ORIGINAL_ARTICLE
Cover vol. 10, no. 1, February 2013
http://ijfs.usb.ac.ir/article_2723_3ee3c7840b0dd11f70a6f651d5237cbc.pdf
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10.22111/ijfs.2013.2723
ORIGINAL_ARTICLE
A CONSTRAINED SOLID TSP IN FUZZY ENVIRONMENT:
TWO HEURISTIC APPROACHES
A solid travelling salesman problem (STSP) is a travelling salesman problem (TSP) where the salesman visits all the cities only once in his tour using dierent conveyances to travel from one city to another. Costs and environmental eect factors for travelling between the cities using dierent conveyances are dierent. Goal of the problem is to nd a complete tour with minimum cost that damages the environment least. An ant colony optimization (ACO) algorithm is developed to solve the problem. Performance of the algorithm for the problem is compared with another soft computing algorithm, Genetic Algorithm(GA). Problems are solved with crisp as well as fuzzy costs. For fuzzy cost and environmental eect factors, cost function as well as environment constraints become fuzzy. As optimization of a fuzzy objective function is not well de ned, fuzzy possibility approach is used to get optimal decision. To test the eciency of the algorithm, the problem is solved considering only one conveyance facility ignoring the environmental eect constraint, i.e., a classical two dimensional TSP (taking standard data sets from TSPLIB for solving the problem). Dierent numerical examples are used for illustration.
http://ijfs.usb.ac.ir/article_153_100415578c754927aaf8d608b87dfdd1.pdf
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10.22111/ijfs.2013.153
Solid travelling salesman problem
Fuzzy possibility
Ant colony optimization
Genetic algorithm
Chiranjit
Changdar
chiranjit changdar@yahoo.co.in
true
1
Department of Computer Science, Raja N.L. Khan Women's
College, Midnapore, Paschim- Medinipur, West Bengal, India-721102
Department of Computer Science, Raja N.L. Khan Women's
College, Midnapore, Paschim- Medinipur, West Bengal, India-721102
Department of Computer Science, Raja N.L. Khan Women's
College, Midnapore, Paschim- Medinipur, West Bengal, India-721102
LEAD_AUTHOR
Manas Kumar
Maiti
manasmaiti@yahoo.co.in
true
2
Department of Mathematics, Mahishadal Raj College, Mahishadal,
Purba- Medinipur, West Bengal, India-721628
Department of Mathematics, Mahishadal Raj College, Mahishadal,
Purba- Medinipur, West Bengal, India-721628
Department of Mathematics, Mahishadal Raj College, Mahishadal,
Purba- Medinipur, West Bengal, India-721628
AUTHOR
Manoranjan
Maiti
mmaiti2005@yahoo.co.in
true
3
Department of Mathematics, Vidyasagar University, Midnapore,
Paschim- Medinipur, West Bengal, India-721102
Department of Mathematics, Vidyasagar University, Midnapore,
Paschim- Medinipur, West Bengal, India-721102
Department of Mathematics, Vidyasagar University, Midnapore,
Paschim- Medinipur, West Bengal, India-721102
AUTHOR
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[2] L. Bianchi, M. Dorigo and L. M. Gambardella, Ant colony optimization approach to the probabilistic travelling salesman problem, PPSN VII, LNCS,2439 (2002), 883-892.
2
[3] T. Chang, Y. Wan and W. T. OOI.,A stochastic dynamic travelling salesman problem with hard time windows, European Journal of Operational Research, 198(3) (2009),748-759.
3
[4] S. Chen and C. Chien,Multi-objective ant colony optimisation: parallelized genetic ant colony systems for solving the traveling salesman problem, Expert Systems with Applications, 38(2011), 3873-3883.
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[5] W. C. Chiang and R. A. Russell,Simulated annealing metaheuristics for the vehicle routine problem with time windows, Annals of Operations Research, 63 (1996), 3-27.
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[6] G. B. Dantzig, D. R. Fulkerson, S. M. Johnson,Solution of large-scale travelling salesman problem, Operations Research, 2 (1954), 393-410.
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[7] M. Dorigo and L. M. Gambardella,Ant colony system: an cooperative learning approach to the travelling salesman problem, IEEE Transactions on Evolutionary Computation,1(1)(1997).
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[8] M. Dorigo and T. Stutzle,Ant colony optimization, prentice hall of India private limitde,New Delhi, 2006
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[9] D. Dubois and H. Prade,Fuzzy sets and system - theory and application, Academic, NewYork, 1980.
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[10] A. P. Engelbrech,Fundamentals of computational swarm intelligence, Wiley, 2005.
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[11] O. Ergan and J. B. Orlin,A dynamic programming methodology in very large sccale neigh-bourhood applied to travelling Salesman problem, Discrete Optimization, 3 (2006), 78-85.
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[12] F. Focacci, A. Lodi, M. Milano ,A hybrid exact algorithm for the TSPTW, INFORM Journal on Computing,14(4) (2002),403-417.
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[13] D. E. Goldberg,Genetic algorithms: search, optimization and machine learning, Addison Wesley, assachusetts, 1989.
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[14] T. Ibaraki, S. Imahori, M. Kubo, T. Masuda, T. Uno and M. Yagiura,fective local search algorithm for routing and scheduling problems with general time window constraints, Transportation Science,39(2)(2005), 206-232.
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[15] J. Knox,The application of Tabu search to the symmetric traveling salesman problem, h.D.Dissertation, University of Colorado, 1989.
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[16] A. Kumar, A. Gupta and M. K. Sharma,Application of Tabu search for solving the bi-objective warehouse problem in a fuzzy environment, Iranian Journal of Fuzzy Systems, 9(1)(2012), 1-19.
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[17] E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan and D. B. Shmoys,The traveling salesman problem: G. E. Re Guided tour of combinatorial optimization, Wiley and Sons, New York,1985.
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[18] S. Lin and B. W. Kernighan,An effective heuristic algorithm for the traveling salesman problem, erations Research, 21 (1973), 498-516.
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[19] Y. Liu ,Dierent initial solution generators in genetic algorithms for solving the probabilistic traveling salesman problem, Applied Mathematics and Computation, 216 (2010), 125-137.
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[20] I. Mahdavi, N. Madhavi-Amiri AND S. Nejati,Algorithms for biobjective shortest path prob-lems in fuzzy networks, Iranian Journal of Fuzzy Systems, 8(4) (2011), 7-37.
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[21] M. K. Maiti and M. Maiti,Two-storage inventory model with lot-size dependent fuzzy lead-time under possibility constraints via genetic algorithm, European Journal of Operational Research,179 (2007), 352-371.
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[22] M. K. Maiti and M. Maiti,Fuzzy inventory model with two warehouses under possibility constraints, Fuzzy Sets and Systems, 157 (2006), 52-73.
22
[23] A. K. Majumder and A. K. Bhunia,Genetic algorithm for asymatric traveling salesman problem with imprecise travel times, Journal of Computational and Applied Mathematics,235(9)(2011), 3063-3078.
23
[24] Z. Michalewicz,Genetic Algorithms + data structures= evolution programs, Springer, Berlin,1992.
