18032

ON (a,B)-FUZZY HV-IDEALS OF HV -RINGS

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Using the notion of "belongingness (€)" and "quasi-coincidence (q)" of fuzzy points with fuzzy sets, we introduce the concept of an (a, (3)- , ^ fuzzy Hv-ideal of an Hv-ring, where a, (3 are any two of {£, q, G Vg, G Ag} with a ^G Aq. Since the concept of (G,G Vg)-fuzzy Hv,-ideals is an important and" useful generalization of ordinary fuzzy Hv.-ideals, we discuss some fundamental aspects of (G, G Vg)-fuzzy Hv-ideals. A fuzzy subset A of an Hv,-ring R is an (G,G Vg)-fuzzy Hv,-ideal if and only if an At, level cut of A, is an Hv,-ideal of R, for all t € (0,0.5]. This shows that an (G,G Vg)-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.

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