uncertainty: A Hybrid Fuzzy-stochastic Programming Method
In this research, we address the application of uncertaintyprogramming to design a multi-site, multi-product, multi-period,closed-loop supply chain (CLSC) network. In order to make theresults of this article more realistic, a CLSC for a case study inthe iron and steel industry has been explored. The presentedsupply chain covers three objective functions: maximization ofprofit, minimization of new products' delivery time, collectiontime and disposal time of used products, and maximizingflexibility. To solve the proposed model, an interactive hybridsolution methodology is adopted through combining a hybridfuzzy-stochastic programming method and a fuzzy multi-objectiveapproach. Finally, the numerical experiments are given todemonstrate the significance of the proposed model and thesolution approach.
http://ijfs.usb.ac.ir/article_2084_06fa0c96a161e557d8e35fa38ff247a5.pdf
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57
10.22111/ijfs.2015.2084
Closed-loop supply chain network design
Multi-objective decision making
Fuzzy mathematical
programming
Stochastic programming
Behnam
Vahdani
b.vahdani@ut.ac.ir
true
1
Faculty of Industrial and Mechanical Engineering, Qazvin Branch,
Islamic Azad University, Qazvin, Iran
Faculty of Industrial and Mechanical Engineering, Qazvin Branch,
Islamic Azad University, Qazvin, Iran
Faculty of Industrial and Mechanical Engineering, Qazvin Branch,
Islamic Azad University, Qazvin, Iran
LEAD_AUTHOR
[1] F. Altiparmak, M. Gen, L. Lin and T. A. Paksoy,genetic algorithm approach for multi-
1
objective optimization of supply chain networks, Computers and Industrial Engineering, 51
2
(2006), 197-216.
3
[2] B. Bilgen,Application of fuzzy mathematical programming approach to the production alloca-
4
tion and distribution supply chain network problem, Expert Syst Appl, 37 (2010), 4488-4495.
5
[3] J. R. Birge and F. V. Louveaux,A multi cut algorithm for two-stage stochastic linear pro-
6
grams, European Journal of Operational Research, 34 (1988), 384-392.
7
[4] SL. Chung , HM.Wee and PC. Yang ,Optimal policy for a closed-loop sup-ply chain inventory
8
system with remanufacturing, Math Comput Model, 48 (2008), 867-881.
9
[5] F. Du and GW. Evans, A bi-objective reverse logistics network analysis for post-sale service,
10
Computers and Operations Research, 35 (2008), 26-34.
11
[6] D. Dubois and H. Prade, Possibility Theory - An Approach to the Computerized Processing
12
of Uncertainty, Plenum Press, New York, (1988), 24-54.
13
[7] M. El-Sayed, N. Aa and A. El-Kharbotly, A stochastic model for forward-reverse logistics
14
network design under risk, Comput Ind Eng, 58 (2010), 423-431.
15
[8] M. Fleischmann, P. Beullens, JM. Bloemhof ruwaard and L. Wassenhove, The impact of
16
product recovery on logistics network design, Production and Operations Management, 10
17
(1) (2001), 56-73.
18
[9] R. A.Freeze, J. Massmann, L. Smith, J. Sperling and B. James, Hydrogeological decision
19
analysis, 1, a framework. Ground Water, 28 (1990), 738-766.
20
[10] P. Guo, G. H.Huang and Y. P. Li, An inexact fuzzy-chance-constrained two-stage mixed-
21
integer linear programming approach for
22
ood diversion planning under multiple uncertain-
23
ties, Advances in Water Resources, 33 (2010), 81-91.
24
[11] G. H. Huang and D. P. Loucks, An inexact two stage stochastic programming model for water
25
resources management under uncertainty, Civil Engineering and Environmental Systems, 17
26
(2000), 95-118.
27
[12] G. H. Huang, A hybrid inexact-stochastic water management model, European Journal of
28
Operational Research, 107 (1998), 137-158.
29
[13] A. Hasani, SH. Zegordi and E. Nikbakhsh, Robust closed-loop supply chain network design
30
for perishable goods in agile manufacturing under uncertainty, Int J Prod Res, 50 (2012),
31
4649-4669.
32
[14] MA. Ilgin and SM. Gupta, Environmentally conscious manufacturing and product recovery
33
(ECMPRO): a review of the state of the art, J Environ Manage, 91 (2010), 563-591.
34
[15] M. Inuiguchi and T. Tanino, Portfolio selection under independent possibilistic information,
35
Fuzzy Sets and Systems, 115 (2000), 83-92.
36
[16] M. G. Iskander, A suggested approach for possibility and necessity dominance indices in
37
stochastic fuzzy linear programming, Applied Mathematics Letters, 18 (2005), 395-399.
38
[17] S. Kara and S. A. Onut, Stochastic optimization approach for paper recycling reverse logistics
39
network design under uncertainty, Int J Environ Sci Technol, 4 (2010), 717-730.
40
[18] D. Lee and M. A. Ong, Heuristic approach to logistics network design for end of lease com-
41
puter products recovery, Transportation Research Part E, 44 (2008), 455-474.
42
[19] DH. Lee, M. Dong and W. Bian, The design of sustainable logistics network under uncer-
43
tainty, Int J Prod Econ, 128 (2010), 159-166.
