Multiobjective linear programming model having fuzzy random variables following joint extreme value distribution

Abstract

This paper presents a new technique for solving fuzzy multiobjective chance constrained programming problems in which the right sided parameters associated with the system constraints follow joint extreme value distribution. At first the multiobjective fuzzy stochastic model is converted into an equivalent fuzzy programming model applying chance constrained programming methodology and using the properties ofα - cuts. Then using the method of defuzzification of fuzzy numbers the fuzzy programming model is converted into a comparable deterministic model. Afterwards, solving each objective independently, the imprecise aspiration level to each of the individual objectives are obtained. Then the membership function for each objective is defined to measure the degree of achievements of the goal levels of the objectives. Finally, weighted fuzzy goal programming technique is applied to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing under deviational variables of the fuzzy goals in the fuzzy stochastic decision making context. To illustrate the proposed approach, a numerical example is considered and solved.