Prioritization of Alternatives Based on Analytic Hierarchy Process Using Interval Type-2 Fuzzy Sets and Probability-Theoretical Interval Comparison

International Journal of the Analytic Hierarchy Process. 2018. Vol. 10. No. 3. P. 447–468.

Konstantin Y. Degtiarev, Borisov M.

The Analytic Hierarchy Process (AHP) is aimed at enabling decision-makers to prioritize alternatives. However, when expert expresses judgments using natural language statements (e.g. words or phrases), they can be interpreted not precisely due to inherent vagueness of the language constructs. 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 of existing FAHP approaches do not consider human’s confidence in estimates provided. The paper presents a model that gives a weigh to constraints on domain 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.

Keywords: метод анализа иерархий (МАИ), экспертная оценка, analytic hierarchy process (AHP), нечеткие числа, fuzzy numbers, expert assessment, degree of confidence, type-1 membership function, interval type-2 membership function, Fuzzy Synthetic Extents, defuzzification, interval calculations, prioritizing alternatives, степень уверенности, функция принадлежности типа 1, интервальная функция принадлежности типа 2, дефаззификация, интервальные вычисления, приоритизация альтернатив