44
[20] W. Li, Y. P. Li, C. H. Li and G. H. Huang, An inexact two-stage water management model
45
for planning agricultural irrigation under uncertainty, Agricultural Water Management, 97
46
(2010), 1905-1914.
47
[21] Y. P. Li, J. Liu and G. H. Huang,A hybrid fuzzy-stochastic programming method for water
48
trading within an agricultural system, Agricultural Systems, 123 (2014), 71-83.
49
[22] Y. P. Li, G. H. Huang and S. L.Nie, Planning water resources management systems using
50
a fuzzy-boundary interval stochastic programming method, Advances in Water Resources, 33
51
(2010), 1105-1117.
52
[23] Y. P. Li, G. H. Huang, Y. F. Huang and H. D. Zhou, A multistage fuzzy-stochastic program-
53
ming model for supporting sustainable water resources allocation and management, Environ-
54
mental Modelling and Software, 7 (2009), 786-797.
55
[24] Y. J. Lai and C. L. Hwang, Possibilistic linear programming for managing interest rate risk,
56
Fuzzy Sets and Systems, 54 (1993), 135-146.
57
[25] E. Melachrinoudis, A. Messac and H. Min, Consolidating a warehouse network: a physical
58
programming approach, International Journal of Production Economics, 97 (2005), 1-17.
59
[26] G. A. Mendoza, B. Bruce Bare and Z. H. Zhou, A fuzzy multiple objective linear programming
60
approach to forest planning under uncertainty, Agricultural Systems, 41 (1993), 257-274.
61
[27] EU. Olugu and KY. Wong, An expert fuzzy rule-based system for closed-loop supply chain
62
performance assessment in the automotive industry, Expert Syst Appl, 39 (2012), 375-384.
63
[28] S. Pokharel and A. Mutha, Perspectives on reverse logistics: a review, Resources, Conserva-
64
tion and Recycling, 53(4) (2009) 175-82.
65
[29] MS. Pishvaee and SA. Torabi, A possibilistic programming approach for closed-loop supply
66
chain network design under uncertainty, Fuzzy Set Syst, 161 (2010), 2668-2683.
67
[30] MS.Pishvaee and J.Razmi, Environmental supply chain network design using multi objective
68
fuzzy mathematical programming, Appl Math Model, 36 (2012), 3433-3446.
69
[31] Q. Qiang, K. Ke and T. Anderson , J.Dong,The closed loop supply chain network with com-
70
petition, distribution channel investment, and uncertainties, Omega, 41 (2013), 186-194.
71
[32] S. Rubio, A. Chamorro and FJ. Miranda, Characteristics of the research on reverse logistics,
72
International Journal of Production Research, 46(4) (2008), 1099-1120.
73
[33] D. Stindt and R. Sahamie, Review of research on closed loop supply chain management in
74
the process industry, Flexible Services and Manufacturing Journal, 43(2) (2014), 23-45.
75
[34] SK. Srivastava, Green supply chain management: a state of the art literature review, Inter-
76
national Journal of Management Reviews, 9(1) (2007), 53-80.
77
[35] MIG. Salema, AP.Barbosa-Povoa and AQ.Novais, An optimization model for the design of
78
a capacitated multi-product reverse logistics network with uncertainty, Eur J Oper Res, 179
79
(2007), 1063-1077.
80
[36] K. Subulan, AS. Tasan and A.Baykasoglu, Fuzzy mixed integer programming model for
81
medium term planning in a closed-loop supply chain with remanufacturing option, J Intel
82
Fuzzy Syst, 23 (2012), 345-368.
83
[37] S. A. Torabi and E. Hassini, An interactive possibilistic programming approach for multiple
84
objective supply chain master planning, Fuzzy Sets and Systems, 159 (2008), 193-214.
85
[38] S. Verstrepen, F. Cruijssen, M. De Brito and W.Dullaert, An exploratory analysis of reverse
86
logistics in Flanders., European Journal of Transport and Infrastructure Research, 7(4)
87
(2007), 301-316.
88
[39] B. Vahdani, J. Razmi and R. Tavakkoli Moghaddam, Fuzzy possibilistic modeling for closed
89
loop recycling collection networks, Environ Model Assess, 17 (2012), 623-637.
90
[40] B. Vahdani, R. Tavakkoli Moghaddam, F. Jolai and A. Baboli, Reliable design of a closed loop
91
supply chain network under uncertainty: an interval fuzzy possibilistic chance constrained
92
model, Eng Optim, 45 (2013), 745-765.
93
[41] B. Vahdani, R. Tavakkoli Moghaddam, M. Modarres and A. Baboli, Reliable design of a
94
forward/reverse logistics network under uncertainty: a robust-M M c queuing model, Transp
95
Res Part E, 48 (2012), 1152-1168.
96
[42] P. Wells and M. Seitz, Business models and closed loop supply chains: a typology, Supply
97
Chain Management: An International Journal, 10(4) (2005), 249-251.
98
[43] HF. Wang and HW. Hsu, Resolution of an uncertain closed-loop logistics model: an applica-
99
tion to fuzzy linear programs with risk analysis, J Environ Manage, 91(21) (2010), 48-62.
