TY - EJOU
AU - Aliev, R. A.
AU - Kreinovich, Vladik
TI - Z-Numbers and Type-2 Fuzzy Sets: A Representation Result
T2 - Intelligent Automation \& Soft Computing
PY - 2018
VL - 24
IS - 1
SN - 2326-005X
AB - 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.
KW - Z-number; type-2 fuzzy set; extension principle
DO - 10.1080/10798587.2017.1330310