On fuzzy equality and approximation in fuzzy logic
type: Item
instance of: scholarly article
title: On fuzzy equality and approximation in fuzzy logic
zbMATH Open document ID: 1066.03037
published in: Soft Computing
publication date: 2005-02-25T00:00:00Z
review text: The paper shows that the theory of fuzzy approximation of relations and functions can be elaborated inside the formal theory of fuzzy logic with evaluated syntax. Moreover, it illustrates that fuzzy logic is not only a generalization of classical logic, but that it departs from the latter by solving specific problems which make no sense in classical logic. In detail, the concept of fuzzy equality is discussed, and it is shown that, together with provability degree, it enables one to generalize the concept of fuzzy approximation. Finally, approximation of functions by the Mamdani-Assilian formula based on totally bounded fuzzy equalities is studied.
reviewed by: Radko Mesiar
Mathematics Subject Classification ID: 03B52
zbMATH DE Number: 2138690
zbMATH Keywords: Fuzzy logic
zbMATH Keywords: Fuzzy equality
zbMATH Keywords: Evaluated syntax
zbMATH Keywords: Fuzzy approximation
author: Vilém Novák
MaRDI profile type: Publication
full work available at URL: s00500-003-0324-9
OpenAlex ID: W1590591595
DOI: 10.1007/S00500-003-0324-9
Recommended article: Q4801913
Recommended article: Q4025366
Recommended article: Q4650782
Recommended article: On (un)suitable fuzzy relations to model approximate equality
Recommended article: Q3328546
Recommended article: Fuzzy equivalence relations and their equivalence classes
Recommended article: Q4414865
Recommended article: On fuzzy equivalence. II
Recommended article: Fuzzy equivalence relations
Recommended article: Q3082769
description: scientific article; zbMATH DE number 2138690