ON (∈,∈∨ q)-FUZZY IDEALS OF BCI-ALGEBRAS
نویسندگان
چکیده
The aim of this paper is to introduce the notions of (∈,∈ ∨ q)fuzzy p-ideals, (∈,∈ ∨ q)-fuzzy q-ideals and (∈,∈ ∨ 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 (∈,∈∨ q)-fuzzy a-ideal if and only if it is both an (∈,∈∨ q)-fuzzy p-ideal and an (∈,∈∨ 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.
منابع مشابه
ON ($epsilon, epsilon vee q$)-FUZZY IDEALS OF BCI-ALGEBRAS
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 characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras i...
متن کاملSome types of $(in,ivq)$-interval-valued fuzzy ideals of BCI algebras
In this paper, we introduce the notions of interval-valued and $(in,ivq)$-interval-valued fuzzy ($p$-,$q$- and $a$-) ideals of BCI algebras and investigate some of their properties. We then derive characterization theorems for these generalized interval-valued fuzzy ideals and discuss their relationship.
متن کاملSoft subalgebras and soft ideals of BCK/BCI-algebras related to fuzzy set theory
The notion of ∈-soft set and q-soft set based on a fuzzy set is introduced, and characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCIalgebras are provided. Using the notion of (∈,∈∨ q)-fuzzy BCK/BCI subalgebras/ideals, characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCI-algebras are established. AMS subject classifications: 06D72, ...
متن کامل-fuzzy Sub- Commutative Ideals in Bci-algebras
The concept of fuzzy set, which was published by Zadeh in his classic paper [24] of 1965, was applied by many researchers to generalize some of the basic concepts of algebra. The fuzzy algebraic structures play a central role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, topo...
متن کاملSoft Bci-implicative Ideals of Soft Bci-algebras
The notion of soft BCI-implicative ideals and BCI-implicative idealistic soft BCI-algebras is introduced and their basic properties are discussed. Relations between soft ideals and soft BCI-implicative ideals of soft BCI-algebras are provided. Also idealistic soft BCI-algebras and BCI-implicative idealistic soft BCI-algebras are being related. The intersection, union, “AND” operation and “OR” o...
متن کامل