Entropy and probability based Fuzzy Induced Ordered Weighted Averaging operator

Abstract

The traditional Ordered Weighting Average (OWA) operator is suitable for aggregating numerical attributes. However, this method fails when the attribute values are given in a linguistic form. In this paper, a novel aggregating method named Entropy and Probability based Fuzzy Induced Ordered Weighted Averaging (EPFIOWA) is proposed for Gaussian-fuzzy-number-based linguistic attributes. A method is first designed to obtain a reasonable weighting vector based on probability distribution and maximal entropy. Such optimal weighting vectors can be obtained under any given level of optimism, and the symmetric properties of the proposed model are proven. The linguistic attributes of EPFIOWA are represented by Gaussian fuzzy numbers because of their concise form and good operational properties. In particular, the arithmetic operations and distance measures of Gaussian fuzzy numbers required by EPFIOWA are given systematically. A novel method to obtain the order-inducing variables of linguistic attribute values is proposed in the EPFIOWA operators by calculating the distances between any Gaussian fuzzy number and a set of ordered grades. Finally, two numerical examples are used to illustrate the proposed approach, with evaluation results consistent with the observed situation.