Studies of stochastic programming models using possibility and necessity measures for linear programming problems with fuzzy random variable coefficients

2004 ◽  
Vol 88 (1) ◽  
pp. 68-75 ◽  
Author(s):  
Hideki Katagiri ◽  
Masatoshi Sakawa ◽  
Hiroaki Ishii
Keyword(s):  
Linear Programming ◽  
Stochastic Programming ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Variable Coefficients ◽  
Programming Models ◽  
Linear Programming Problems ◽  
Fuzzy Random

Multiobjective Programming Problems Involving Fuzzy Coefficients, Random Variable Coefficients and Fuzzy Random Variable Coefficients

2015 ◽  
Vol 23 (04) ◽  
pp. 483-504 ◽  
Author(s):  
Hitoshi Yano
Keyword(s):  
Multiobjective Programming ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Variable Coefficients ◽  
Pareto Optimal ◽  
Possibility Measure ◽  
Generalized Pareto ◽  
Interactive Algorithm ◽  
Fuzzy Goal ◽  
Fuzzy Random

In this paper, we propose an interactive method for multiobjective linear programming problems, in which fuzzy coefficients, random variable coefficients and fuzzy random variable coefficients are involved in the objective functions respectively. In the proposed method, it is assumed that the decision maker has a fuzzy goal for each objective function, and such a fuzzy goal can be quantified by eliciting the membership function. Through a possibility measure and a fractile optimization model, the original problem is transformed to the well-defined multiobjective programming problem. Then, a generalized Pareto optimal concept is defined, and an interactive algorithm is proposed to obtain a satisfactory solution from among a generalized Pareto optimal solution set.

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