| Title of paper:
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Multiobjective intuitionistic fuzzy linear programming and its application in transportation model
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| Author(s):
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| Bablu Jana
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| Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah, West-Bengal, Pin 711103, India
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| Tapan Kumar Roy
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| Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah, West-Bengal, Pin 711103, India
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| Published in:
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"Notes on Intuitionistic Fuzzy Sets", Volume 13 (2007) Number 1, pages 34—51
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| Download:
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 PDF (365 Kb, File info)
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| Abstract:
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This paper presents a new Intuitionistic Fuzzy Optimization (IFO) approach to solve the a Multi-Objective Linear Programming Problem (MOLPP) under uncertainty. The idea is based on extension of fuzzy optimization. This approach is an application of the intuitionistic fuzzy set. First we have considered a multi-objective linear programming with equality and inequality constraints with Intuitionistic Fuzzy (IF) goals. Their fuzzy non-linear membership and non-membership function have been taken for the degree of rejection of objectives and constraints together with the degree of
satisfaction. Then it converts the said problem into a conventional linear programming problem. Finally we have showed application of this approach in the Capacitated Transportation Problem. Numerical examples are provided to illustrate our new approach.
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| Keywords:
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Fuzzy optimization, Intuitionistic fuzzy sets, Pareto optimal, Non-membership function, Capacitated transportation problem
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| References:
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- A. K. Bit, M. P. Biswal and S. S. Alam, “Fuzzy programming approach to multiobjective solid transportation problem.”, Fuzzy Sets and Systems 57 (1993) 183-194.
- 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.
- R. E. Bellman, L. A. Zadeh, “Decision making in a fuzzy environment.” Management Science 17 (1970) B141-B164.
- D. Chanas, “Fuzzy programming in multiobjective linear programming- a parametric approach”, Fuzzy Set and system 29 (1989) 303-313
- K. Atanassov, “Idea for intuitionistic fuzzy sets equation” Notes on Intuitionistic Fuzzy Sets, 1 (1995) 17-24.
- K. Atanassov, “Intuitionistic fuzzy sets”, Fuzzy sets and systems, 20 (1986) 87-96.
- K. Atanassov, “Two theorems for Intuitionistic fuzzy sets”, Fuzzy sets and systems, 110 (2000) 267-269.
- J. Kacprzyk, “A generalization of fuzzy multistage decision making and control via linguistic quantifiers” Internat. J. Control, 38(1983) 1249-1270.
- H. Rommelfanger, “Inequality relation in fuzzy constraint and its use in linear optimization” in:J.L. Verdegay and M. Delgado, Eds., The interface between artificial intelligence and operational research in fuzzy environment( Verlag TUV, Rheinland, Koln, 1989) 195-211.
- H. Tanaka and K. Asai, “Fuzzy linear programming problems with fuzzy numbers” Fuzzy sets and systems, 13(1984) 1-10.
- M. Sakawa, and H. Yano, “Interactive decision making for multi-objective linear fractional programming problems with fuzzy parameters.”, Cybernetics Systems 16 (1985) 377-394.
- M. Sakawa and H.Yano, “An interactive fuzzy satisfaction method for multiobjective non-linear programming problem with fuzzy parameters” Fuzzy sets and System, 30 (1989)221-238.
- H.J.Zimmermann, “Fuzzy sets – Theory and its application” (Kluwer, Dordrecht,1985).
- S. K. Das A. Goswami, S. S. Alam, “Multiobjective transportation problem with interval; cost, source and destination parameters.”, European Journal of Operational Research 117 (1999) 100-112.
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