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
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trapezoidal fuzzy numbers, Applied mathematical modeling, 37 (1/2) (2013), 318-327.
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with interval-valued intuitionistic trapezoidal fuzzy numbers, Computers and Industrial
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Engineering, 66 (2013), 311-324.
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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
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1
objective optimization of supply chain networks, Computers and Industrial Engineering, 51
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model, Eng Optim, 45 (2013), 745-765.
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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
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monitor proles, Int. J. Engineering, Transactions A: Basics, 20(3) (2007), 233-242.
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erage control chart for univariate data with a real case application, Applied Soft Computing,
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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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2018-05-25T11:23:20
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,
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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@ipm.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.
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[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
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applications to ordinary dierential equations, Order, 22 (3) (2005), 223{239.
38
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39
[22] E. Rakotch, A note on contractive mappings, Proc. Amer. Math. Soc., 13 (1962), 459{465.
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[23] B. E. Rhoades, A comparison of various denitions of contractive mappings, Transaction.
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Amer. Math. Soc., 226 (1977), 257{290.
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[24] V. M. Sehgal, A xed point theorem for mappings with a contractive iterate, Proc. Amer.
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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.
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[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.
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[28] J. S. W. Wong, Mappings of contractive type on abstract spaces, J. Math. Anal. Appl., 37
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(1972), 331-340.
52
[29] L. A. Zadeh, Fuzzy Sets, Informations and Control, 8 (1965), 103-112.
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[30] E. H. Zarantonello, Solving functional equations by contractive averaging, Mathematical Re-
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search Center, Madison, Wisconsin, Technical Summary Report No. 160, June 1960.
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[31] E. Zeidler, Nonlinear functional analysis and its applications I: Fixed Point Theorems,
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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