Asymmetric Equivalences in Fuzzy Logic

Asymmetric Equivalences in Fuzzy Logic

We introduce a new class of operations called asymmetric equivalences. Several properties of asymmetric equivalence operations have been investigated. Based on the asymmetric equivalence, quasi-metric spaces are constructed on [0, 1]. Finally, we discuss symmetrization of asymmetric equivalences.

Bibliographic Details
Main Authors: Bo Hu, Lvqing Bi, Sizhao Li, Songsong Dai
Format: Article
Language:English
Published: MDPI AG 2017-10-01
Series:Symmetry
Subjects:
fuzzy logic
t-norm
fuzzy implication
asymmetric equivalence
quasi-metric
Online Access:https://www.mdpi.com/2073-8994/9/10/224
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spelling doaj-3b0a5601a1404428960b200c684d7bf92020-11-24T22:10:56ZengMDPI AGSymmetry2073-89942017-10-0191022410.3390/sym9100224sym9100224Asymmetric Equivalences in Fuzzy LogicBo Hu0Lvqing Bi1Sizhao Li2Songsong Dai3School of Mechanical and Electrical Engineering, Guizhou Normal University, Guiyang 550025, ChinaSchool of Electronics and Communication Engineering, Yulin Normal University, Yulin 537000, ChinaSchool of Information Science and Engineering, Xiamen University, Xiamen 361005, ChinaSchool of Information Science and Engineering, Xiamen University, Xiamen 361005, ChinaWe introduce a new class of operations called asymmetric equivalences. Several properties of asymmetric equivalence operations have been investigated. Based on the asymmetric equivalence, quasi-metric spaces are constructed on [0, 1]. Finally, we discuss symmetrization of asymmetric equivalences.https://www.mdpi.com/2073-8994/9/10/224fuzzy logict-normfuzzy implicationasymmetric equivalencequasi-metric
collection DOAJ
language English
format Article
sources DOAJ
author Bo Hu
Lvqing Bi
Sizhao Li
Songsong Dai
spellingShingle Bo Hu
Lvqing Bi
Sizhao Li
Songsong Dai
Asymmetric Equivalences in Fuzzy Logic
Symmetry
fuzzy logic
t-norm
fuzzy implication
asymmetric equivalence
quasi-metric
author_facet Bo Hu
Lvqing Bi
Sizhao Li
Songsong Dai
author_sort Bo Hu
title Asymmetric Equivalences in Fuzzy Logic
title_short Asymmetric Equivalences in Fuzzy Logic
title_full Asymmetric Equivalences in Fuzzy Logic
title_fullStr Asymmetric Equivalences in Fuzzy Logic
title_full_unstemmed Asymmetric Equivalences in Fuzzy Logic
title_sort asymmetric equivalences in fuzzy logic
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2017-10-01
description We introduce a new class of operations called asymmetric equivalences. Several properties of asymmetric equivalence operations have been investigated. Based on the asymmetric equivalence, quasi-metric spaces are constructed on [0, 1]. Finally, we discuss symmetrization of asymmetric equivalences.
topic fuzzy logic
t-norm
fuzzy implication
asymmetric equivalence
quasi-metric
url https://www.mdpi.com/2073-8994/9/10/224
work_keys_str_mv AT bohu asymmetricequivalencesinfuzzylogic
AT lvqingbi asymmetricequivalencesinfuzzylogic
AT sizhaoli asymmetricequivalencesinfuzzylogic
AT songsongdai asymmetricequivalencesinfuzzylogic
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