Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables

High computation complexity restricts the application prospects of the interval type-2 fuzzy variable (IT2-FV), despite its high degree of freedom in representing uncertainty. Thus, this paper studies the fuzzy operations for the regular symmetric triangular IT2-FVs (RSTIT2-FVs)—the simplest IT2-FVs...

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Autores principales:	Hui Li, Junyang Cai
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	interval type-2 fuzzy variable membership function expected value operational law Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/1dd03c1c66794683a4914218e347e70b
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spelling	oai:doaj.org-article:1dd03c1c66794683a4914218e347e70b2021-11-25T19:07:30ZArithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables10.3390/sym131121962073-8994https://doaj.org/article/1dd03c1c66794683a4914218e347e70b2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2196https://doaj.org/toc/2073-8994High computation complexity restricts the application prospects of the interval type-2 fuzzy variable (IT2-FV), despite its high degree of freedom in representing uncertainty. Thus, this paper studies the fuzzy operations for the regular symmetric triangular IT2-FVs (RSTIT2-FVs)—the simplest IT2-FVs having the greatest membership degrees of 1. Firstly, by defining the medium of an RSTIT2-FV, its membership function, credibility distribution, and inverse distribution are analytically and explicitly expressed. Secondly, an operational law for fuzzy arithmetic operations regarding mutually independent RSTIT2-FVs is proposed, which can simplify the calculations and directly output the inverse credibility of the functions. Afterwards, the operational law is applied to define the expected value operator of the IT2-FV and prove the linearity of the operator. Finally, some comparative examples are provided to verify the efficiency of the proposed operational law.Hui LiJunyang CaiMDPI AGarticleinterval type-2 fuzzy variablemembership functionexpected valueoperational lawMathematicsQA1-939ENSymmetry, Vol 13, Iss 2196, p 2196 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	interval type-2 fuzzy variable membership function expected value operational law Mathematics QA1-939
spellingShingle	interval type-2 fuzzy variable membership function expected value operational law Mathematics QA1-939 Hui Li Junyang Cai Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables
description	High computation complexity restricts the application prospects of the interval type-2 fuzzy variable (IT2-FV), despite its high degree of freedom in representing uncertainty. Thus, this paper studies the fuzzy operations for the regular symmetric triangular IT2-FVs (RSTIT2-FVs)—the simplest IT2-FVs having the greatest membership degrees of 1. Firstly, by defining the medium of an RSTIT2-FV, its membership function, credibility distribution, and inverse distribution are analytically and explicitly expressed. Secondly, an operational law for fuzzy arithmetic operations regarding mutually independent RSTIT2-FVs is proposed, which can simplify the calculations and directly output the inverse credibility of the functions. Afterwards, the operational law is applied to define the expected value operator of the IT2-FV and prove the linearity of the operator. Finally, some comparative examples are provided to verify the efficiency of the proposed operational law.
format	article
author	Hui Li Junyang Cai
author_facet	Hui Li Junyang Cai
author_sort	Hui Li
title	Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables
title_short	Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables
title_full	Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables
title_fullStr	Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables
title_full_unstemmed	Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables
title_sort	arithmetic operations and expected values of regular interval type-2 fuzzy variables
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/1dd03c1c66794683a4914218e347e70b
work_keys_str_mv	AT huili arithmeticoperationsandexpectedvaluesofregularintervaltype2fuzzyvariables AT junyangcai arithmeticoperationsandexpectedvaluesofregularintervaltype2fuzzyvariables
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Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables

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