ON ( $\alpha, \beta$ )-FUZZY Hv-IDEALS OF H_{v}-RINGS

Document Type : Research Paper


1 Department of Mathematics, Yazd University, Yazd, Iran

2 Dipartimento di Matematica e Informatica, Via delle Scienze 206, 33100 Udine, Italy


Using the notion of “belongingness ($\epsilon$)” and “quasi-coincidence
(q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ \alpha, \beta$)-
fuzzyHv-ideal of an Hv-ring, where , are any two of {$\epsilon$, q,$\epsilon$ $\vee$ q, $\epsilon$ $\wedge$ q} with
$ \alpha$ $\neq$ $\epsilon$ $\wedge$ q. Since the concept of ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy Hv-ideals is an important and
useful generalization of ordinary fuzzy Hv-ideals, we discuss some fundamental
aspects of ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy Hv-ideals. A fuzzy subset A of an Hv-ring R is an
($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy Hv-ideal if and only if an At, level cut of A, is an Hv-ideal
of R, for all t$\epsilon$(0, 0.5]. This shows that an($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy Hv-ideal is a
generalization of the existing concept of fuzzy Hv-ideal. Finally, we extend
the concept of a fuzzy subgroup with thresholds to the concept of a fuzzy
H_{v}-ideal with thresholds.


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