Paper:

# Interactive Decision Making for Fuzzy Random Multiobjective Linear Programming Problems with Variance Covariance Matrices Through Fractile Optimization

## Hitoshi Yano

School of Humanities and Social Sciences, Nagoya City University, 1 Yamanohata, Mizuho-cho, Mizuho-ku, Nagoya 467-8501, Japan

In this paper, we focus on fuzzy random multiobjective linear programming problems with variance covariance matrices through fractile optimization, and propose an interactive decision making method to obtain a satisfactory solution. In the proposed method, it is assumed that the decision maker has fuzzy goals for not only permissible probability levels but also the corresponding objective functions. Such fuzzy goals are quantified by eliciting the corresponding membership functions. Using the fuzzy decision, such two kinds of membership functions are integrated, and *D _{f}* -Pareto optimal solution concept is defined in the integrated membership space. By using the bisection method and the convex programming technique, a satisfactory solution is obtained from among a

*D*-Pareto optimal solution set through the interaction with the decision maker.

_{f}*J. Adv. Comput. Intell. Intell. Inform.*, Vol.18, No.3, pp. 383-390, 2014.

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