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ON ( $\alpha, \beta$ )-FUZZY Hv-IDEALS OF H_{v}-RINGS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 4، دوره 5، شماره 2، شهریور 2008، صفحه 35-47 اصل مقاله (192.63 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2008.331 | ||
| نویسندگان | ||
| B. Davvaz* 1؛ P. Corsini2 | ||
| 1Department of Mathematics, Yazd University, Yazd, Iran | ||
| 2Dipartimento di Matematica e Informatica, Via delle Scienze 206, 33100 Udine, Italy | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Hyperstructure؛ H_{v}-ring؛ Fuzzy set؛ Fuzzy H_{v}-ideal | ||
| مراجع | ||
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