100
[44] L. A. Zadeh, The concept of a linguistic variables and its application to approximate
101
reasoning-1, Information Sciences, 8 (1975), 199-249.
102
[45] H. J. Zimmermann, Fuzzy Set Theory and its Applications, third ed, Kluwer Academic Pub-
103
lishers, (1996), 32-47.
104
[46] H. J. Zimmermann, Fuzzy programming and linear programming with several objective func-
105
tions, Fuzzy Sets and Systems, 1 (1978), 45-55.
106
ORIGINAL_ARTICLE
Developing new methods to monitor phase II fuzzy linear profiles
In some quality control applications, the quality of a process or a product is described by the relationship between a response variable and one or more explanatory variables, called a profile. Moreover, in most practical applications, the qualitative characteristic of a product/service is vague, uncertain and linguistic and cannot be precisely stated. The purpose of this paper is to propose a method for monitoring simple linear profiles with a fuzzy and ambiguous response. To this end, fuzzy EWMA and fuzzy Hotelling's $T^2$ statistics are developed using the extension principle. To monitor phase II of fuzzy linear profiles, two methods using fuzzy hypothesis testing, are presented based on these statistics. A case study in ceramic and tile industry, is provided. A simulation study to evaluate the performance of the proposed methods in terms of average run length (ARL) criterion showed that the proposed methods are very efficient in detecting various sized shifts in process profiles.
http://ijfs.usb.ac.ir/article_2085_a27ba11215a248cd57d2125dd6d95839.pdf
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77
10.22111/ijfs.2015.2085
Fuzzy qualitative profiles
Fuzzy EWMA statistic
Fuzzy Hotelling's $T^2$
statistic
Fuzzy hypothesis testing
ARL criterion
G.
Moghadam
g.moghadam@in.iut.ac.ir
true
1
Department of Industrial Engineering, Isfahan University Of Technology, Isfahan, Iran
Department of Industrial Engineering, Isfahan University Of Technology, Isfahan, Iran
Department of Industrial Engineering, Isfahan University Of Technology, Isfahan, Iran
LEAD_AUTHOR
G. A.
Raissi Ardali
raissi@cc.iut.ac.ir
true
2
Department of Industrial Engineering, Isfahan University Of
Technology, Isfahan, Iran
Department of Industrial Engineering, Isfahan University Of
Technology, Isfahan, Iran
Department of Industrial Engineering, Isfahan University Of
Technology, Isfahan, Iran
AUTHOR
V.
Amirzadeh
v_amirzadeh@uk.ac.ir
true
3
Department of Statistics, Shahid Bahonar University Of Kerman, Kerman, Iran
Department of Statistics, Shahid Bahonar University Of Kerman, Kerman, Iran
Department of Statistics, Shahid Bahonar University Of Kerman, Kerman, Iran
AUTHOR
[1] C. Croarkin and R.Varner, Measurement Assurance for Dimensional Measurements on
1
Integrated-Circuit Photo masks, NBS Technical Note 1164, U.S. Department of Commerce,
2
Washington D.C., USA, 1982.
3
[2] M. H. FazelZarandi and A. Alaeddini, Using Adaptive Nero-Fuzzy Systems to Monitor Linear
4
Quality Proles, J. Uncertain System, 4(2) (2010 ), 147-160.
5
[3] Sh. Ghobadi, K. Noghondarian, R. Noorossana and S. M. Sadegh Mirhosseini, Developing
6
a multivariate approach to monitor fuzzy quality proles, Quality & Quantity, 48 (2014),
7
[4] H. Hassanpur, H. R. Maleki and M. A. Yaghoobi, A goal programming approach for fuzzy
8
linear regression with nonfuzzy input and fuzzy output data, Asia Pacic J. Operational
9
Research., 26(5) (2009), 1-18.
10
[5] S. Z. Hosseinifard, M. Abdollahian and P. Zeephongsekul, Application of articial neural
11
networks in linear prole monitoring, Expert Systems with Applications, 38 (2011), 4920-
12
[6] L. Kang and S. L. Albin, On-line monitoring when the process yields a linear prole, J.
13
Quality Technology, 32(4) (2000), 418-426.
14
[7] K. Kim, M. A. Mahmoud and W. H. Woodall, On the monitoring of linear proles, J. Quality
15
Technology, 35 (2003), 317-328.
16
[8] R. Korner and W. Nather, Linear regression with random fuzzy variables: extended classical
17
estimates, best linear estimates, least squares estimates, J. Information Sciences, 109 (1998),
18
[9] Z. Li and Z. Wang, An exponentially weighted moving average scheme with variable sampling
19
intervals for monitoring linear proles, Computers & Industrial Engineering, 59 (2010), 630-
20
[10] V. Monov, B. Sokolov and S. Stefan, Grinding in Ball Mill: Modeling and Process Control,
21
Cybernetics and Information Technologies, 12(2) (2012).
22
[11] D. C. Montgomery, Introduction to Statistical Quality Control, John Wiley and Sons, New
23
York, 2009.
24
[12] S. T. A. Niaki, B. Abbasi and J. Arkat, A generalized linear statistical model approach to
25
monitor proles, Int. J. Engineering, Transactions A: Basics, 20(3) (2007), 233-242.
