Paper:

# Multiobjective Random Fuzzy Linear Programming Problems Based on the Possibility Maximization Model

## Takashi Hasuike^{*}, Hideki Katagiri^{**}, and Hiroaki Ishii^{*}

^{*}Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan

^{**}Graduate School of Engineering, Hiroshima University, 1-4-1, Kagamiyama Higashi Hiroshima 739-8527, Japan

Two multiobjective random fuzzy programming problems considered based on the possibility maximization model using possibilistic and stochastic programming are not initially well defined due to the random variables and fuzzy numbers included. To solve them analytically, probability criteria are set for objective functions and chance constraints are introduced. Taking into account the decision maker’s subjectivity and the original plan’s flexibility, a fuzzy goal is introduced for each objective function. The original problems are then changed into deterministic equivalent problems to make the possibility fractile optimization problem equivalent to a linear programming problem. The possibility maximization problem for probability is changed into a nonlinear programming problem, and an analytical solution is constructed extending previous solution approaches.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.13, No.4, pp. 373-379, 2009.

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