GENERALIZED FUZZY POLYGROUPS

Document Type: Research Paper

Authors

1 Department of Mathematics, Yazd University, Yazd, Iran

2 Dipartimento Di Matematica E Informatica, Via Delle Scienze 206, 33100 Udin, Italy

Abstract

small Polygroups are multi-valued systems that satisfy group-like
axioms. Using the notion of “belonging ($\epsilon$)” and “quasi-coincidence (q)” of
fuzzy points with fuzzy sets, the concept of ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy subpolygroups is
introduced. The study of ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy normal subpolygroups of a polygroup
are dealt with. Characterization and some of the fundamental properties of
such fuzzy subpolygroups are obtained. ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy cosets determined by
($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy subpolygroups are discussed. Finally, a fuzzy subpolygroup
with thresholds, which is a generalization of an ordinary fuzzy subpolygroup
and an ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy subpolygroup, is defined and relations between two
fuzzy subpolygroups are discussed.

Keywords


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