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[25] L. A. Moncayo-Martinez and D. Z. Zhang,Multi-objective ant colony optimisation : a meta-heuristic approach to supply chain design, International Journal of Production Economics,1(131)(2011), 407420.
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[26] C. Moon, J. Ki, G. Choi and Y. Seo,An ecient genetic algorithm for the traveling salesman problem with precedence constraints, European Journal of Operational Research, 140(2002),606-617.
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[27] H. Nezamabadi-Pour, S. Yazdani, M. M. Farsangi and M. Neyestani,A solution to an eco-nomic dispatch problem by a fuzzy adaptive genetic algorithm, Iranian Journal of Fuzzy Systems,8(3)(2011), 1-21.
27
[28] H. D. Nguyen, I. Yoshihara, K. Yamamori and M. Yasunaga,Implementation of an effective hybrid GA for large scale traveling salesman problem, IEEE Transactions on Systems, Man,and Cybernatics,37(1) 007), 92-99.
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[32] H. L. Petersen. and O. B. G. Madsen,The double travelling salesman problem with multi-ple stack-formulation and heuristic solution approaches, European Journal of Operational Research,198 (2009), 339-347.
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[33] A. Vescan and C-M. Pintea,Ant colony component-based system for travelling salesman problem, Applied Mathematical Sciences, 1(28) (2007), 1347-1357.
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[34] J. Wang, J. Huang, S. Rao, S. Xue and J. Yin,An adaptive genetic algorithm for solving traveling salesman problem, Springer-Verlag Berlin Heidelberg 2008 , ICIC 2008, LNAI 5227,(2008), 182-189.
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[35] L. Yang, X. Li, Z. Gao and K. Li,A fuzzy minimum risk model for the railway transportation planning problem, Iranian Journal of Fuzzy Systems 8(4) (2011), 39-60.
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37
ORIGINAL_ARTICLE
A COGNITIVE STYLE AND AGGREGATION OPERATOR
MODEL: A LINGUISTIC APPROACH FOR CLASSIFICATION
AND SELECTION OF THE AGGREGATION OPERATORS
Aggregation operators (AOs) have been studied by many schol- ars. As many AOs are proposed, there is still lacking approach to classify the categories of AO, and to select the appropriate AO within the AO candidates. In this research, each AO can be regarded as a cognitive style or individual dierence. A Cognitive Style and Aggregation Operator (CSAO) model is pro- posed to analyze the mapping relationship between the aggregation operators and the cognitive styles represented by the decision attitudes. Four algorithms are proposed for CSAO: CSAO-1, CSAO-2 and two selection strategies on the basis of CSAO-1 and CSAO-2. The numerical examples illustrate how the choice of the aggregation operators on the basis of the decision attitudes can be determined by the selection strategies of CSAO-1 and CSAO-2. The CSAO model can be applied to decision making systems with the selection problems of the appropriate aggregation operators with consideration of the cognitive styles of the decision makers.
http://ijfs.usb.ac.ir/article_154_6135966bcbefde837de8dc2560d927ba.pdf
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10.22111/ijfs.2013.154
Cognitive styles
Aggregation operators
Information fusion
Decision
attitudes
decision making
Kevin Kam Fung
Yuen
kevinkf.yuen@gmail.com
true
1
Department of Computer science and Software Engineering,
Xi'an Jiaotong-Liverpool University, 111 Ren Ai Road, Suzhou Industrial Park, Suzhou,
Jiangsu Province, 215123, P. R. China
Department of Computer science and Software Engineering,
Xi'an Jiaotong-Liverpool University, 111 Ren Ai Road, Suzhou Industrial Park, Suzhou,
Jiangsu Province, 215123, P. R. China
Department of Computer science and Software Engineering,
Xi'an Jiaotong-Liverpool University, 111 Ren Ai Road, Suzhou Industrial Park, Suzhou,
Jiangsu Province, 215123, P. R. China
LEAD_AUTHOR
[1] B. S. Ahn and H. Park,Least-squared ordered weighted averaging operator weights, Interna-tional Journal of Intelligent Systems,23 (2008), 33-49.
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[2] G. W. Allport,Personality: a psychological interpretation, Holt & Co, New York, 1937.
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[3] G. R. Amin and A. Emrouznejad,Parametric aggregation in ordered weighted averaging,International Journal of Approximate Reasoning,52 (2011), 819-827.
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[4] N. Braisby and A. Gellatly,Foundations of cognitive psychology, in Braisby, N. and Gellatly,A. , eds., Cognitive Psychology, Oxford University Press Inc., Chapter 1, (2005), 1-32.
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[5] P. S. Bullen, D. S. Mitrinovic and O. M. Vasic,Means and their inequalities, D. Reidel Publishing Company, Dordrecht, 1988.
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[6] N. Cagman and S. Enginoglu,Fuzzy soft matrix theory and its application in decision making Iranian Journal of Fuzzy Systems,(2012), 109-119.
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[7] T. Calvo and R. Mesiar,Weighted triangular norms-based aggregation operators, Fuzzy Sets and Systems,137 (2003), 3-10.
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[8] M. DetynieckI,Mathematical aggregation operators and their application to video querying,Doctoral Thesis Research Report 2001-2002, Laboratoire dInformatique de Paris, 2000.
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[9] D. Dubois, H. Prade and C. Testemale,Weighted fuzzy pattern-matching, Fuzzy Sets and Systems,28 (1988), 313-331.
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[10] D. Dubois, H. Fargier and H. Prade,Re nements of the maximin approach to decision-making in a fuzzy environment, Fuzzy Sets and Systems, 81 (1996), 103-122.
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[11] D. Dubois and H. Prade,An introduction to bipolar representations of information and preference, International Journal of Intelligent Systems, 23 (2008), 866-877.
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[12] M. Espinilla, J. Liu and L. Martnez,An extended hierarchical linguistic model for decision-making problems, Computational Intelligence, 27 (2011), 489-512.
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[13] J. Fodor and M. Roubens,Fuzzy preference modeling and multicriteria decision support,Kluwer Academic Publisher, Dordrecht, 1994.
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[14] J. L. Garca-Lapresta and M. Martnez-Panero,Linguistic-based voting through centered OWA operators, Fuzzy Optimization and Decision Making, 8(2009), 381-393.
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[15] R. R. Ghiselli and R. Mesiar,Multi-attribute aggregation operators, Fuzzy Sets and Systems,181(2011), 1-13.
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[16] M. Grabisch, H. T. Nguyen and E. A. Walker,amentals of uncertainty calculi with applications to fuzzy inference, Kluwer Academics Publishers, Dordrecht, 1995.
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[17] F. Herrera, S. Alonso, F. Chiclana and E. Herrera-Viedma,Computing with words in decision making: foundations, trends and prospects, Fuzzy Optimization and Decision Making, 8(2009), 337-364.
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[18] F. Herrera and L. Martinez,A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems, 8 (2000), 746-752.
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[19] J. L. Marichal,Aggregation operators for multicriteria decision aid PhD. Thesis, University of Lige, Belgium, 1998.
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[20] J. Martn, G. Mayor and O. Valero,On aggregation of normed structures, Mathematical and Computer Modelling,54 (2011), 815-827.
