University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 6 1 2009 02 11 ON ($\epsilon, \epsilon \vee q$)-FUZZY IDEALS OF BCI-ALGEBRAS ON ($\epsilon, \epsilon \vee q$)-FUZZY IDEALS OF BCI-ALGEBRAS 81 94 222 10.22111/ijfs.2009.222 EN Jianming Zhan Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province,445000, P. R. China Young Bae Jun Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea Bijan Davvaz Department of Mathematics, Yazd University, Yazd, Iran Journal Article 2007 11 11 The aim of this paper is to introduce the notions of ($\epsilon, \epsilon \vee q$)-<br />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<br />theorems for these generalized fuzzy ideals are proved and the relationship<br />among these generalized fuzzy ideals of BCI-algebras is discussed. It is shown<br />that a fuzzy set of a BCI-algebra is an ($\epsilon, \epsilon \vee q$)-fuzzy a-ideal if and only if it<br />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,<br />in particular, the implication operators in Lukasiewicz system of continuousvalued<br />logic are discussed. https://ijfs.usb.ac.ir/article_222_5803dad8f3359c0150f261e18f2d8330.pdf