A New Vision of Zadeh’s Z-numbers

Abstract

From their introduction Z-numbers have been deeply studied and many investigations have appeared trying to reduce the inherent complexity in their computation. In this line, this paper presents a new vision of Z-numbers based on discrete fuzzy numbers with support in a finite chain \(L_n\). In this new approach, a Z-number associated with a variable, X, is a pair \((A,\,B)\) of discrete fuzzy numbers, where A is interpreted as a fuzzy restriction on X, while the estimation of the reliability of A is interpreted as a linguistic valuation based on the discrete fuzzy number B. In this non-probabilistic approach an aggregation method is proposed with the aim of applying it in group decision making problems.