Solving systems of equivalentions
type: Item
instance of: scholarly article
title: Solving systems of equivalentions
zbMATH Open document ID: 1104.15005
DOI: 10.1007/BF02831926
author: A. A. Bica
author: Adrian I. Ban
published in: Journal of Applied Mathematics and Computing
publication date: 2006-02-20T00:00:00Z
review text: The paper deals with algebras of fuzzy numbers and fuzzy number matrices. Arithmetic operations on fuzzy numbers are difficult for calculation and are not invertible [cf. \textit{H. J. Zimmermann}, Fuzzy set theory and its applications, (Boston), MA etc.: Kluwer Academic Publishers. (1991; Zbl 0719.04002), Chapter 5]. Therefore, the authors apply a congruence relation between fuzzy numbers [cf. \textit{M. Mareš}, Kybernetica 29, 121-132 (1993; Zbl 0788.04006)]. This leads to a quotient algebra which is a ring of fuzzy number cosets. Such algebra is used in the solution of systems of linear equivalences with fuzzy number coefficients (\(LR\)-fuzzy numbers). Property of distributivity is used in the Laplace rule for determinants over the algebra of fuzzy numbers. The final result can be defuzzified by using expected values of fuzzy numbers [cf. \textit{S. Heilpern}, Fuzzy Sets Syst. 91, 259-268 (1997; Zbl 0920.04011)].
reviewed by: Józef Drewniak
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 08A72
zbMATH DE Number: 5007499
zbMATH Keywords: fuzzy number
zbMATH Keywords: fuzzy arithmetic
zbMATH Keywords: fuzzy coefficients
zbMATH Keywords: equivalence of fuzzy quantities
zbMATH Keywords: system of linear equivalences
zbMATH Keywords: quotient algebra
MaRDI profile type: Publication
cites work: Q5699548
cites work: Q4716903
cites work: Solving linear and quadratic fuzzy equations
cites work: Solving fuzzy equations: A new solution concept
cites work: Solving systems of linear fuzzy equations
cites work: A new approach for ranking fuzzy numbers by distance method
cites work: On a canonical representation of fuzzy numbers
cites work: A fuzziness measure for fuzzy numbers: Applications
cites work: Fuzzy sets and systems. Theory and applications
cites work: Fuzzy interval analysis
cites work: The expected value of a fuzzy number
cites work: Q4886969
cites work: Representation and application of fuzzy numbers
cites work: Graded numbers and graded convergence of fuzzy numbers
cites work: On the convergence of \(T\)-sum of \(L\)-\(R\) fuzzy numbers
cites work: A law of large numbers for fuzzy numbers in a Banach space
cites work: Fuzzy arithmetic with requisite constraints
cites work: Q4886972
cites work: Q5288888
cites work: Q4281793
cites work: Q4886976
cites work: Q5687663
cites work: Weak arithmetic of fuzzy numbers
cites work: \(T\)-sums of L-R fuzzy numbers
cites work: New approaches for the comparison of L-R fuzzy numbers: A theoretical and operational analysis
cites work: A note to the \(T\)-sum of \(L\)-\(R\) fuzzy numbers
cites work: Shape preserving additions of fuzzy intervals
cites work: Generalized pseudo-convolution in the theory of probabilistic metric spaces, information, fuzzy numbers, optimization, system theory
cites work: Fuzzy addition in the L-fuzzy real line
cites work: Two new operators on fuzzy matrices.
cites work: Computational aspects of fuzzy arithmetics based on Archimedean t-norms
cites work: A method for solving a fuzzy linear programming
description: scientific article; zbMATH DE number 5007499