Decomposition of the fuzzy parametric space in multiobjective nonlinear programming problems |
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| Institution: | 1. Wuchang Institute of Technology, Wuhan, China;2. Department of Computer Science and Engineering, European University Cyprus, Nicosia 1516, Cyprus;3. CIICESI-ESTG, Politécnico do Porto, 4610-156 Felgueiras, Portugal;4. Mathematics-Computer Department, Art-Science Faculty, Eskişehir Osmangazi University, Eskişehir, Turkey;5. Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia;6. Department of Mathematics and Statistics, Washington State University, Pullman, WA 99163, USA;7. Jabalia Camp, United Nations Relief and Works Agency (UNRWA) Palestinian Refugee Camp, Gaza Strip Jabalya, Palestine;8. Department of Computer Engineering, Faculty of Engineering and Architecture, Kastamonu University, Kastamonu, Turkey |
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| Abstract: | This paper deals with a method for decomposing the fuzzy parametric space in multiobjective nonlinear programming problems using the generalized Tchebycheff norm. This approach is simpler than the corresponding one using the nonnegative weighted sum of objectives. Also, several results are introduced which relate two fuzzy programs with each other, one with fuzzy parameters in the constraints and the other with fuzzy parameters in both objective functions and constraints. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the decomposition of parametric space in multiobjective convex programs using the generalized Tchebycheff norm are reformulated to study under the concept of α-pareto optimality. Such results make the study of the first type of problems rather simple. Three illustrated examples are presented in the paper which clarify the developed theory. |
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