Mathematical aspects of fuzzy sets and fuzzy logic. Some reflections after 40 years
type: Item
instance of: scholarly article
title: Mathematical aspects of fuzzy sets and fuzzy logic. Some reflections after 40 years
zbMATH Open document ID: 1088.03024
published in: Fuzzy Sets and Systems
publication date: 2006-01-24T00:00:00Z
review text: This survey paper considers some of the main trends of the development of mathematical fuzzy logic and of formalized fuzzy set theory. In four decades of fuzzy set theory and fuzzy logic, the last one has seen a tremendous wealth of new and important approaches and results which paved the way for the future success. Especiall BL-algebras, introduced by P. Hájek, brought a qualitative jump in the fuzzy logic theory and they have initiated several new streams of research. Some important open problems for further research are mentioned in the concluding remarks of this interesting paper that is worth reading for any scientist interested in logic, artificial intelligence or soft computing.
reviewed by: Radko Mesiar
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 03-02
Mathematics Subject Classification ID: 03-03
zbMATH DE Number: 5001351
zbMATH Keywords: mathematical fuzzy logic
zbMATH Keywords: fuzzy set theory
zbMATH Keywords: universes of fuzzy sets
zbMATH Keywords: categories of fuzzy sets
zbMATH Keywords: survey
author: Siegfried J. Gottwald
MaRDI profile type: Publication
full work available at URL: j.fss.2005.05.031
OpenAlex ID: W1530258601
cites work: Q4146730
cites work: Q3037428
cites work: Q3712467
cites work: Monoidal t-norm based logic: Towards a logic for left-continuous t-norms
cites work: Equational characterization of the subvarieties of BL generated by t-norm algebras
cites work: Fuzzy sets: A topos-logical point of view
cites work: Q3050433
cites work: Łukasiewicz logic and fuzzy set theory
cites work: A formal system for fuzzy reasoning
cites work: L-fuzzy sets
cites work: Concept representation in natural and artificial languages: Axioms, extensions and applications for fuzzy sets
cites work: Q4106199
cites work: Set theory for fuzzy sets of higher level
cites work: Q3331217
cites work: Q3135091
cites work: Mathematical fuzzy logic as a tool for the treatment of vague information
cites work: Q5692481
cites work: Metamathematics of fuzzy logic
cites work: A complete many-valued logic with product-conjunction
cites work: Q4010274
cites work: Q4836218
cites work: Q4836221
cites work: Q4944912
cites work: Foundations of fuzzy sets
cites work: A proof of standard completeness for Esteva and Godo's logic MTL
cites work: Q5534933
cites work: Q5534934
cites work: Q5553267
cites work: AN ELEMENTARY THEORY OF THE CATEGORY OF SETS
cites work: Q3328546
cites work: Q3208629
cites work: Topoi and categories of fuzzy sets
cites work: Q4836223
cites work: Intuitionistic fuzzy logic and intuitionistic fuzzy set theory
cites work: Q3722491
cites work: Fuzzy logic and fuzzy set theory
cites work: Q3998741
cites work: Q4836224
cites work: Fuzzy sets
cites work: A unified treatment of fuzzy set theory and Boolean-valued set theory - fuzzy set structures and normal fuzzy set structures
cites work: Q3310613
cites work: Q3748967
DOI: 10.1016/J.FSS.2005.05.031
description: scientific article; zbMATH DE number 5001351