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[21] L. Martnez, D. Ruan and F. Herrera,Computing with words in decision support systems:an overview on models and applications, International Journal of Computational Intelligence Systems,3 (2010), 382-395.
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[22] R. J. Riding and I. Cheema,Cognitive styles-an overview and integration, Educational Psy-chology,11 (1991), 193-215.
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[23] R. Smolikava and M. P. Wachowiak,Aggregation operators for selection problems, Fuzzy Sets and Systems,131(2002), 23-34.
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[24] Z. X. Su, G. P. Xia, M. Y. Chen and L. Wang,Induced generalized intuitionistic fuzzy OWA operator for multi-attribute group decision making, Expert Systems with Applications,39(2012), 1902-1910.
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[25] W. Wang and X. Liu,Intuitionistic fuzzy geometric aggregation operators based on einstein operations, International Journal of Intelligent Systems, 26 (2011), 1049-1075.
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[26] G. Wei,Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making, Applied Soft Computing, 10 (2010), 423-431.
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[27] M. Xia and Z. Xu,Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment, Information Fusion, 13(2012), 31-47.
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[28] Z. Xu and X. Cai,Recent advances in intuitionistic fuzzy information aggregation, Fuzzy Optimization and Decision Making,9 (2010), 359-381.
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[29] R. R. Yager,On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE trans. Systems, Man Cybernet., 18 (1988), 183-190.
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[30] R.R. Yager,On weighted median aggregation, Internat. J. Uncertainty, Fuzziness Knowledge-based Systems,2 (1994), 101-113.
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[31] R. R. Yager,On the analytic representation of Leximin ordering and its application to exible constraint propagation, European J. Oper. Res., 102 (1997), 176-192.
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[32] R. R. Yager and A. Rybalov,Full reinforcement operators in aggregation techniques, IEEE Trans. On Systems, Man, and Cybernetics Part B,28 (1998), 757-769.
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[33] R. R. Yager,OWA aggregation over a continuous interval argument with applications to decision making, IEEE Trans. On Systems, Man and Cybernetics- Part B, 34(2004), 1952-1963.
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[34] R. R. Yager and A. Rybalov,Bipolar aggregation using the Uninorms, Fuzzy Optimization and Decision Making,10(2011), 59-70.
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[35] K. K. F. Yuen and H. C. W. Lau,A linguistic-possibility-probability aggregation model for decision analysis with imperfect knowledge, Applied Soft Computing, 9(2009), 575-589.
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[36] K. K. F. Yuen,Selection of aggregation operators with decision attitudes, In J. Mehnen,A. Tiwari, M. Kppen and A. Saad, eds., Applications of Soft Computing: From Theory to Praxis, Advances in Intelligent and Soft Computing,58 (2009), 255-264.
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[37] K. K. F. Yuen,Cognitive network process with fuzzy soft computing technique for collective decision aiding, The Hong Kong Polytechnic University, PhD. Thesis, 2009.
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[38] K. K. F. Yuen,The primitive cognitive network process: comparisons with the analytic hi-erarchy process, International Journal of Information Technology and Decision Making, 10(2011), 659-680.
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[39] K. K. F. Yuen, Membership maximization prioritization methods for fuzzy analytic hierarchy process, Fuzzy Optimization and Decision Making, 11 (2012), 113-133.
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[40] S. Zeng and W. Su,Intuitionistic fuzzy ordered weighted distance operator, Knowledge-Based Systems,24 (2011), 1224-1232.
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[41] H. J. Zimmermann and P. Zysno,Latent connectives in human decision making, Fuzzy Sets and ystems, 4 (1980), 37-51.
41
ORIGINAL_ARTICLE
FUZZY GOAL PROGRAMMING TECHNIQUE TO SOLVE
MULTIOBJECTIVE TRANSPORTATION PROBLEMS WITH
SOME NON-LINEAR MEMBERSHIP FUNCTIONS
The linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conicting in nature. This paper presents an application of fuzzy goal programming to the linear multiobjective transportation problem. In this paper, we use a special type of nonlinear (hyperbolic and exponential) membership functions to solve multiobjective transportation problem. It gives an optimal compromise solution. The obtained result has been compared with the solution obtained by using a linear membership function. To illustrate the methodology some numerical examples are presented.
http://ijfs.usb.ac.ir/article_155_3287502ac100353886714e75cecddc84.pdf
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10.22111/ijfs.2013.155
Multiobjective decision making
Goal programming
Transportation
problem
Membership function
Fuzzy programming
Maryam
Zangiabadi
zangiabadi-m@sci.sku.ac.ir
true
1
Department of Applied Mathematics, Faculty of Mathematical
Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran
Department of Applied Mathematics, Faculty of Mathematical
Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran
Department of Applied Mathematics, Faculty of Mathematical
Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran
LEAD_AUTHOR
Hamid Reza
Maleki
maleki@sutech.ac.ir
true
2
Department of Basic Sciences, Shiraz University of Technology,
Shiraz, Iran
Department of Basic Sciences, Shiraz University of Technology,
Shiraz, Iran
Department of Basic Sciences, Shiraz University of Technology,
Shiraz, Iran
AUTHOR
[1] W. F. Abd El-Wahed and S. M. Lee,Interactive fuzzy goal programming for multi-objective transportation problems, Omega, 34 (2006), 158-166.
1
[2] R. S. Aenaida and N. W. Kwak,A linear goal programming for transshipment problems with exible supply and demand constraints, Fuzzy Sets and Systems, 45 (1994), 215-224.
2
[3] A. K. Bit, M. P. Biswal and S. S. Alam,Fuzzy programming approach to multicriteria decision making transportation problem, Fuzzy Sets and Systems, 50 (1992), 135-141.
3
[4] J. Brito, J. A. Moreno and J. L. Verdegay,Transport route planning models based on fuzzy approach, Iranian Journal of Fuzzy Systems, 9(1) (2012), 141{158.
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[5] S. Chanas and D. Kuchta,A concept of the optimal solution of the transportation problem with fuzzy cost coecients, Fuzzy Sets and Systems, 28(1996), 299-305.
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[6] A. Charnes and W. W. Cooper,Management models and industrial applications of linear programming, Wiley, New York, 1961.
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[7] A. Charnes, W. W. Cooper and A. Henderson,An introduction to linear programming, Wiley,New York, 1953.
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[8] J. Current and H. Min,Multiobjective design of transportation networks: taxonomy and annotation, European J. Oper. Res., 26 (1986), 187-201.
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[9] G. B. Dantzig,Linear programming and extensions, Princeton University Press, Princeton,N J, 1963.
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[10] A. K. Dhingra and H. Moskowitz,Application of fuzzy theories to multiple objective decision making in system design, European J. Oper. Res., 55 (1991), 348-361.
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[11] J. A. Diaz,Solving multiobjective transportation problem, Ekonom.-Mat. Obzor., 14 (1978),267-274.
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[12] J. A. Diaz,Finding a complete description of all ecient solutions to a multiobjective trans-portation problem, Ekonom.-Mat. Obzor., 15(1979), 62-73.
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[13] W. Edwards,How to use multiattribute utility measurement for social decision making, IEEE Trans. Systems Man Cybernet.,7 (1977), 326-340.
