Robust Expectation Optimization Model Using the Possibility Measure for the Fuzzy Random Programming Problem

2009 ◽  
pp. 285-294 ◽  
Author(s):  
Takashi Hasuike ◽  
Hiroaki Ishii
Keyword(s):  
Programming Problem ◽  
Optimization Model ◽  
Possibility Measure ◽  
Expectation Optimization ◽  
Fuzzy Random Programming ◽  
Fuzzy Random

Multiobjective Two-Level Fuzzy Random Programming Problems with Simple Recourses and Estimated Pareto Stackelberg Solutions

2018 ◽  
Vol 22 (3) ◽  
pp. 359-368 ◽  
Author(s):  
Hitoshi Yano ◽  
Keyword(s):  
Multiobjective Programming ◽  
Objective Functions ◽  
Possibility Measure ◽  
Weighting Method ◽  
Complementarity Conditions ◽  
Stackelberg Solutions ◽  
Weighting Vector ◽  
Fuzzy Random Programming ◽  
Multiobjective Programming Problems ◽  
Fuzzy Random

In this paper, we focus on multiobjective two-level fuzzy random programming problems with simple recourses, in which multiple objective functions are involved in each level, shortages and excesses resulting from the violation of the constraints with fuzzy random variables are penalized, and sums of the objective functions and expectation of the amount of the penalties are minimized. To deal with such problems, the concept of estimated Pareto Stackelberg solutions of the leader is introduced under the assumption that the leader can estimate the preference of the follower as a weighting vector of the weighting problems. Employing the possibility measure for fuzzy numbers, weighting method for multiobjective programming problems, and Kuhn-Tucker approach for two-level programming problems, a nonlinear optimization problem under complementarity conditions is formulated to obtain the estimated Pareto Stackelberg solutions for the leader. A numerical example illustrates the proposed method for a multiobjective two-level fuzzy random programming problem with simple recourses. Several types of estimated Pareto Stackelberg solutions are derived corresponding to the weighting vectors and permissible possibility levels specified by the leader.

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