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

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.