Abstract
Using the idea of the new sort of fuzzy subnear-ring of a near-ring, fuzzy subgroups, and their generalizations defined by various researchers, we try to introduce the notion of (ϵ,ϵ∨q)-fuzzy ideals of N-groups. These fuzzy ideals are characterized by their level ideals, and some other related properties are investigated.
Highlights
Introduction and Basic DefinitionsThe concept of a fuzzy set was introduced by Zadeh [1] in 1965, utilizing what Rosenfeld [2] defined as fuzzy subgroups
We extend the idea of (ε, ε ∨ q)-fuzzy ideals of nearrings to the case of N-groups and introduce the idea of fuzzy cosets with some results
We prove the result for (ε, ε ∨ q)-fuzzy ideal S
Summary
Introduction and Basic DefinitionsThe concept of a fuzzy set was introduced by Zadeh [1] in 1965, utilizing what Rosenfeld [2] defined as fuzzy subgroups. A fuzzy subset A of a group G is called a fuzzy subgroup of G if it satisfies the following conditions: (i) A(x + y) ≥ min{A(x), A(y)}, (ii) A(−x) ≥ A(x), for all x, y ∈ G.
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