A new methodological development for solving linear bilevel integer programming problems in hybrid fuzzy environment

Year 2016, Volume: 4 Issue: 2, 180 - 192, 01.03.2016

Animesh Biswas Arnab Kumar

Abstract

This paper deals
with fuzzy goal programming approach to solve fuzzy linear bilevel integer
programming problems with fuzzy
probabilistic constraints following Pareto distribution and Frechet
distribution. In the proposed approach a new chance constrained programming
methodology is developed from the view point of managing those probabilistic
constraints in a hybrid fuzzy environment. A method of defuzzification of fuzzy
numbers using a−cut
has been adopted to reduce the problem into a linear bilevel integer programming
problem. The individual optimal value of the objective of each DMis found in
isolation to construct the fuzzy membership goals. Finally, fuzzy goal
programming approach is used to achieve maximum degree of each of the
membership goals by minimizing under deviational variables in the decision
making environment. To demonstrate the efficiency of the proposed approach, a
numerical example is provided.

Keywords

Bilevel programming, fuzzy goal programming, ranking function, stochastic programming

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