A solid transportation problem with type-2 fuzzy variables |
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Affiliation: | 1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, West Bengal, India;2. Department of Engineering Science, Haldia Institute of Technology, Haldia, Purba Midnapore 721657, West Bengal, India |
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Abstract: | This paper focuses on generating the optimal solutions of the solid transportation problem under fuzzy environment, in which the supply capacities, demands and transportation capacities are supposed to be type-2 fuzzy variables due to the instinctive imprecision. In order to model the problem within the framework of the credibility optimization, three types of new defuzzification criteria, i.e., optimistic value criterion, pessimistic value criterion and expected value criterion, are proposed for type-2 fuzzy variables. Then, the multi-fold fuzzy solid transportation problem is reformulated as the chance-constrained programming model with the least expected transportation cost. To solve the model, fuzzy simulation based tabu search algorithm is designed to seek approximate optimal solutions. Numerical experiments are implemented to illustrate the application and effectiveness of the proposed approaches. |
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Keywords: | Fuzzy sets Fuzzy possibility space Type-2 fuzzy variable Solid transportation problem |
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