13
[14] A. Gupta and G. W. Evans,A goal programming model for the operation of closed-loop supply chains, Engineering Optimization, 41 2009), 713-735.
14
[15] E. L. Hannan,On fuzzy goal programming, Decision Sci., 12 (1981), 522-531.
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[16] H. Hassanpour, H. R. Maleki and M. A. Yaghoobi,uzzy linear regression model with crisp coecients: a Goal programming appproach, Iranian Journal of Fuzzy Systems, 7(2) (2010),19-39.
16
[17] ] F. L. Hitchcock,The distribution of a product from several sources to numerous localities,J. Math. Phys.,20 (1941), 224-230.
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[18] H. Isermann,The enumeration of all ecient solutions for a linear multiobjective trans portation problem, Naval Res. Logist. Quart., 2 (1979), 123-139.
18
[19] F. Jimenez and J. L. Verdegay,Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach, European Journal of Operational Research, 117 (1999),485-510.
19
[20] Amarpreet Kaur and Amit Kumar,A new method for solving fuzzy transportation problems using ranking function, Applied Mathematical Modelling, 35 (2011), 5652-5661.
20
[21] ] H. Leberling,On nding compromise solutions for multicriteria problems using the fuzzy minoperator, Fuzzy Sets and Systems, 6 (1981), 105-118.
21
[22] S. M. Lee and L. J. Moore,Optimizing transportation problems with multiple objectives,AIEE Transactions,5 (1973), 333-338.
22
[23] L. S. Li and K. K. Lai,A fuzzy approach to the multiobjective transportation problem, Computers and Operations Research,27 2000), 43-57.
23
[24] R. H. Mohamed,The relationship between goal programming and fuzzy programming, Fuzzy Sets and Systems,89 (1997), 215-222.
24
[25] B. B. Pal, B. N. Moitra and U. Maulik,A goal programming procedure for fuzzy multiobjectivelinear programming problem, Fuzzy Sets and Systems, 139(2003), 395-405.
25
[26] D. Peidro and P. Vasant,Transportation planning with modi ed s-curve membership functions using an interactive fuzzy multi-objective approach, Applied Soft Computing, 11 2011),2656-2663.
26
[27] J. L. Ringuest and D. B. Rinks,Interactive solutions for the linear multiobjective transportation problem, European J. Oper. Res., 32(1987), 96{106.
27
[28] M. Sakawa,Fuzzy sets and interactive multiobjective optimization, Plenum Press, New York,1993.
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[29] R. N. Tiwari, S. Dharmar and J. R. Rao,Fuzzy goal programming-an additive model, Fuzzy Sets and Systems,24(1987), 27-34.
29
[30] R. Verma, M. P. Biswal and A. Biswas,Fuzzy programming technique to solve multi bjectivetransportation problem with some non-linear membership functions , Fuzzy Sets and Systems, 91(1997), 37 43.
30
[31] M. A. Yaghoobi and M. Tamiz,A short note on the relationship between goal programming and fuzzy programming for vectormaximum problems, Iranian Journal of Fuzzy Systems,2(2)(1979), 31-36.
31
[32] M. Zangiabadi and H. R. Maleki,Fuzzy goal programming for multiobjective transportation problems, J. Appl. Math. and Computing, 24(1-2) (2007), 449-460.
32
[33] H. J. Zimmermann,Application of fuzzy set theory to mathematical programming, Information Sciences, 36 (1985), 29-58.
33
ORIGINAL_ARTICLE
MINIMIZATION OF DETERMINISTIC FINITE AUTOMATA
WITH VAGUE (FINAL) STATES AND INTUITIONISTIC
FUZZY (FINAL) STATES
In this paper, relations among the membership values of gener- alized fuzzy languages such as intuitionistic fuzzy language, interval-valued fuzzy language and vague language are studied. It will aid in studying the properties of one language when the properties of another are known. Further, existence of a minimized nite automaton with vague ( final) states for any vague regular language recognized by a nite automaton with vague ( final) states is shown in this paper. Finally, an ecient algorithm is given for minimizing the nite automaton with vague ( final) states. Similarly, it can be shown for intuitionistic fuzzy regular language. These may contribute to a better understanding of the role of nite automaton with vague ( final) states or the nite automaton with intuitionistic fuzzy ( final) states while studying lexical analysis, decision making etc.
http://ijfs.usb.ac.ir/article_164_8f88d3102db5acd9349513069a44355a.pdf
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88
10.22111/ijfs.2013.164
Intuitionistic fuzzy regular language
Interval-valued fuzzy regular
language
Vague regular language
Finite automaton with vague (final) states
Finite automaton
with intuitionistic fuzzy (nal) states
Myhill-Nerode theorem
Alka
Choubey
alka.choubey@jiit.ac.in, alka.choubey@gmail.com
true
1
Mathematics Department, Jaypee Institute of Information Technol-
ogy, A-10, Sector-62, Noida-201307 (U. P.), India
Mathematics Department, Jaypee Institute of Information Technol-
ogy, A-10, Sector-62, Noida-201307 (U. P.), India
Mathematics Department, Jaypee Institute of Information Technol-
ogy, A-10, Sector-62, Noida-201307 (U. P.), India
LEAD_AUTHOR
K. M.
Ravi
rv.km19@gmail.com, rv km@yahoo.com
true
2
Department of Mathematics, JSS Academy of Technical Education, C-
20/1, Sector-62, Noida-201301 (U. P), India
Department of Mathematics, JSS Academy of Technical Education, C-
20/1, Sector-62, Noida-201301 (U. P), India
Department of Mathematics, JSS Academy of Technical Education, C-
20/1, Sector-62, Noida-201301 (U. P), India
AUTHOR
[1] K. T. Atanassov,Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87{96.
1
[2] K. T. Atanassov,More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33(1989), 37{45.
2
[3] K. T. Atanassov and G. Gargov,Interval valued intuitionistic fuzzy sets , Fuzzy Sets and Systems,31 (1989), 343{349.
3
[4] H. Bustince and P. Burillo,Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems,79(1996), 403{405.
4
[5] A. Choubey and K. M. Ravi,Intuitionistic fuzzy automata and intuitionistic fuzzy regular expressions, Jr. Appl. Math. & Informatics, 27(1-2) (2009), 409{417.
5
[6] A. Choubey and K. M. Ravi,Vague Regular Language, Advances in Fuzzy Mathematics,4(2)(2009), 147{165.
6
[7] W. L. Gau and D. J. Buchrer,Vague sets, IEEE Transactions on Systems, Man, and Cybernetics,23(2) h/April 1993), 610{614.
7
[8] M. B. Gorzalczany,A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems, 21 (1987), 1{17.
8
[9] J. E. Hopcroft and J. D. Ullman,Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 1979.
9
[10] M. Horry and M. M. Zahedi,Hypergroups and general fuzzy automata, Iranian Journal of Fuzzy Systems, 6(2) (2009), 61-74.
10
[11] M. Horry and M. M. Zahedi,On general fuzzy recognizers, Iranian Journal of Fuzzy Systems,8(3)(2011), 125-135.
11
[12] E. T. Lee and L. A. Zadeh,Note on fuzzy languages, Information Sciences, 1 (1969), 421{434.
