ON ($\epsilon, \epsilon \vee q$)-FUZZY IDEALS OF BCI-ALGEBRAS

Document Type : Research Paper


1 Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province,445000, P. R. China

2 Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea

3 Department of Mathematics, Yazd University, Yazd, Iran


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.


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