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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, Volume 9, Issue 4, Pages 590–601
DOI: https://doi.org/10.21638/spbu01.2022.402 (Mi vspua54) 		 
MATHEMATICS

Algebra of fuzzy numbers with unimodal membership function

I. V. Germasheva, E. V. Derbisherb, V. E. Derbisherb, A. V. Kartashovac, A. V. Titova

a Volgograd State University, 100, pr. Universitetskiy, Volgograd, 400062, Russian Federation
b Volgograd State Technical University, 28, pr. im. Lenina, Volgograd, 400005, Russian Federation
c Volgograd State Socio-Pedagogical University, 27, pr. im. Lenina, Volgograd, 400005, Russian Federation
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DOI: https://doi.org/10.21638/spbu01.2022.402
Abstract: Fuzzy numbers with a unimodal membership function are presented, which have found application in the fuzzy analysis of such subject fields as ecology, chemical technology. In this article, a set of fuzzy numbers with an unimodal membership function of a special type is considered. Two binary operations (addition and multiplication) are given over this set, formulas for calculation are obtained and some properties of this algebra are investigated. It is proved that addition and multiplication are commutative and associative. Moreover, multiplication is distributive over addition. It is shown that there are no neutral and inverse elements over both operations. Note that if we add neutral elements under addition and multiplication to the given algebra, we will obtain a commutative semiring. The conditions under which quasineutral or quasiinverse elements exist are also given.
Keywords: algebra, fuzzy numbers, arithmetic operations, associativity, distributivity.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0633-2020-0003
The work is supported by state task of the Ministry of Science and Higher Education of Russia (project no. 0633-2020-0003).
Received: 26.04.2022
Revised: 08.06.2022
Accepted: 09.06.2022
English version:
Vestnik St. Petersburg University, Mathematics, 2022, Volume 9, Issue 4, Pages 380–388
DOI: https://doi.org/10.1134/S1063454122040069
Bibliographic databases:
Document Type: Article
UDC: 511.26
MSC: 08A72
Language: Russian
Citation: I. V. Germashev, E. V. Derbisher, V. E. Derbisher, A. V. Kartashova, A. V. Titov, “Algebra of fuzzy numbers with unimodal membership function”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9:4 (2022), 590–601; Vestn. St. Petersbg. Univ., Math., 9:4 (2022), 380–388
Citation in format AMSBIB
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\by I.~V.~Germashev, E.~V.~Derbisher, V.~E.~Derbisher, A.~V.~Kartashova, A.~V.~Titov
\paper Algebra of fuzzy numbers with unimodal membership function
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2022
\vol 9
\issue 4
\pages 590--601
\mathnet{http://mi.mathnet.ru/vspua54}
\crossref{https://doi.org/10.21638/spbu01.2022.402}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4529132}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2022
\vol 9
\issue 4
\pages 380--388
\crossref{https://doi.org/10.1134/S1063454122040069}
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