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(۰, ۰.۵]. 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.

Keywords:

Hyperstructure , H_{v}-ring , Fuzzy set , Fuzzy H_{v}-ideal