Calculating Fuzzy Inverse Matrix Using Linear Programming Problem: An Improved Approach

Abstract

Calculating the matrix inverse is a key point in solving linear equation system, which involves complex calculations, particularly when the matrix elements are (Left and Right) fuzzy numbers. In this paper, first, the method of Kaur and Kumar for calculating the matrix inverse is reviewed, and its disadvantages are discussed. Then, a new method is proposed to determine the inverse of fuzzy matrix based on linear programming problem. It is demonstrated that the proposed method is capable of overcoming the shortcomings of the previous matrix inverse. Numerical examples are utilized to verify the performance and applicability of the proposed method.

Approximate Fuzzy Inverse Matrix Calculation Method using Scenario-based Inverses and Bisection

“…Example 4.4. Our fourth example is from [11]. Consider the following fuzzy matrix with triangular entries: A = (5, 5, 1, 1) LR (6, 6, 2, 2) LR (4, 4, 2, 2) LR (7, 7, 1, 1) LR .…”

“…Chen and Huang [10] proposed a mathematical programming model to acquire the fuzzy weights of the fuzzy analytical network process by utilizing the fuzzy inverse matrix on the basis of the criterion of the minimum spread of FNs. Babakordi and Taghi-Nezhad [11] also employed linear programming for the calculation of fuzzy inverse matrix. Farahani and Ebadi [12] discussed the sufficient and necessary conditions for the invertibility of a fuzzy matrix by analyzing a system of fuzzy polynomial equations.…”