Deriving Fuzzy Weights of the Fuzzy Analytic Network Process via Fuzzy Inverse Matrix

Abstract

The analytic hierarchical process/network process (AHP/ANP) is a popular multi-criteria decision making approach for determining the optimal alternative or weights of criteria. Many papers have extended the AHP/ANP to consider the fuzzy environment to reflect the subjective uncertainty of decision-makers. However, the fuzzy ANP (FANP) is not as popular as the fuzzy AHP (FAHP), because the calculation of the fuzzy supermatrix results in the divergence of the steady-state. In this paper, we provide a novel mathematical programming model to calculate the limiting distribution of the fuzzy supermatrix by considering a fuzzy inverse matrix rather than directly calculate the fuzzy supermatrix by limiting powers. In addition, we use a numerical example to illustrate the proposed method and compare the results with the previous method. The numerical results indicate the proposed method has the least spread of the fuzzy weights, thus justifying the usefulness of the proposed method.

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

“…Guo et al [9] designed a numerical procedure to derive the fuzzy inverse of the matrix with LR−type FNs and supplied a sufficient condition for its existence. 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.…”