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ON ($\epsilon, \epsilon \vee q$)-FUZZY IDEALS OF BCI-ALGEBRAS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 7، دوره 6، شماره 1، اردیبهشت 2009، صفحه 81-94 اصل مقاله (198.14 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2009.222 | ||
| نویسندگان | ||
| Jianming Zhan* 1؛ Young Bae Jun2؛ Bijan Davvaz3 | ||
| 1Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province,445000, P. R. China | ||
| 2Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea | ||
| 3Department of Mathematics, Yazd University, Yazd, Iran | ||
| چکیده | ||
| The aim of this paper is to introduce the notions of ($\epsilon, \epsilon \vee q$)- fuzzy p-ideals, ($\epsilon, \epsilon \vee q$)-fuzzy q-ideals and ($\epsilon, \epsilon \vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterization theorems for these generalized fuzzy ideals are proved and the relationship among these generalized fuzzy ideals of BCI-algebras is discussed. It is shown that a fuzzy set of a BCI-algebra is an ($\epsilon, \epsilon \vee q$)-fuzzy a-ideal if and only if it is both an ($\epsilon, \epsilon \vee q$)-fuzzy p-ideal and an ($\epsilon, \epsilon \vee q$)-fuzzy q-ideal. Finally, the concept of implication-based fuzzy a-ideals in BCI-algebras is introduced and, in particular, the implication operators in Lukasiewicz system of continuousvalued logic are discussed. | ||
| کلیدواژه‌ها | ||
| BCI-algebra؛ ($\epsilon؛ \epsilon \vee q$)-fuzzy (p-؛ q- and a-) ideal؛ Fuzzy logic؛ Implication operator | ||
| مراجع | ||
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