ON (, )-FUZZY Hv-IDEALS OF Hv-RINGS

Using the notion of "belongingness (2)" and "quasi-coincidence (q)" of fuzzy points with fuzzy sets, we introduce the concept of an (, )- fuzzy Hv-ideal of an Hv-ring, where , are any two of {2,q,2 _q,2 ^q} with 62 ^q. Since the concept of (2,2 _q)-fuzzy Hv-ideals is an important and useful generalization of ordinary fuzzy Hv-ideals, we discuss some fundamental aspects of (2, 2 _q)-fuzzy Hv-ideals. A fuzzy subset A of an Hv-ring R is an (2,2 _q)-fuzzy Hv-ideal if and only if an At, level cut of A, is an Hv-ideal of R, for all t 2 (0,0.5). This shows that an (2,2 _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 Hv-ideal with thresholds.