Abstract
In this paper, we generalize anti-fuzzy ideals of near-rings, introduce the concept of (<,< ∨ϒ)-fuzzy ideals, prime (<,< ∨ϒ)-fuzzy ideals, semiprime (<,< ∨ϒ)-fuzzy ideals of near-rings and discuss some properties of such ideals.
Highlights
The notion of near-ring was first introduced by Dickson and Leonard in 1905 [1]
We note that the ideals of near-rings play a central role in the structure theory, they do not in general coincide with the usual ring ideals of a ring
The fuzzy algebraic structures play a major role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, topological spaces, logic, set theory, group theory, real analysis, measure theory etc
Summary
The notion of near-ring was first introduced by Dickson and Leonard in 1905 [1]. We note that the ideals of near-rings play a central role in the structure theory, they do not in general coincide with the usual ring ideals of a ring. Fuzzy set theory has been shown to be a useful tool to describe situations in which the data are imprecise or vague. In Biswas [6] introduced the concept of anti-fuzzy subgroups of groups, Kim and Jun studied the notion of anti-fuzzy R-subgroups of near-ring in [7], and Kim et al studied the notion of anti-fuzzy ideals in near-rings in [8]. We generalize anti-fuzzy ideals of nearrings, introduce the concept of (
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