26
[13] K. Noghondarian and Sh. Ghobadi, Developing a univariate approach to phase-I monitoring
27
of fuzzy quality proles, Int. J. Industrial Engineering Computations, 3 (2012), 829-842.
28
[14] R. Noorossana, A. Saghaei and A. H. Amiri, Statistical Analysis of Prole Monitoring, John
29
Wiley and Sons, Inc. Hoboken, New Jersey, 2011.
30
[15] A. Saghaei, M. Mehrjoo and A. Amiri, ACUSUM-based method for monitoring simple linear
31
proles, Int. J. Advanced Manufacturing Technology, 45(11) (2009), 1252-1260.
32
[16] S. Senturk, N. Erginel, I. Kaya and C. Kahraman, Fuzzy exponentially weighted moving av-
33
erage control chart for univariate data with a real case application, Applied Soft Computing,
34
22 (2014), 1-10
35
[17] S. M. Taheri and M. Are, Testing fuzzy hypotheses based on fuzzy test statistic, Soft Computing
36
, 13 (2009), 617-625.
37
[18] R. Viertl, Statistical Methods for Fuzzy Data, John Wiley and Sons, Austria, 2011.
38
[19] J. Zhang, Z. Li and Z. Wang, Control chart based on likelihood ratio for monitoring linear
39
proles, Computational Statistics and Data Analysis, 53 (2009), 1440-1448.
40
[20] J. Zhu and D. K. J. Lin, Monitoring the slops of linear proles, Quality Engineering, 22(1)
41
(2010), 1-12.
42
[21] C. Zou, Y. Zhang and Z. Wang, Control chart based on change-point model for monitoring
43
linear proles, IIE Transactions, 38(12) (2006), 1093-1103.
44
[22] C. Zou, C. Zhou, Z. Wang and F. Tsung, A self-starting control chart for linear proles, J.
45
Quality Technology, 39(4) (2007), 364-375.
46
ORIGINAL_ARTICLE
Effects of Project Uncertainties on Nonlinear Time-Cost Tradeoff Profile
This study presents the effects of project uncertainties on nonlinear time-cost tradeoff (TCT) profile of real life engineering projects by the fusion of fuzzy logic and artificial neural network (ANN) models with hybrid meta-heuristic (HMH) technique, abridged as Fuzzy-ANN-HMH. Nonlinear time-cost relationship of project activities is dealt with ANN models. ANN models are then integrated with HMH technique to search for Pareto-optimal nonlinear TCT profile. HMH technique incorporates simulated annealing in the selection process of multiobjective genetic algorithm. Moreover, in real life engineering projects, uncertainties like management experience, labor skills, and weather conditions are commonly involved, which affect the duration and cost of the project activities. Fuzzy-ANN-HMH analyses responsiveness of nonlinear TCT profile with respect to these uncertainties. A comparison of Fuzzy-ANN-HMH is made with another method in literature to solve nonlinear TCT problem and the superiority of Fuzzy-ANN-HMH is demonstrated by results. The study gives project planners to carry out the best plan that optimizes time and cost to complete a project under uncertain environment.
http://ijfs.usb.ac.ir/article_2086_403c29a14527408bbc45deea8ecbb8d0.pdf
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2018-12-16T11:23:20
79
100
10.22111/ijfs.2015.2086
fuzzy logic
Artificial neural network
Hybrid Meta-Heuristic
Time-Cost Tradeoff
Bhupendra Kumar
Pathak
pathak.maths@gmail.com
true
1
Department of Mathematics, Jaypee University, Anoop-
shahr, Bulandshahr, 203390 India
Department of Mathematics, Jaypee University, Anoop-
shahr, Bulandshahr, 203390 India
Department of Mathematics, Jaypee University, Anoop-
shahr, Bulandshahr, 203390 India
LEAD_AUTHOR
Sanjay
Srivastava
ssrivastava.engg@gmail.com
true
2
Department of Mechanical Engineering, Dayalbagh Educational
Institute (Deemed University), Dayalbagh, Agra, 282005 India
Department of Mechanical Engineering, Dayalbagh Educational
Institute (Deemed University), Dayalbagh, Agra, 282005 India
Department of Mechanical Engineering, Dayalbagh Educational
Institute (Deemed University), Dayalbagh, Agra, 282005 India
AUTHOR
[1] M. V. Arias and C. A. C. Coello, Asymptotic convergence of metaheurisitcs for multiobjective
1
optimization problems, Soft Comput., 10 (2005), 1001{1005.
2
[2] S. P. Chen, M. J. Tsai, Time-cost trade-o analysis of project networks in fuzzy environments,
3
Eur. J. Oper.Res., 212(2) (2011), 386{397.
4
[3] K. Deb, Multi-objective optimization using evolutionary algorithms, NewYork: JohnWiley
5
and Sons, 2001.
6
[4] E. Eshtehardian, A. Afshar and R. Abbasnia, Fuzzy-based MOGA approach to stochastic
7
time cost trade-o problem, Automation in Construction, 18 (2009), 692{701.
