Binary fuzzy linear programming problems: a new solution

Abstract

Purpose: In this paper, a Binary Fuzzy Linear Programming Problem (BFLPP) with fuzzy objective function and fuzzy constraints is considered. This paper proposes a new approach that solves the problem based on Kerre's adapted method, which maintains the assumption of being fuzzy in the solving process. Therefore, the solution is more consistent with the uncertainty governing the problem.Methodology: This paper proposes a new fuzzy branch-and-bound approach based on Kerre's adapted method to solve the fuzzy binary integer programming problem. In each node of the branch-and-bound tree, the linear relaxation of the fuzzy problem is solved with a new fuzzy simplex method based on Kerre's adapted method.Findings: Numerical examples are presented to illustrate the proposed method step by step, and the results are compared with those of other approaches that solve fuzzy binary integer programming problems.Originality/Value: Unlike the available defuzzification procedures and fuzzy ranking functions in the research problem literature, the proposed approach considers the assumption of being fuzzy in the solution process and thus offers a more realistic solution.

Keywords

• fuzzy binary integer programming problem
• fuzzy branch-and-bound algorithm
• fuzzy simplex algorithm
• adapted kerre's method