Interactive decision making for fuzzy random multiobjective linear programming problems with variance-covariance matrices through probability maximization

2012 ◽  
Author(s):  
Hitoshi Yano
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Covariance Matrices ◽  
Multiobjective Linear Programming ◽  
Interactive Decision Making ◽  
Linear Programming Problems ◽  
Fuzzy Random

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

2014 ◽  
Vol 18 (3) ◽  
pp. 383-390
Author(s):  
Hitoshi Yano ◽  
Keyword(s):  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Covariance Matrices ◽  
Pareto Optimal ◽  
Membership Functions ◽  
Multiobjective Linear Programming ◽  
Satisfactory Solution ◽  
Interactive Decision Making ◽  
Linear Programming Problems ◽  
Fuzzy Random

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, andDf-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 aDf-Pareto optimal solution set through the interaction with the decision maker.

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