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Interactive Fuzzy Programming for Random Fuzzy Two-Level Integer Programming Problems through Fractile Criteria with Possibility

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DOI: 10.4236/am.2013.48A006    4,093 Downloads   5,767 Views   Citations

ABSTRACT

This paper considers two-level integer programming problems involving random fuzzy variables with cooperative behavior of the decision makers. Considering the probabilities that the decision makers’ objective function values are smaller than or equal to target variables, fuzzy goals of the decision makers are introduced. Using the fractile criteria to optimize the target variables under the condition that the degrees of possibility with respect to the attained probabilities are greater than or equal to certain permissible levels, the original random fuzzy two-level integer programming problems are reduced to deterministic ones. Through the introduction of genetic algorithms with double strings for nonlinear integer programming problems, interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example demonstrates the feasibility and efficiency of the proposed method.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Sakawa and T. Matsui, "Interactive Fuzzy Programming for Random Fuzzy Two-Level Integer Programming Problems through Fractile Criteria with Possibility," Applied Mathematics, Vol. 4 No. 8A, 2013, pp. 34-43. doi: 10.4236/am.2013.48A006.

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