R. A. Aliev^a,b, Vladik Kreinovich^c

Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 205-210, 2018, DOI:10.1080/10798587.2017.1330310

Abstract Traditional [0; 1] based fuzzy sets were originally invented to describe expert knowledge expressed in terms of imprecise “fuzzy” words from the natural language. To make this description more adequate, several generalizations of the traditional [0; 1] based fuzzy sets have been proposed, among them type- 2 fuzzy sets and Z-numbers. The main objective of this paper is to study the relation between these two generalizations. As a result of this study, we show that if we apply data processing to Z-numbers, then we get type-2 sets of special type —that we call monotonic. We also prove that every monotonic… More >

Mark J. Wierman

Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 179-186, 2018, DOI:10.1080/10798587.2017.1327160

Abstract The theory of Zets is presented and the standard techniques of set theory allows for the development of a rich algebra of Zets. It shows that Zets and fuzzy sets are essentially interchangeable. However, the fundamental manipulations, techniques, and definitions of Zets are simple and more amenable to analyze. For example, the extension principle is easy to define. More >