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

Chin-Yi Chen and Jih-Jeng Huang
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Chin-Yi Chen: Department of Business Administration, Chung Yuan Christian University, Taoyuan 32023, Taiwan
Jih-Jeng Huang: Department of Computer Science & Information Management, SooChow University, Taipei 100, Taiwan

Mathematics, 2019, vol. 7, issue 10, 1-14

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.

Keywords: fuzzy analytic network process; fuzzy supermatrix; mathematical programming; fuzzy inverse matrix; fuzzy weights (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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