12
[13] H. S. Lee,Minimizing fuzzy nite automata , Fuzzy Systems, FUZZ IEEE 2000. The Ninth IEEE International Conference on,1 (2000), 65{70.
13
[14] D. S. Malik and J. N. Mordeson,Fuzzy Automata and Languages: Theory and Applications, Chapman Hall, CRC Boca Raton, London, New York, Washington DC, 2002.
14
[15] A. Mateescu, A. Salomaa, K. Salomaa and S. Yu,Lexical Analysis with a Simple FiniteFuzzy-Automaton Model, Jr. Of Uni.Comp. Sci, 1(5) (1995), 292{311.
15
[16] M. Nikolova, N. Nikolova, C. Cornelis and G. Deschrijvier, Survey of the research on intuitionistic fuzzy sets, Advanced studies in Contemporary Mathematics, 4(2) (2002), 127{157.
16
[17] K. M. Ravi and A. Choubey,Intuitionistic fuzzy regular language, Proceedings of International Conference on Modelling and Simulation, CITICOMS 2007, ISBN. No. 81{8424{218{2,(2007), 659{664.
17
[18] K. M. Ravi and A. Choubey,Interval-valued fuzzy regular language, Jr. Appl. Math. &Informatics,28(3-4) (2010), 639{649.
18
[19] L. A. Zadeh,Fuzzy Sets, Information And Control, 8 (1965), 338{353.
19
ORIGINAL_ARTICLE
On the Diagram of One Type Modal Operators on Intuitionistic fuzzy
sets: Last expanding with $Z_{alpha ,beta }^{omega ,theta
Intuitionistic Fuzzy Modal Operator was defined by Atanassov in cite{at3}in 1999. In 2001, cite{at4}, he introduced the generalization of thesemodal operators. After this study, in 2004, Dencheva cite{dencheva} definedsecond extension of these operators. In 2006, the third extension of thesewas defined in cite{at6} by Atanassov. In 2007,cite{gc1}, the authorintroduced a new operator over Intuitionistic Fuzzy Sets which is ageneralization of Atanassov's and Dencheva's operators. At the same year,Atanassov defined an operator which is an extension of all the operatorsdefined until 2007. The diagram of One Type Modal Operators onIntuitionistic Fuzzy Sets was introduced first in 2007 by Atanassovcite{at10}. In 2008, Atanassov defined the most general operator and in2010 the author expanded the diagram of One Type Modal Operators onIntuitionistic Fuzzy Sets with the operator $Z_{alpha ,beta }^{omega }$.Some relationships among these operators were studied by several researchers%cite{at5}-cite{at8} cite{gc1}, cite{gc3}, cite{dencheva}- cite%{narayanan}.The aim of this paper is to expand the diagram of one type modal operatorsover intuitionistic fuzzy sets . For this purpose, we defined a new modaloparator $Z_{alpha ,beta }^{omega ,theta }$ over intuitionistic fuzzysets. It is shown that this oparator is the generalization of the operators$Z_{alpha ,beta }^{omega },E_{alpha ,beta },boxplus _{alpha ,beta},boxtimes _{alpha ,beta }.$
http://ijfs.usb.ac.ir/article_166_54fe632cc30a351a943cae82a4dd7742.pdf
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89
106
10.22111/ijfs.2013.166
Modal operator
$Z_{alpha
beta }^{omega
theta }$ operator
Modal operator diagram
g.
cuvalcioglu
gcuvalcioglu@mersin.edu.tr
true
1
department of mathematics, university of mersin, ciftlikkoy, 33016,
mersin turkey
department of mathematics, university of mersin, ciftlikkoy, 33016,
mersin turkey
department of mathematics, university of mersin, ciftlikkoy, 33016,
mersin turkey
LEAD_AUTHOR
bibitem{at1} K. T. Atanassov, emph{Intuitionistic fuzzy sets}, VII ITKR's Session,
1
Sofia, June 1983.
2
bibitem{at2} K. T. Atanassov, emph{Intuitionistic fuzzy sets}, Fuzzy Sets and
3
Systems, textbf{20} (1986), 87-96.
4
bibitem{at3} K. T. Atanassov, emph{Intuitionistic fuzzy sets}, Phiysica-Verlag,
5
Heidelberg, NewYork, 1999.
6
bibitem{at4} K. T. Atanassov, emph{Remark on two operations over intuitionistic
7
fuzzy sets,} Int. J. of Unceratanity, Fuzzyness and Knowledge Syst.,
8
textbf{9(1)} (2001), 71-75.
9
bibitem{at5} K. T. Atanassov, emph{On the type of intuitionistic fuzzy modal
10
operators}, NIFS, textbf{11(5)} (2005), 24-28.
11
bibitem{at6} K. T. Atanassov, emph{The most general form of one type of
12
intuitionistic fuzzy modal operators}, NIFS, textbf{12(2)} (2006), 36-38.
13
bibitem{at7} K. T. Atanassov, emph{Some properties of the operators from one type
14
of intuitionistic fuzzy modal operators}, Advanced Studies on Contemporary
15
Mathematics, textbf{15(1)} (2007), 13-20.
16
bibitem{at8} K. T. Atanassov, emph{The most general form of one type of
17
intuitionistic fuzzy modal operators, part 2}, NIFS, textbf{14(1)} (2008), 27-32.
18
bibitem{at9} K.T. Atanassov, emph{Theorem for equivalence of the two most
19
general intuitionistic fuzzy modal operators}, NIFS, textbf{15(1)}(2008), 26-31.
20
bibitem{at10} K. T. Atanassov, emph{25 years of intuitionistic fuzzy sets, or:
21
the most important results and mistakes of mine}, 7 th Int. workshop on IFSs
22
and gen. nets. , Poland, 2008.
23
bibitem{gc1} G. c{C}uvalci ou{g}lu, emph{Some properties of $E_{alpha
24
,beta }$ operator}, Advanced Studies on Contemporary Mathematics, textbf{14(2)} (2007), 305-310.
25
bibitem{gc2} G. c{C}uvalci ou{g}lu, emph{Expand the modal operator diagram
26
with $Z_{alpha ,beta }^{omega },$}, Proc. Jangjeon Math. Soc., textbf{13(3)} (2010), 403-412
27
bibitem{gc3} G. c{C}uvalci ou{g}lu, S. Yi lmaz, emph{Some properties of
28
OTMOs on IFSs, Advanced Studies on Contemporary Mathematics}, textbf{14(2)} (2010),
29
bibitem{dencheva} K. Dencheva, emph{Extension of intuitionistic fuzzy modal
30
operators $boxplus $ and $boxtimes ,$}, Proc.of the Second Int. IEEE Symp.
31
Intelligent systems, Varna, June 22-24, textbf{3} (2004), 21-22.
32
bibitem{doycheva} B. Doycheva, emph{Inequalities with intuitionistic fuzzy
33
topological and G"{o}khan c{C}uvalci ou{g}lu's operators}, NIFS, textbf{14(1)} (2008), 20-22.
34
bibitem{hasan} A. Hasankhani, A. Nazari and M. Saheli, emph{Some properties of
35
fuzzy Hilbert spaces and norm of operators}, Iranian Journal of Fuzzy Systems,
36
textbf{7(3)} (2010), 129-157.
