Fuzzy PMS Ideals in PMS Algebras

Abstract

In this paper, a new notion, namely fuzzification of PMS-algebra, a generalization of BCK/BCI/TM/KUS/PS-algebras is initiated along with fuzzified PMSideal and discussed some of its properties in detail.

t-Intuitionistic Fuzzy Structures on PMS-Ideals of a PMS-Algebra

“…Definition 1 (see [23]). A PMS-algebra is a nonempty set X with a constant 0 and a binary operation * of type (2, 0) satisfying the following axioms:…”

“…Definition 2 (see [23]). A nonempty subset S of a PMSalgebra is called a PMS-subalgebra of X if x * y ∈ S, for all x, y ∈ S. Definition 3 (see [23]).…”

“…Definition 2 (see [23]). A nonempty subset S of a PMSalgebra is called a PMS-subalgebra of X if x * y ∈ S, for all x, y ∈ S. Definition 3 (see [23]). A nonempty subset I of a PMS-algebra (X, * , 0) is said to be a PMS-ideal of X if it satisfies the following conditions:…”

“…Iseki [22] introduced another class of abstract algebra called BCI-algebra as a generalization of BCK-algebra. In 2016, Sithar Selvam and Nagalakshmi [23] introduced a new algebraic structure, known as PMS-algebra, as a generalization of BCK \BCI \TM \PS-algebras and investigated various related results. In the same year, Sithar Selvam and Nagalakshmi [24] also fuzzified a PMS-ideal in a PMS-algebra and investigated its basic properties.…”

On Homomorphism and Cartesian Products of Intuitionistic Fuzzy PMS-subalgebra of a PMS-algebra

“…In 2011, Anitha and Arjunan [1] studied the strongest intuitionistic fuzzy relations on intuitionistic fuzzy ideals of Hemirings and obtained some interesting results. In 2016, Sithar Selvam and Nagalakshmi [8] introduced a new class of algebra called PMS-algebra. Sithar Selvam and Nagalakshmi [7] fuzzified PMS-subalgebras and PMS ideals in PMS-algebra.…”