8
[5] L. Fausett, Fundamentals of neural networks," NJ: Prentice Hall Englewood Clis, 1994.
9
[6] C. W. Feng, L. Liu, and S. A. Burns, Using genetic algorithms to solve construction time-cost
10
trade-o problems, J. Comput. Civil Eng., 11 (1997), 184{189.
11
[7] H. Ke, W. Ma, X. Gao and W. Xu, New fuzzy models for time-cost trade-o problem, Fuzzy
12
Optim Decis Making, 9 (2010), 219{231.
13
[8] S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Optimization by simulated annealing, Sci.,
14
220 (1983), 671{680.
15
[9] S. S. Leu, A. T. Chen and C. H. Yang, A GA-based fuzzy optimal model for construction
16
time-cost trade-o, Int. J. Project Manage., 19 (2001), 47{58.
17
[10] L. Liu, S. Burns and C. Feng, Construction time-cost trade-o analysis using LP/IP hybrid
18
method, J. Const. Eng. Manage., 121(4) (1995), 446{454.
19
[11] E. H. Mamdani, Application of fuzzy logic to approximate reasoning using linguistic synthesis,
20
Trans. Comput., 26(12) (1977), 1182{1191.
21
[12] E. H. Mamdani, Applications of fuzzy algorithms for control of simple dynamic plant, In:
22
Proc. IEEE, 121(12) (1974), 1585{1588.
23
[13] B. K. Pathak and S. Srivastava, Integrated Fuzzy-HMH for project uncertainties in time-cost
24
tradeo problem, Applied Soft Computing, 21 (2014), 320-329.
25
[14] B. K. Pathak and S. Srivastava, MOGA based time-cost tradeos: responsiveness for project
26
uncertainties, In: Proc. CEC, (2007), 3085{3092.
27
[15] B. K. Pathak, S. Srivastava and K. Srivastava, Neural network embedded multiobjective ge-
28
netic algorithm to solve nonlinear time-cost tradeo problems of project scheduling, J. Sci.
29
Ind. Res., 67(2) (2008), 124{131.
30
[16] S. Srivastava, B. Pathak and K. Srivastava, Project scheduling: time-cost tradeo problems,
31
In: Comput. Intell.Optimization, Y. Tenne and C-K Goh Ed., Springer-Verlag Berlin Heidel-
32
berg, 7 (2010), 325{357.
33
[17] S. Srivastava, K. Srivastava, R. S. Sharma and K. H. Raj, Modelling of hot closed die forging
34
of an automotive piston with ANN for intelligent manufacturing, J. Sci. Ind. Res., 63 (2004),
35
[18] M. O. Suliman, V. S. S. Kumar and W. Abdulal, Optimization of uncertain construction time-
36
cost trade o problem using simulated annealing algorithm, World Congr. Inform. Commun.
37
Tech., (2011), 489{494.
38
[19] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8(3) (1965), 333{353.
39
[20] L. A. Zadeh, Outline of a New Approach to the Analysis of a Complex System and Decision
40
Processes, IEEE Trans. Syst. Man Cybern., 3 (1973), 28{44.
41
ORIGINAL_ARTICLE
On the compactness property of extensions of first-order G"{o}del logic
We study three kinds of compactness in some variants of G"{o}del logic: compactness,entailment compactness, and approximate entailment compactness.For countable first-order underlying language we use the Henkinconstruction to prove the compactness property of extensions offirst-order g logic enriched by nullary connective or the Baaz'sprojection connective. In the case of uncountable first-order languagewe use the ultraproduct method to derive the compactness theorem.
http://ijfs.usb.ac.ir/article_2087_5cf9578eb43b78cc8613cbd97e4aa22d.pdf
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101
121
10.22111/ijfs.2015.2087
G"{o}del logic
Compactness theorem
Seyed Mohammad Amin
Khatami
khatami@birjandut.ac.ir
true
1
Department of Mathematics and Computer Science,
Amirkabir University of Technology, Tehran, Iran
Department of Mathematics and Computer Science,
Amirkabir University of Technology, Tehran, Iran
Department of Mathematics and Computer Science,
Amirkabir University of Technology, Tehran, Iran
AUTHOR
Massoud
Pourmahdian
pourmahd@ipm.ir
true
2
Department of Mathematics and Computer Science, Amirk-
abir University of Technology, Tehran, Iran
Department of Mathematics and Computer Science, Amirk-
abir University of Technology, Tehran, Iran
Department of Mathematics and Computer Science, Amirk-
abir University of Technology, Tehran, Iran
LEAD_AUTHOR
1] M. Baaz and R. Zach, Compact propositional Godel logics, Multiple-Valued Logic, 28th IEEE
1
International Symposium on, (1998), 108-113.
2
[2] I. Ben-Yaacov and A. Usvyatsov, Continuous rst order logic and local stability, Transactions
3
of the American Mathematical Society, 362(10) (2010), 5213-5259.
4
[3] R. Cignoli, F. Esteva and L. Godo, On Lukasiewicz logic with truth constants, Theoretical
5
Advances and Applications of Fuzzy Logic and Soft Computing, Springer, (2007), 869-875.
6
[4] P. Cintula, Two notions of compactness in Godel logics, Studia Logica, 81(1) (2005), 99-123.
