Solving Fuzzy Linear Programming Problem Using Defuzzification Method - Veerraju, Nalla; Prasannam, V. Lakshmi (Communications in Mathematics and Applications, 2021)
Linear Programming (LP) has been one of the efficient, reliable and time tested techniques in Optimization. Conventional LP is not suitable for many real time problems which involve data with inherent vagueness or impreciseness. Fuzzy set theory is proved to be quite good in addressing the inherent vagueness or impreciseness and thus Fuzzy Linear Programming (FLP) is brought to light and developed over the years. A quite good number of techniques have been proposed for solving FLP problems to obtain optimal solution for real world problems involving fuzzy (vague or imprecise) environment. In this paper, "Extended Geometric Mean Defuzzification” is defined and based on it, a method is proposed for solving FLP problems. To showcase the advantages of the proposed method, different problems of FLP, available in the literature, are discussed. Numerical comparisons are also provided to validate the authentication of the proposed method.
Keywords: Fuzzy sets; Fuzzy numbers; Geometric mean defuzzification; Fuzzy linear programming