A Psychometric Approach for Ranking Fuzzy Numbers

Since much of human reasoning is based on imprecise, vague and subjective values, most of decision-making processing, in reality, requires handling and evaluation of fuzzy numbers. Zadeh’s (Zadeh 1965) fuzzy logic has given analysts a tool to represent the human behaviour more precisely, especially where relatively few data exist, and where the expert knowledge about the system is vague and linguistic (Hoogerdoorn et al. 1999). Bortolon and Degani (1985) reviewed different fuzzy ranking methods and they found that most of the methods are questionable regarding their counterintuitive results. The purpose of this paper is to develop a psychometric approach for ranking fuzzy numbers to be used in a multiattribute or multi-criterion decision making process. Weber’s psycho-physical law of 1834 is used to subdivide decision makers’ input space into subjectively equal subintervals, then a fuzzy “if-then” rule base is prepared to represent humans’ cognitive comparisons made between alternatives in a pairwise way over these intervals. Analytic Hierarchy Process (AHP) (Saaty 1980) is, then, utilized as a satisfying technique that can represent humans’ cognitive decision process properly to predict the preferences and rank the fuzzy numbers. The method is applied on a real world sample which is based on the stated preferences by subjects. Three fuzzy triangular numbers for each case are compared and the results are evaluated. This new procedure provides intuitively promising and statistically significant results and can be extended to any type of fuzzy numbers.