Solving systems of equivalentions
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)].
scientific article; zbMATH DE number 5007499