Interactive multiobjective fuzzy random programming through the level set-based probability model

Authors:
Hideki Katagiri;Masatoshi Sakawa
Affiliations:
Graduate School of Engineering, Hiroshima University, 1-4-1, Kagami-Yama, Higashi-Hiroshima, Hiroshima 739-8527, Japan;Graduate School of Engineering, Hiroshima University, 1-4-1, Kagami-Yama, Higashi-Hiroshima, Hiroshima 739-8527, Japan
Venue:
Information Sciences: an International Journal
Year:
2011

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Abstract

This paper considers a multiobjective linear programming problem involving fuzzy random variable coefficients. A new fuzzy random programming model is proposed by extending the ideas of level set-based optimality and a stochastic programming model. The original problem involving fuzzy random variables is transformed into a deterministic equivalent problem through the proposed model. An interactive algorithm is provided to obtain a satisficing solution for a decision maker from among a set of newly defined Pareto optimal solutions. It is shown that an optimal solution of the problem to be solved iteratively in the interactive algorithm is analytically obtained by a combination of the bisection method and the simplex method.