Fuzzy analytic hierarchy process: a comparison of the existing algorithms with new proposals
Ahmed, Faran (2015) Fuzzy analytic hierarchy process: a comparison of the existing algorithms with new proposals. [Thesis]
In a multiple-criteria decision analysis, prioritizing and assigning weights to each criteria with reference to set of available alternatives is key to effective decision making. Analytic Hierarchy Process (AHP) is one such technique through which experts provide pairwise comparisons and this information is processed in a comparison matrix to calculate priority vector which ranks the available alternatives. Original AHP as proposed by Thomas L. Saaty used crisp numbers to represent pairwise comparisons. However, human judgments are often vague and traditional 1-9 scale is not capable to incorporate the inherent human uncertainty into pairwise comparisons. In order to address this issue, fuzzy set theory is being used along side original AHP where human judgments are recorded in the form of fuzzy numbers and thus comparison matrices are formed in such a way that its elements are fuzzy numbers. Various algorithms have been proposed over the past three decades through which priority vector can be calculated from fuzzy comparison matrices. This study performs an extensive review of the most common algorithms proposed in fuzzy AHP (FAHP) and conducts a performance analysis of nine algorithms, out of which ve are existing FAHP algorithms namely Logarithmic Least Square Method (LLSM), Modified LLSM, Fuzzy Extent Analysis (FEA), modified FEA and Buckley's Geometric Mean method, while four models are introduced in this study which includes Geometric Mean method, Arithmetic Mean method, Row Sum method and Inverse of Column Sum method. A separate algorithm is also proposed to construct fuzzy comparison matrices of varying sizes, level of fuzziness and inconsistency, so as to carry out performance analysis of the selected nine FAHP algorithms. We found that Geometric Mean method discussed in this study performs significantly better than other algorithms, while FEA is the worst performing algorithm. Although at high inconsistency levels, performance of FEA method improves however, even at high inconsistency levels, Geometric Mean method performs significantly better. Modi cation to FEA method (Row Sum method) proposed in this study significantly improves its performance and this modified FEA method is the second best performing algorithm among the selected nine FAHP models. In addition, we also conducted a comparative analysis based on popularity, computational time, applicability of fuzzy numbers, ease of understanding and ease of implementation. Through this study, we attempt to consolidate the existing literature on FAHP algorithms and identify the best performing methodologies to calculate priority vector from fuzzy comparison matrices.
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