7
[5] P. Cintula and M. Navara, Compactness of fuzzy logics, Fuzzy Sets and Systems, 143(1)
8
(2004), 59-73.
9
[6] F. Esteva, J. Gispert, L. Godo and C. Noguera, Adding truth-constants to logics of continuous
10
t-norms: Axiomatization and completeness results, Fuzzy Sets and Systems, 158(6) (2007),
11
[7] F. Esteva, L. Godo and C. Noguera. First-order t-norm based fuzzy logics with truthconstants:
12
Distinguished semantics and completeness properties, Annals of Pure and Applied
13
Logic, 161(2) (2009), 185-202.
14
[8] G. Gerla, Abstract fuzzy logic, Fuzzy Logic, Springer (2001), 19-44.
15
[9] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic Pub, (1998).
16
[10] S. M. A. Khatami, M. Pourmahdian and N. R. Tavana, From rational Godel logic to ultrametric
17
logic, Journal of Logic and Computation, doi: 10.1093/logcom/exu065, 2014.
18
[11] M. Navara and U. Bodenhofer, Compactness of fuzzy logics, Neural Network World, Citeseer,
19
[12] J. Pavelka, On fuzzy logic i, ii, iii, Mathematical Logic Quarterly, 25(3-6,7-12,25-29)
20
(1979), 45-52,119-134,447-464.
21
[13] M. Pourmahdian and N. R. Tavana, Compactness in rst-order Godel logics, Journal of Logic
22
and Computation, 23(3) (2013), 473-485.
23
[14] N. Preining, Complete recursive axiomatizability of Godel logics, PhD thesis, Technische
24
Universitat Wien, 2003.
25
[15] N. R. Tavana, M. Pourmahdian and F. Didevar, Compactness in rst-order Lukasiewicz
26
logics, Journal of Logic and Computation, 20(1) (2012), 254-265.
27
[16] S. Willard. General topology, Courier Dover Publications, 2004.
28
ORIGINAL_ARTICLE
Remarks on completeness of lattice-valued Cauchy spaces
We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.
http://ijfs.usb.ac.ir/article_2088_d882c9cec06c103eb07a676c35f36c08.pdf
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123
132
10.22111/ijfs.2015.2088
$L$-topology
$L$-Cauchy space
Completeness
Completion
Gunther
Jager
g.jager@ru.ac.za, gunther.jaeger@fh-stralsund.de
true
1
School of Mechanical Engineering, University of Applied Sciences
Stralsund, 18435 Stralsund, Germany
School of Mechanical Engineering, University of Applied Sciences
Stralsund, 18435 Stralsund, Germany
School of Mechanical Engineering, University of Applied Sciences
Stralsund, 18435 Stralsund, Germany
LEAD_AUTHOR
[1] H. Boustique and G. Richardson, Regularity: Lattice-valued Cauchy spaces, Fuzzy Sets and
1
Systems, 190 (2012), 94-104.
2
[2] P. V. Flores, R. N. Mohapatra and G. Richardson, Lattice-valued spaces: fuzzy convergence,
3
Fuzzy Sets and Systems, 157 (2006), 2706-2714.
4
[3] U. Hohle and A. P. Sostak, Axiomatic foundations of xed-basis fuzzy topology, In: U. Hohle,
5
S. E. Rodabauch (eds.), Mathematics of Fuzzy Sets. Logic, Topology and Measure Theory,
6
Kluwer, Boston/Dordrecht/London, 1999.
7
[4] G. Jager, A category of L-fuzzy convergence spaces, Quaest. Math., 24 (2001), 501-517.
8
[5] G. Jager, Subcategories of lattice-valued convergence spaces, Fuzzy Sets and Systems, 156
9
(2005), 1-24.
10
[6] G. Jager, Lattice-valued convergence spaces and regularity, Fuzzy Sets and Systems, 159
11
(2008), 2488-2502.
12
[7] G. Jager, Lattice-valued Cauchy spaces and completion, Quaest. Math., 33 (2010), 53-74.
13
[8] G. Jager, Largest and smallest T2-compactications of lattice-valued convergence spaces,
14
Fuzzy Sets and Systems, 190 (2012), 32-46.
15
[9] G. Jager, On diagonal completion of lattice-valued diagonal Cauchy spaces, Fuzzy Sets and
16
Systems, to appear.
17
[10] H. H. Keller, Die Limes-Uniformisierbarkeit der Limesraume, Math. Ann., 176 (1968), 334-
18
[11] D. C. Kent and G. D. Richardson, Completions of probabilistic Cauchy spaces, Math. Japonica,
19
48 (1998), 399-407.
20
[12] H. Nusser, A generalization of probabilistic uniform spaces, Appl. Cat. Structures, 10 (2002),
21
[13] B. Pang, The category of stratied L-lter spaces, Fuzzy Sets and Systems, 247 (2014),
22
108-126. .
23
[14] E. E. Reed, Completions of uniform convergence spaces, Math. Ann., 194 (1971), 83-108.
24
[15] X. F. Yang and S. G. Li, Completion of stratied (L,M)-lter tower spaces, Fuzzy Sets
25
Systems, 210 (2013), 22-38.