37
bibitem{li} D. Li, F. Shan and C. Cheng, emph{On properties of four IFS
38
operators}, Fuzzy Sets and Systems, textbf{154} (2005), 151-155.
39
bibitem{luo} X. Luo and J. Fang, emph{Fuzzifying closure systems and closure
40
operators}, Iranian Journal of Fuzzy Systems, textbf{8(1)} (2011), 77-94.
41
bibitem{narayanan} A. Narayanan, S. Vijayabalaji and N. Thillaigovindan, emph{Intuitionistic fuzzy bounded linear operators}, Iranian Journal of Fuzzy Systems, textbf{4(1)} (2007), 89-101.
42
bibitem{zadeh} L. A. Zadeh, emph{Fuzzy sets}, Information and Control, textbf{8} (1965) ,
43
ORIGINAL_ARTICLE
FUZZY INTEGRO-DIFFERENTIAL EQUATIONS: DISCRETE
SOLUTION AND ERROR ESTIMATION
This paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. Then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. Finally an example is given to illustrate the performance of the methods.
http://ijfs.usb.ac.ir/article_169_4d7ef7b69c85251841a56ba41099c819.pdf
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107
122
10.22111/ijfs.2013.169
Fuzzy integro-differential equation
Discrete solution
Fuzzy quadrature
rule
Masoumeh
Zeinali
zeynali@tabrizu.ac.ir
true
1
Faculty of mathematical sciences, University of Tabriz, Tabriz,
Iran
Faculty of mathematical sciences, University of Tabriz, Tabriz,
Iran
Faculty of mathematical sciences, University of Tabriz, Tabriz,
Iran
AUTHOR
Sedaghat
Shahmorad
shahmorad@tabrizu.ac.ir
true
2
Faculty of mathematical sciences, University of Tabriz, Tabriz,
Iran
Faculty of mathematical sciences, University of Tabriz, Tabriz,
Iran
Faculty of mathematical sciences, University of Tabriz, Tabriz,
Iran
LEAD_AUTHOR
Kamal
Mirnia
mirnia-kam@tabrizu.ac.ir
true
3
Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran
Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran
Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran
AUTHOR
[1] S. Abbasbandy and T. Allahviranloo,Numerical solution of fuzzy differential equation by Runge-Kutta method, Nonlinear Stud., 11 (2004), 117-129.
1
[2] S. Abbasbandy and T. Allahviranloo,The adomian decomposition method applied to the fuzzy system of Fredholm integral equations of the second kind, Int. J. Uncertain. Fuzziness Knowl.-Based Syst.,14(1) 2006), 101-110.
2
[3] T. Allahviranloo and M. Afshar Kermani, Numerical methods for fuzzy linear partial differential equations under new definition for derivative, Iranian journal of fuzzy systems, 7(2010), 33-50.
3
[4] E. Babolian, H. Sadeghi and S. Javadi, Numerically solution of fuzzy differential equations by Adomian method, Appl. Math. Comput., 149 (2004), 547-557.
4
[5] K. Balachandran and K. Kanagarajan, Existence of solutions of general nonlinear fuzzy Volterra-Fredholm integral equations, J. Appl. Math. Stochast. Anal., 3 (2005), 333-343.
5
[6] K. Balachandran and P. Prakash,Existence of solutions of nonlinear fuzzy integral equations in Banach spaces, Libertas Math., 21 (2001), 91-97.
6
[7] K. Balachandran and P. Prakash, Existence of solutions of nonlinear fuzzy Volterra-Fredholm integral quations , Indian J. Pure Appl. Math., 33(3) (2002), 329-343.
7
[8] B. Bede and S. G. Gal,Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151 (2005),581-599.
8
[9] B. Bede and S. G. Gal,Qudrature rules for integrals of fuzzy-number-valued functions, Fuzzy Sets and systems,145 (2004), 359-380.
9
[10] A. M. Bica,Error estimation in the approximation of the solution of nonlinear fuzzy Fredholm integral equations, Information Sciences, 178 (2008), 1279-1292.
10
[11] M. Friedman, M. Ma and A. Kandel, Numerical solutions of fuzzy differential and integral equations, Fuzzy Sets and Systems, 106(1999), 35-48.
11
[12] M. Friedmann, M Ming and A. Kandel, Solution to fuzzy integral equations with arbitrary kernels, Int. J. Approx. Reason., 20 (1999), 249-262.
12
[13] R. Goetschel and W. Voxman,Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986),31-43.
13
[14] W. Hackbusch, Integral equations: theory and numerical treatment, Birkhuser Verlag, Basel,1995.
14
[15] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24 (1987), 301-317.
15
[16] O. Kaleva,The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems, 35(1990), 389-96.
16
[17] V. Lakshmkanihtan and R. N. Mohapatra, Theory of fuzzy differential equations and inclusions,Taylor and Francis, London, 2003.
17
[18] V. Lakshmkanihtan, K. N. Murty and J. Turner,Two point boundary value problems associated with nonlinear fuzzy differential equations, Math. Inequal. Appl., 4 (2003), 527-533.
18
[19] M. Ma , M. Friedman and Abraham Kandel, Numerical solutions of fuzzy differential equations,Fuzzy Sets and Systems,105 (1999), 133-138.
19
[20] A. Molabahrami, A. Shidfar and A. Ghyasi, An analytical method for solving linear Fredholmfuzzy integral equations of the second kind, Computers and Mathematics with applications,61(2011), 2754-2761.
20
[21] J. J. Nieto,The Cauchy problem for continuous fuzzy differential equations, Fuzzy Sets and Systems,102 999), 259-262.
21
[22] D. O’Regan, V. Lakshmikantham and J. J. Nieto,Initial and boundary value problems for fuzzy differential equations, Nonlinear Anal., 54 (2003), 405-415.
22
[23] J. Y. Parka and J. U. Jeong,
23
A note on fuzzy integral equations
24
, Fuzzy Sets and Systems,
25
(1999), 193-200.
26
[24] P. Prakash, J. J. Nieto, J. H. Kim and R. Rodriguez-Lopez,
27
Existence of solutions of fuzzy
28
neutral differential equations in Banach spaces
29
, Dyn. Syst. Appl., 14(3-4)
30
(2005), 407-417.
31
[25] M. Puri and D. Ralescu,
32
Differentials of fuzzy functions, J. Math. Anal. Appl., 91
33
[26] O. Solaymani Fard, A. Esfahani and A. Vahidian Kamyad,
34
On solution of a class of fuzzy
35
, Iranian journal of fuzzy systems, 9
36
(2012), 49-60.
37
[27] P. V. Subrahmanyam and S. K. Sudarsanam,
38
A note on fuzzy Volterra integral equations
39
Fuzzy Sets and Systems,
40
(1996), 237-240.
41
[28] C. Wu and Z. Gong,
42
On Henstock integral of fuzzy-number-valued functions I
43
, Fuzzy Sets
44
and Systems,
45
(2001), 523-532.
46
[29] C. Wu and M. Ma,
47
Existence theorem to the Cauchy problem of fuzzy differential equations
48
under compactness-type conditions
49
, Information Sciences, 108
50
(1998), 123-134.
