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Published Dec 6, 2018
Konstantin Yury Degtiarev Mikhail Yury Borisov

Abstract

The Analytic Hierarchy Process (AHP) enables decision-makers to prioritize alternatives. However, when an expert expresses judgments using natural language statements (e.g. words or phrases) inherent vagueness of language constructs can cause the interpretation to be imprecise. The fuzzy Analytic Hierarchy Process (FAHP) can be viewed in the context of the classical AHP expansion. While performing pairwise comparisons domain experts are accustomed to operating with verbal terms in their judgments. Most existing FAHP approaches do not consider a human’s confidence in the estimates provided. This paper presents a model that gives weight to the constraints on domains of expert assessments as they are almost always supplied with certain degrees of confidence. Interval type-2 membership functions (IT2MF) along with the probability-theoretical procedure for comparison of intervals can be applied here as suitable modeling options. Empirical comparison of FAHP that makes use of triangular fuzzy numbers and IT2MF-based FAHP is also presented.   

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Keywords

Analytic Hierarchy Process, expert assessment, degree of confidence, fuzzy logic, linguistic label, type-1 membership function, interval type-2 membership function, Fuzzy Synthetic Extents, interval calculations, threshold values, prioritizing alternatives

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