Algebra of Fuzzy Numbers with a Unimodal Membership Function

Fuzzy numbers with a unimodal membership function are presented, which have found application in fuzzy analysis in such fields as ecology and chemical technology. In this article, a set of fuzzy numbers with a unimodal membership function of a special type is considered. Two binary operations (addit...

Full description

Saved in:
Bibliographic Details
Published inVestnik, St. Petersburg University. Mathematics Vol. 55; no. 4; pp. 380 - 388
Main Authors Germashev, I. V., Derbisher, E. V., Derbisher, V. E., Kartashova, A. V., Titov, A. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2022
Springer Nature B.V
Subjects
Algebra
Analysis
Chemical technology
Fuzzy sets
Mathematics
Mathematics and Statistics
Multiplication
algebra
associativity
distributivity
arithmetic operations
fuzzy numbers
Online AccessGet full text

Cover

More Information
Summary:Fuzzy numbers with a unimodal membership function are presented, which have found application in fuzzy analysis in such fields as ecology and chemical technology. In this article, a set of fuzzy numbers with a unimodal membership function of a special type is considered. Two binary operations (addition and multiplication) are defined for this set, calculation formulas 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 with respect to both operations. We note that if we add neutral elements with respect to addition and multiplication to the given algebra, we obtain a commutative semiring. Conditions are formulated under which there exist quasineutral and quasi-inverse elements.
ISSN:1063-4541
1934-7855
DOI:10.1134/S1063454122040069