Geodesic
Quotient algebraic structures on the set of fuzzy numbers
Kybernetika, Tome 51 (2015) no. 2, pp. 255-267 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A. M. Bica has constructed in [6] 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 $[0,1]$.
A. M. Bica has constructed in [6] 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 $[0,1]$.
DOI : 10.14736/kyb-2015-2-0255
Classification : 08A72, 54H11
Keywords: fuzzy number; function with bounded variation; semigroup (monoid) with involution; topological group; metric space 
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Fechete, Dorina; Fechete, Ioan. Quotient algebraic structures on the set of fuzzy numbers. Kybernetika, Tome 51 (2015) no. 2, pp. 255-267. doi: 10.14736/kyb-2015-2-0255

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