In this paper, a quadratic programming (FFQP) problem is considered in which all of the cost coefficients, constraints coefficients, and right hand side of the constraints are characterized by L-R fuzzy numbers. Through this paper, the concept of α- level of fuzzy numbers for the objective function, and the order relations on the fuzzy numbers for the constraints are considered.  To optimize th...

This paper deals with the competitive location problems using fuzzy sets. The basic notions on fuzzy optimization and linear programming using fuzzy sets are briefly reviewed. The standard leader-follower location problem and its linear mathematical programming formulation are described. The works appeared in the literature concerning the use of fuzzy sets are analyzed. Keywords— Fuzzy Optimiza...

We examine a linear programming problem formulation in which the constraint coefficients are not precisely given in the work. We investigate the possibility of applying GAs to solve this kind of fuzzy linear programming problem without defining membership functions for fuzzy numbers, using the extension principle, interval arithmetic, and α-cut operations for fuzzy computations, and using a pen...

Abstract In this paper, we use interval-valued fuzzy numbers to fuzzify the crisp linear programming to three cases. The first case, we use intervalvalued fuzzy numbers to fuzzify the coefficients in the objective function. We get a linear programming in the fuzzy sense. The second case, we use interval-valued fuzzy numbers to fuzzify the coefficients akj in the constraints about xj, j = 1, 2, ...