Abstract
In this paper, the notion of interval-valuedm-polar fuzzy positive implicative ideals in BCK-algebras is presented. Then, the relationships between interval-valuedm-polar fuzzy positive implicative ideals and interval-valuedm-polar fuzzy ideals are investigated. After that, the concepts of interval-valuedm-polar∈,∈∨qκ˜-fuzzy positive implicative ideals and interval-valuedm-polar∈,∈ ∨qκ˜-fuzzy ideals are defined and some equivalent conditions are provided. Furthermore, we show that interval-valuedm-polar∈,∈ ∨qκ˜-fuzzy positive implicative ideals are interval-valuedm-polar∈,∈ ∨qκ˜-fuzzy ideals, but the converse need not be true in general and an example is given in this aim.
Highlights
IntroductionAs an extension of fuzzy sets, Zadeh [1] defined fuzzy sets with an interval-valued membership function proposing the concept interval-valued fuzzy sets. is concept has been studied from various points of view in different algebraic structures as BCK-algebras and some of its generalization (see, for example, [2,3,4,5,6,7]), groups (see, for example, [8,9,10]), and rings (see, for example, [11,12,13])
As an extension of fuzzy sets, Zadeh [1] defined fuzzy sets with an interval-valued membership function proposing the concept interval-valued fuzzy sets. is concept has been studied from various points of view in different algebraic structures as BCK-algebras and some of its generalization, groups, and rings
When more than one agreement has to work with the m-polar fuzzy model, it offers the system more accuracy, flexibility, and compatibility. e investigation of m-polar fuzzy algebraic structures started with the idea of textitm-pF lie subalgebras proposed by Akram et al [26]
Summary
As an extension of fuzzy sets, Zadeh [1] defined fuzzy sets with an interval-valued membership function proposing the concept interval-valued fuzzy sets. is concept has been studied from various points of view in different algebraic structures as BCK-algebras and some of its generalization (see, for example, [2,3,4,5,6,7]), groups (see, for example, [8,9,10]), and rings (see, for example, [11,12,13]). By generalizing the concept of m-polar fuzzy positive implicative ideals of BCK-algebras, Al-Masarwah et al [33] introduced the notions of (∈, ∈ ∨q)-fuzzy positive implicative ideals and (∈ , ∈ ∨q)-fuzzy positive implicative ideals in BCK-algebras. The notion of interval-valued m-polar fuzzy positive implicative ideals in BCK-algebras is presented. We. Mathematical Problems in Engineering prove that every interval-valued m-polar fuzzy positive implicative ideal of BCK-algebras is an interval-valued m-polar fuzzy ideal but the converse statement is not true in general and an example is given in this aim. We show that interval-valued m-polar (∈, ∈ ∨q κ)-fuzzy positive implicative ideals are interval-valued m-polar (∈, ∈ ∨q κ)-fuzzy ideals, but converse need not be true in general and an example is given in this aim
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