Generalized m-Polar Fuzzy Positive Implicative Ideals of BCK-Algebras

Abstract

This study focuses on combining the theories of m -polar fuzzy sets over BCK -algebras and establishing a new framework of m -polar fuzzy BCK -algebras. In this paper, we define the idea of m -polar fuzzy positive implicative ideals in BCK -algebras and investigate some related properties. Then, we introduce the concepts of m -polar ∈ , ∈ ∨ q -fuzzy positive implicative ideals and m -polar ∈ ¯ , ∈ ¯ ∨ q ¯ -fuzzy positive implicative ideals in BCK -algebras as a generalization of m -polar fuzzy positive implicative ideals. Several properties, examples, and characterization theorems of these concepts are considered.

Interval-Valuedm-Polar Fuzzy Positive Implicative Ideals inBCK-Algebras

“…A subset (� ≠ )A of Z is called a subalgebra if, for all ϑ, ω ∈ Z, ϑ * ω ∈ A and is called an ideal of Z if 0 ∈ A and, for all ϑ, ω ∈ Z, ϑ * ω ∈ A, ω ∈ A implies ϑ ∈ A. Definition 1 (see [33]). A subset (∅ ≠ )P of Z is called a positive implicative ideal of Z if ∀ ϑ, ω, Z ∈ Z: (i) 0 ∈ P (ii) (ϑ * ω) * Z ∈ P and ω * Z ∈ P imply ϑ * Z ∈ P e interval number t is the interval [t − , t + ], where 0 ≤ t − ≤ t + ≤ 1, and D[0, 1] is the set of all interval numbers.…”

“…Takallo et al [32] proposed the notion of (∈, ∈)-fuzzy p-ideal in BCI-algebras and studied related properties of m-polar (∈, ∈)-fuzzy ideals and m-polar (∈, ∈)-fuzzy p-ideals in BCI-algebras. Recently, 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. Also, different kinds of concepts, related to this study, were investigated in various ways (see, for example, [34][35][36][37][38][39][40]).…”

New Class of Doubt Bipolar Fuzzy Sub Measure Algebra

“…The related characteristics of BCK-algebras using the fuzzy group notion are examined [9]. Jun et al have also researched fuzzy features of numerous ideas in BCK/BCI/RHOalgebras [10][11][12][13][14][15][16][17][18][19][20][21]. Huang [22], on the other hand, are concerned with BCI algebra in other ways.…”

A Novel Study Based on Fuzzy p-Ideals of BCI-Algebras

“…Eventually, the theory of these algebras has been developed rapidly and successfully with a specific focus on the ideal theory, for instance, Liu et al [3] studied qðaÞ-ideals while fuzzy h-ideals are given in [4], and hybrid ideals are considered by Muhiuddin et al [5,6] in BCK/ BCI-algebras. Recent research focused on several kinds of related ideals are studied in [7][8][9][10].…”