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Quotient algebraic structures on the set of fuzzy numbers

Dorina Fechete, Ioan Fechete (2015)

Kybernetika

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 ] .

Quotients and homomorphisms of relational systems

Ivan Chajda, Helmut Länger (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Relational systems containing one binary relation are investigated. Quotient relational systems are introduced and some of their properties are characterized. Moreover, homomorphisms, strong mappings and cone preserving mappings are introduced and the interplay between these notions is considered. Finally, the connection between directed relational systems and corresponding groupoids is investigated.

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