Linear programming with fuzzy parameters: An interactive method resolution |
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Authors: | Mariano Jimé nez,Mar Arenas,Amelia Bilbao,M. Victoria Rodrı´ guez |
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Affiliation: | 1. Department of Applied Economy I, University of The Basque Country, Plaza Oñati 1. 20018-San Sebastián, Spain;2. Department of Quantitative Economy, University of Oviedo, Avda. del Cristo s/n. 33006-Oviedo, Spain |
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Abstract: | This paper proposes a method for solving linear programming problems where all the coefficients are, in general, fuzzy numbers. We use a fuzzy ranking method to rank the fuzzy objective values and to deal with the inequality relation on constraints. It allows us to work with the concept of feasibility degree. The bigger the feasibility degree is, the worst the objective value will be. We offer the decision-maker (DM) the optimal solution for several different degrees of feasibility. With this information the DM is able to establish a fuzzy goal. We build a fuzzy subset in the decision space whose membership function represents the balance between feasibility degree of constraints and satisfaction degree of the goal. A reasonable solution is the one that has the biggest membership degree to this fuzzy subset. Finally, to illustrate our method, we solve a numerical example. |
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Keywords: | Fuzzy sets Fuzzy linear programming Ranking fuzzy numbers Decision making |
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