Kybernetika 51 no. 2, 255-267, 2015

Quotient algebraic structures on the set of fuzzy numbers

Dorina Fechete and Ioan FecheteDOI: 10.14736/kyb-2015-2-0255


A. M. Bica has constructed in \cite{Bica 2007} two isomorphic Abelian groups, defined on quotient sets of the set of those unimodal fuzzy numbers which have strictly monotone and continuous sides. In this paper, we extend the results of above mentioned paper, to a larger class of fuzzy numbers, by adding the flat fuzzy numbers. Furthermore, we add the topological structure and we characterize the constructed quotient groups, by using the set of the continuous functions with bounded variation, defined on $[0,1]$.


fuzzy number, function with bounded variation, semigroup (monoid) with involution, topological group, metric space


08A72, 54H11


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