51
ORIGINAL_ARTICLE
SET-NORM EXHAUSTIVE SET MULTIFUNCTIONS
In this paper we present some properties of set-norm exhaustive set multifunctions and also of atoms and pseudo-atoms of set multifunctions taking values in the family of non-empty subsets of a commutative semigroup with unity.
http://ijfs.usb.ac.ir/article_170_2bb1c36480ee857421fd93fd71dde045.pdf
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123
134
10.22111/ijfs.2013.170
Set-norm
Exhaustive
Continuous
Null-null-additive
Atom
Pseudo-
atom
Anca
Croitoru
croitoru@uaic.ro
true
1
Faculty of Mathematics, "A.I. Cuza" University, Bd. Carol I, no 11,
Iasi-700506, Romania
Faculty of Mathematics, "A.I. Cuza" University, Bd. Carol I, no 11,
Iasi-700506, Romania
Faculty of Mathematics, "A.I. Cuza" University, Bd. Carol I, no 11,
Iasi-700506, Romania
AUTHOR
Alina
Gavrilut
gavrilut@uaic.ro
true
2
Faculty of Mathematics, "A.I. Cuza" University, Bd. Carol I, no
11, Iasi-700506, Romania
Faculty of Mathematics, "A.I. Cuza" University, Bd. Carol I, no
11, Iasi-700506, Romania
Faculty of Mathematics, "A.I. Cuza" University, Bd. Carol I, no
11, Iasi-700506, Romania
LEAD_AUTHOR
[1] S. Asahina, K. Uchino and T. Murofushi,Relationship among continuity conditions and nulladditivity ditions in non-additive measure theory, Fuzzy Sets and Systems, 157 (2006),691-698.
1
[2] R. J. Aumann and L. S. Shapley,Values of non-atomic games, Princeton University Press,Princeton, New Jersey, 1974.
2
[3] I. Chitescu,Finitely purely atomic measures: coincidence and rigidity properties, Rendiconti del Circolo Matematico di Palermo, Serie II, Tomo L, (2001), 455-476.
3
[4] G. Choquet,Theory of capacities, Ann. Inst. Fourier (Grenoble), 5 (1953-1954), 131-292.
4
[5] A. Croitoru,Set-norm continuity of set multifunctions, ROMAI Journal, 6 (2010), 47-56.
5
[6] A. Croitoru, A. Gavrilut, N. E. Mastorakis and G. Gavrilut On dierent types of non-additiveset multifunctions,WSEAS Transactions on Mathematics, 8 (2009), 246-257.
6
[7] A. Daneshgar and A. Hashemi,Fuzzy sets from a meta-system-theoretic point of view, Iranian Journal of Fuzzy Systems,3(2) (2006), 1-20.
7
[8] A. P. Dempster,Upper and lower probabilities induced by a multivalued mapping, Ann. Mat.Statist.,38(1967), 325-339.
8
[9] D. Denneberg,Non-additive Measure and Integral, Kluwer Academic Publishers, Dorrecht/Boston/London, 1994.
9
[10] L. Drewnowski,Topological rings of sets, continuous set functions. Integration, I, II, III,Bull. Acad. Polon. Sci. Ser. Math. Astron. Phy, s20(1972), 269-286.
10
[11] D. Dubois and H. Prade, Fuzzy sets and systems. Theory and applications, Academic Press,New York, 1980.
11
[12] T. Funiokova,LK-Interior systems of "almost open" L-sets, Iranian JournaL of Fuzzy Systems,4(2)(2007), 47{55.
12
[13] A. Gavrilut,Non-atomicity and the Darboux property for fuzzy and non-fuzzy Borel/Bairemultivalued set functions, Fuzzy Sets and Systems, 160 2009), 1308-1317.
13
[14] A. Gavrilut and A. Croitoruon-atomicity for fuzzy and non-fuzzy multivalued set functions,Fuzzy Sets and Systems,160(2009), 2106-2116.
14
[15] A. Gavrilut and A. Croitoru, Pseudo-atoms and Darboux property for set multifunction,Fuzzy Sets and Systems,(2010), 2897-2908.
15
[16] J. Li,On Egoro theorem on fuzzy measure spaces, Fuzzy Sets and Systems, 135 (2003),367-375.
16
[17] F. Merghadi and A. Aliouche,A related xed point theorem in n fuzzy metric spaces, Iranian Journal of Fuzzy Systems,7(3) (2010), 73-86.
17
[18] E. Pap,Null-additive set functions, Kluwer Academic Publishers, Dordrecht, 1995.
18
[19] A. M. Precupanu,On the set valued additive and subadditive set functions, An. St. UniIa29(1984), 41-48.
19
[20] G. Shafer,A Mathematical theory of evidence, Princeton University Press, Princeton, N. J.,1976.
20
[21] M. Sugeno,Theory of fuzzy integrals and its applications, PhD. Thesis, Tokyo Institute ofTechnology, 1974.
21
[22] H. Suzuki,Atoms of fuzzy measures and fuzzy integrals, Fuzzy Sets and Systems, 41 (1991),329-342.
22
[23] S. M. Vaezpour and F. Karini,t-Best approximation in fuzzy normed spaces, Iranian Journal of Fuzzy Systems,5(2) (2008), 93-99.
23
[24] G. F. Wen, F. G. Shi and H.Y. Li,Almost S-compactness in L-topological spaces, Iranian Journal of Fuzzy Systems,5(3) (2008), 31-44.
24
[25] C. Wu and S. Bo,Pseudo-atoms of fuzzy and non-fuzzy measures , Fuzzy Sets and Systems,1582007), 1258-1272.
25
[26] L. A. Zadeh,Fuzzy sets, Information and Control, 8 (1965), 338{353.
26
ORIGINAL_ARTICLE
APPROXIMATE FIXED POINT IN FUZZY NORMED SPACES
FOR NONLINEAR MAPS
We de ne approximate xed point in fuzzy norm spaces and prove the existence theorems, we also consider approximate pair constructive map- ping and show its relation with approximate fuzzy xed point.
http://ijfs.usb.ac.ir/article_173_1b3c8fc3ea44800472a6b09a730cd34d.pdf
2013-02-06T11:23:20
2018-05-25T11:23:20
135
142
10.22111/ijfs.2013.173
Fuzzy norm space
$F^z-$approximate
fixed point
Diameter $F^z$-approximate fixed point
S. A. M.
Mohseniailhosseini
amah@vru.ac.ir
true
1
Faculty of Mathematics, Vali-e-Asr University of Raf-
senjan, Rafsenjan, Iran
Faculty of Mathematics, Vali-e-Asr University of Raf-
senjan, Rafsenjan, Iran
Faculty of Mathematics, Vali-e-Asr University of Raf-
senjan, Rafsenjan, Iran
AUTHOR
H.
