A New Algorithm for Solving Fully Fuzzy Bi-Level Quadratic Programming Problems

 Paper Title:

A New Algorithm for Solving Fully Fuzzy Bi-Level Quadratic Programming Problems

Authors:

Azza H. Amer, Helwan University, Egypt

Abstract:

This paper is concerned with new method to find the fuzzy optimal solution of fully fuzzy bi-level non-linear (quadratic) programming (FFBLQP) problems where all the coefficients and decision variables of both objective functions and the constraints are triangular fuzzy numbers (TFNs). A new method is based on decomposed the given problem into bi-level problem with three crisp quadratic objective functions and bounded variables constraints. In order to often a fuzzy optimal solution of the FFBLQP problems, the concept of tolerance membership function is used to develop a fuzzy max-min decision model for generating satisfactory fuzzy solution for FFBLQP problems in which the upper-level decision maker (ULDM) specifies his/her objective functions and decisions with possible tolerances which are described by membership functions of fuzzy set theory. Then, the lower-level decision maker (LLDM) uses this preference information for ULDM and solves his/her problem subject to the ULDMs  restrictions. Finally,

the decomposed method is illustrated by numerical example. 

Keywords:

Fully Fuzzy Quadratic Non-Linear Programming Problems. Triangular Fuzzy Numbers, Decomposed Method, Bi-Level Programming

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