26
ORIGINAL_ARTICLE
Fixed fuzzy points of generalized Geraghty type fuzzy mappings on complete metric spaces
Generalized Geraghty type fuzzy mappings oncomplete metric spaces are introduced and a fixed point theorem thatgeneralizes some recent comparable results for fuzzy mappings incontemporary literature is obtained. Example is provided to show thevalidity of obtained results over comparable classical results for fuzzymappings in fixed point theory. As an application, existence of coincidencefuzzy points and common fixed fuzzy points for hybrid pair of single valuedself mapping and a fuzzy mapping is also established.
http://ijfs.usb.ac.ir/article_2089_fcaab88975e3dd3155939a4cf038845b.pdf
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133
146
10.22111/ijfs.2015.2089
Fixed fuzzy point
Geraghty type
Fuzzy mapping
Fuzzy set
Approximate quantity
M.
Abbas
mujahid.abbas@up.ac.za
true
1
Department of Mathematics and Applied Mathematics, University of Pre-
toria, Hatfield, Pretoria, South Africa
Department of Mathematics and Applied Mathematics, University of Pre-
toria, Hatfield, Pretoria, South Africa
Department of Mathematics and Applied Mathematics, University of Pre-
toria, Hatfield, Pretoria, South Africa
LEAD_AUTHOR
B.
Ali
basit.aa@gmail.com
true
2
Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 0002, Pretoria South Africa
Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 0002, Pretoria South Africa
Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 0002, Pretoria South Africa
AUTHOR
[1] R. P. Agarwal, M. Meehan and D. O'Regan, Fixed point theory and applications, Cambridge
1
University Press, 2001.
2
[2] A. Amini-Harandi and H. Emami, A xed point theorem for contraction type maps in partially
3
ordered metric spaces and application to ordinary dierential equations, Nonlinear Anal., 72
4
(2010), 2238-2242.
5
[3] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations
6
integrales, Fund. Math., 3 (1922), 133{181.
7
[4] R. Baskaran and P. V. Subrahmanyam, A note on the solution of a class of functional
8
equations, Applicable Anal., 22 (1986), 235{241.
9
[5] R. Bellman, Methods of nonliner analysis, vol. II, 61 of Mathematics in Science and Engi-
10
neering, Academic Press, New York, NY, USA, 1973.
11
[6] D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20
12
(1969), 458{464.
13
[7] D. Dukic , Z. Kadelburg and S. Radenovic, Fixed points of Geraghty type mappings in various
14
generalized metric spaces, Abstract Appl. Anal., Article ID 561245 (2011), 13 pages.
15
[8] M. Edelstein, On xed and periodic points under contractive mappings, J. London Math.
16
Soc., 37 (1962), 74{79.
17
[9] M. Edelstein, An extension of Banach contraction principle, Proc. Amer. Math. Soc., 12 (1)
18
(1961), 7{10.
19
[10] V. D. Estruch and A. Vidal, A note on xed fuzzy points for fuzzy mappings, Rend Istit.
20
Univ. Trieste., 32 (2001), 39-45.
21
[11] M. Geraghty, On contractive mappings, Proc Amer Math Soc., 40 (1973), 604{608.
22
[12] M. E. Gordji, M. Ramezani, Y. J. Cho and S. Pirbavafa, A generalization of Geraghty's
23
theorem in partially ordered metric spaces and applications to ordinary dierential equations,
24
Fixed Point Theory Appl., 1 (74) (2012), pages 9.
25
[13] M. E. Gordji, H. Baghani, H. Khodaei and M. Ramezani, Geraghty's xed point theorem for
26
special multivalued mappings, Thai J. Math., 10 (2012), 225{231.
27
[14] R. H. Haghi, Sh. Rezapour and N. Shahzad, Some xed point generalizations are not real
28
generalizations, Nonlinear Anal., 74 (2011), 1799{1803.
29
[15] S. Heilpern, Fuzzy mappings and fuzzy xed point theorems, J. Math. Anal. Appl., 83 (1981),
30
[16] J. Jachymski, Equivalent conditions for generalized contractions on (ordered) metric spaces,
31
Nonlinear Analysis: Theory, Methods Appl., 3 (74), (2011), 768{774.
32
[17] G. Jungck, Commuting mappings and xed points, Amer. Math Monthly, 83 (1976), 261{263.
33
[18] B. S. Lee and S. J. Cho, A xed point theorem for contractive type fuzzy mappings, Fuzzy
34
Sets and Systems, 61 (1994), 309{312.
35
[19] S. B. Nadler, Multivalued contraction mappings, Pacic J. Math., 30 (1969), 475{488.
36
[20] J. J. Nieto and R. R. Lopez, Contractive mapping theorems in partially ordered sets and
37
applications to ordinary dierential equations, Order, 22 (3) (2005), 223{239.
38
[21] S. Park, Fixed points of fcontractive maps, Rocky Mountain J. Math., 8 (4) (1978), 743{
39
[22] E. Rakotch, A note on contractive mappings, Proc. Amer. Math. Soc., 13 (1962), 459{465.
40
[23] B. E. Rhoades, A comparison of various denitions of contractive mappings, Transaction.
41
Amer. Math. Soc., 226 (1977), 257{290.
