A Theory for Measuring the Preference of Fuzzy Numbers

Abstract

Here, sigmoid function-based preference measures for intervals and fuzzy numbers are introduced, and their main properties are outlined. Also, formulas for the numerical computation of the proposed preference measures are presented. Next, it is demonstrated that the proposed preference measures for intervals and fuzzy numbers are asymptotically the well-known probability-based preference measures for intervals and fuzzy numbers. Using the new preference measure, two parametric crisp relations, which have common parameters, over a collection of fuzzy numbers are introduced. Next, it is shown that the limits of these relations can be used to rank fuzzy numbers. Namely, it is proved that the limit of one of these relations is a strict order relation, while the limit of the other may be viewed as an indifference relation. This indifference relation can be used to capture situations where the order of two fuzzy numbers cannot be judged; and so, their order may be considered as being indifferent.