Open Access

ARTICLE

Z-Numbers and Type-2 Fuzzy Sets: A Representation Result

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

^aMBA Department, Azerbaijan State University of Oil and Industry, Baku, Azerbaijan;
^b Department of Computer Engineering, Near East University, Lefkosa, North Cyprus;
^c Department of Computer Science, University of Texas, El Paso, USA

* Corresponding Author: R. A. Aliev,

Intelligent Automation & Soft Computing 2018, 24(1), 205-210. https://doi.org/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 type-2 fuzzy set can be represented as a result of applying an appropriate data processing algorithm to some Z-numbers.

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Keywords

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