Approximating alpha-cut operations approach for effective and efficient fuzzy analytic hierarchy process analysis

Abstract

Fuzzy analytic hierarchy process (FAHP) has been widely applied to multicriteria decision making (MCDM). However, deriving the fuzzy maximal eigenvalue and eigenvector of a fuzzy pairwise comparison matrix is a computationally intensive task. As a result, most existing FAHP methods estimate, rather than derive, the fuzzy maximal eigenvalue and weights. Therefore, the results are inaccurate. By contrast, the alpha-cut operations (ACO) method derives the fuzzy maximal eigenvalue and weights, but is time-consuming. To address these issues, the approximating alpha-cut operations (xACO) approach is proposed in this study. The proposed xACO approach does not enumerate all possible combinations of the α cuts of fuzzy pairwise comparison results, but approximates the membership functions of the fuzzy maximal eigenvalue and weights with logarithmic functions in the process. To evaluate the performance of the xACO approach, it was applied to two real cases. According to the experimental results, the xACO approach estimated the fuzzy maximal eigenvalue and weights effectively and efficiently based on less than 0.2% of the entire results.