Mazaheri
hmazaheri@yazduni.ac.ir
true
2
Faculty of Mathematics, Yazd University, Yazd, Iran
Faculty of Mathematics, Yazd University, Yazd, Iran
Faculty of Mathematics, Yazd University, Yazd, Iran
LEAD_AUTHOR
M. A.
Dehghan
dehghan@vru.ac.ir
true
3
Faculty of Mathematics, Vali-e-Asr University of Rafsenjan, Raf-
senjan, Iran
Faculty of Mathematics, Vali-e-Asr University of Rafsenjan, Raf-
senjan, Iran
Faculty of Mathematics, Vali-e-Asr University of Rafsenjan, Raf-
senjan, Iran
AUTHOR
[1] I. Altun,Some xed point theorems for single and multivalued mappings on ordered nonarchimeden fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 7(1) (2008), 49-62.
1
[2] T. Bag and S. K. Samanta,Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math.,11(3) (2003), 687-705.
2
[3] T. Bag and S. K. Samanta,Fuzzy bounded linear operators, Fuzzy Sets and systems, 151(3)(2005), 513-547.
3
[4] T. Bag and S. K. Samanta,Some xed point theorems in fuzzy normed linear spaces, Information ciences, 177 (2007), 3271-3289.
4
[5] F. E. Browder,Nonexpansive nonlinear operators in a Banach spaces, Proc. Natl. Acad. Sci.USA,54 (1965), 1041-1044.
5
[6] M. Cancan,Browders xed point theorem and some interesting results in intuitionistic fuzzy normed spaces, Fixed Point Theory and Applications, Article ID 642303, 11 pages doi:10.1155/(2010)/642303, 2010.
6
[7] L. Cadariu and V. Radu,On the stability of the Cauchy functional equation: a xed point approach, in Iteration Theory, Grazer Math. Ber., Karl-Franzens-Universitaet, Graz, Austria,346(2004), 43-52.
7
[8] A. Chitra and P. V. Mordeson,Fuzzy linear operators and fuzzy normed linear spaces, Bull.Cal. Math. Soc.,74 (1969), 660-665.
8
[9] R. Espinola,A new approach to relatively nonexpansive mappings, Proc. Amer. Math. Soc.,136(6) (2008), 1987-1995.
9
[10] I. Golet,On fuzzy normed spaces, Southest Asia Bull. Math., 31(2) (2007), 245-254.
10
[11] M. Grabic,Fixed points in fuzzy metric spaces, Fuzzy Sets ans Systems, 27(3) (1988), 385-389.
11
[12] M. Marudai and P. Vijayaraju,Fixed point theorems for fuzzy mapping, Fuzzy Sets and Systems,135(3) (2003), 402-408.
12
[13] F. Merghadi and A. Aliouche,A related xed point theorem in n fuzzy metric spaces, Iranian Journal of Fuzzy Systems,7(3) (2010), 73-86.
13
[14] M. Ra and M. S. M. Noorani,Fixed point theorem on intuitionistic fuzzy metric space,Iranian Journal of Fuzzy Systems,3(1) (2006), 23-29.
14
[15] R. Saadati, S. M. Vaezpour and Y. J. Cho,Quicksort algorithm: application of a fixedpoint theorem in intuitionistic fuzzy quasi-metric spaces at a domain of words, Journal of Computational and Applied Mathematics,228(1) (2009), 219-225.
15
[16] Krishnapal Singh Sisodia, M. S. Rathore, Deepak Singh and Surendra Singh Khichi,A common xed point theorem in fuzzy metric spaces, Int. Journal of Math. Analysis, 5(17) (2011),819-826.
16
[17] T. Zikic,On xed point theorems of Gregori and Sapena, Fuzzy Sets and Systems, 144(3)(2004), 421-429.
17
ORIGINAL_ARTICLE
WEAK AND STRONG DUALITY THEOREMS FOR FUZZY
CONIC OPTIMIZATION PROBLEMS
The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality theorems are extended from crisp conic optimization problems to fuzzy ones.
http://ijfs.usb.ac.ir/article_174_7ccb2ebf7e64971e3e0a4c7c1dd909f7.pdf
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143
152
10.22111/ijfs.2013.174
Fuzzy conic optimization problem
Fuzzy number
Weak and strong
duality theorems
B.
Farhadinia
bfarhadinia@yahoo.com.au
true
1
Department of Mathematics, Quchan Institute of Engineering and
Technology, Iran,
Department of Mathematics, Quchan Institute of Engineering and
Technology, Iran,
Department of Mathematics, Quchan Institute of Engineering and
Technology, Iran,
LEAD_AUTHOR
A. V.
Kamyad
kamyad@math.um.ac.ir
true
2
Department of Mathematics, Ferdowsi University of Mashhad, Iran,
Department of Mathematics, Ferdowsi University of Mashhad, Iran,
Department of Mathematics, Ferdowsi University of Mashhad, Iran,
AUTHOR
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1
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2
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[8] N. Javadian, Y. Maali and N. Mahdavi-Amiri,Fuzzy linear programming with grades of satisfaction in constraints, Iranian Journal of Fuzzy Systems, 6 (2009), 17{35.
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[9] V. Jeykumar and X. Q. Yang,On characterizing the solution sets of pesudolinear programs,J. O. T. A.,87(1995), 747{755.
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[10] A. Kaufmann and L. A. Zadeh,Theory of fuzzy subsets, New York, San Francisco, London,1975.
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[11] D. Luenberger,Optimization by vector space methods, New York, Wiley, 1969.
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[12] N. Mahdavi-Amiri and S. H. Nasseri,Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables Sets and Systems, 158(2007),1961{1978.
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[13] S. K. Mishra, S. Y. Wang and K. K. Lai,Explicitly B-preinvex fuzzy mappings, Int. J.Computer Math.,83 (2006), 39{47.
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[14] S. Nanda and K. Kar,Convex fuzzy mapping, Fuzzy Sets and Systems, 48 (1992), 129{132.
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[15] J. Ramik,Duality theory in fuzzy linear programming: some new concepts and results, Fuzzy Optim. and Decision Making,4 (2005), 25{39.
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[16] W. Rodder and H. J. Zimmermann,Duality in fuzzy linear programming, In: Internat. Symp.on Extremal Methods and Systems Analysis, University of Texas at Austin, (1977), 415{427.
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[17] Y. R. Syau,Generalization of preinvex and B-vex fuzzy mappings, Fuzzy Sets and Systems,120(2001), 533{542.
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[18] Y. R. Syau, L. Jia and E. S. Lee,-1concavity and fuzzy multiple objective decision making,Computers and Mathematics with Applications,55 (2008), 1181{1188.
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[19] J. L. Verdegay,A dual approach to solve the fuzzy linear programming problems, Fuzzy Sets and systems,14 (1984), 131{141.
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[20] H. C. Wu,Duality theory in fuzzy linear programming problems with fuzzy coecients, Fuzzy Optim. and Decision Making,2(2003), 61{73.
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[21] C. Zalinescu,Convex analysis in general vector spaces, Word Scienti c, 2002.
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[22] C. Zhang, X. H. Yuan and E. S. Lee,Duality theory in fuzzy mathematical programming problems with fuzzy coecien, Computers and Mathematics with Applications, 49(2005),1709{1730.
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ORIGINAL_ARTICLE
Persian-translation vol. 10, no. 1, February 2013
http://ijfs.usb.ac.ir/article_2724_70b945a70f7f7d14a5f622dc8b8f9e14.pdf
2013-03-02T11:23:20
2018-05-25T11:23:20
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10.22111/ijfs.2013.2724