42
[24] V. M. Sehgal, A xed point theorem for mappings with a contractive iterate, Proc. Amer.
43
Math. Soc., 23 (3) (1969), 631{634.
44
[25] C. S. Sen, Fixed degree for fuzzy mappings and a generalization of Ky Fan's theorem, Fuzzy
45
Sets and Systems, 24 (1987), 103{112.
46
[26] T. Suzuki, Mizoguchi and Takahashi's xed point theorem is a real generalization of Nadler's,
47
J. Math. Anal. Appl., 340 (2008), 752{755.
48
[27] D. Turkoglu and B. E. Rhoades, A xed fuzzy point for fuzzy mapping in complete metric
49
spaces, Math. Commun., 10 (2005), 115{121.
50
[28] J. S. W. Wong, Mappings of contractive type on abstract spaces, J. Math. Anal. Appl., 37
51
(1972), 331-340.
52
[29] L. A. Zadeh, Fuzzy Sets, Informations and Control, 8 (1965), 103-112.
53
[30] E. H. Zarantonello, Solving functional equations by contractive averaging, Mathematical Re-
54
search Center, Madison, Wisconsin, Technical Summary Report No. 160, June 1960.
55
[31] E. Zeidler, Nonlinear functional analysis and its applications I: Fixed Point Theorems,
56
Springer{Verlag, Berlin, 1986.
57
ORIGINAL_ARTICLE
Quasi-contractive Mappings in Fuzzy Metric Spaces
We consider the concept of fuzzy quasi-contractions initiated by '{C}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{H}$-contractive mappings on M-complete fuzzy metric spaces in the sense of George and Veeramani.The results are illustrated by a representative example.
http://ijfs.usb.ac.ir/article_2090_f9434164fee8710359e4bddbf44257bf.pdf
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147
153
10.22111/ijfs.2015.2090
Fuzzy metric space
Fuzzy quasi-contractive mapping
Fixed point
A.
Amini-Harandi
a.amini@sci.ui.ac.ir
true
1
Department of Mathematics, University of Isfahan, Isfahan, 81745-
163, Iran
Department of Mathematics, University of Isfahan, Isfahan, 81745-
163, Iran
Department of Mathematics, University of Isfahan, Isfahan, 81745-
163, Iran
AUTHOR
D.
Mihet
mihet@math.uvt.ro
true
2
West University of Timisoara, Faculty of Mathematics and Computer
Science, Bv. V. Parvan 4, 300223, Timisoara, Romania
West University of Timisoara, Faculty of Mathematics and Computer
Science, Bv. V. Parvan 4, 300223, Timisoara, Romania
West University of Timisoara, Faculty of Mathematics and Computer
Science, Bv. V. Parvan 4, 300223, Timisoara, Romania
LEAD_AUTHOR
[1] Lj. B. Ciric, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc.,
1
45(2) (1974), 267-273.
2
[2] S. Chang, Y. J. Cho and S. M. Kang, Probabilistic Metric Spaces and Nonlinear Operator
3
Theory, Sichuan Univ. Press, 1994.
4
[3] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,
5
64(3) (1994), 395-399.
6
[4] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27(3) (1988),
7
[5] V. Gregori and A. Sapena, On xed point theorems in fuzzy metric spaces, Fuzzy Sets and
8
Systems, 125(2) (2002), 245-252.
9
[6] O. Hadzic and E. Pap, Fixed point theory in probabilistic metric spaces, Mathematics and its
10
Applications, Kluwer Academic Publishers, Dordrecht, Boston, London, 536 (2001).
11
[7] F. Kiany and A. Amini-Harandi, Fixed points and endpoint theorems for set-valued fuzzy
12
contraction maps in fuzzy metric spaces, Point Theory and Applications 2011, 2011:94.
13
[8] E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Trends in Logics, Kluwer Academic
14
Publishers, Dordrecht, Boston, London, 8 (2000).
15
[9] I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11(5)
16
(1975), 336-344.
17
[10] D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems,
18
144(3) (2004), 431-439.
19
[11] D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems,
20
158(8) (2007), 915-921.
21
[12] D. Mihet, Fuzzy -contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets
22
and Systems, 159(6) (2008), 739-744.
23
[13] D. Mihet, A note on fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and
24
Systems, 251 (2014), 83-91.
25
[14] J. Rodrguez-Lopez and S. Romaguera, The Hausdor fuzzy metric on compact sets, Fuzzy
26
Sets and Systems, 147(2) (2004), 273-283.
27
[15] B. Schweizer and A. Sklar, Statistical metric spaces, Pacic J. Math., 10 (1960), 313-334.
28
[16] C. Vetro, Fixed points in weak non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems,
29
162(1) (2011), 84-90.
30
[17] D. Wardowski, Fuzzy contractive mappings and xed points in fuzzy metric spaces, Fuzzy
31
Sets and Systems, 222 (2013), 108-114.
32
ORIGINAL_ARTICLE
Persian-translation vol. 12, no.4, August 2015
http://ijfs.usb.ac.ir/article_2645_55eaa69a93caf727a23adc9bbe864157.pdf
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157
164
10.22111/ijfs.2015.2645