Abstract
We introduce the notion of (i-v) semiprime (irreducible) fuzzy ideals of semigroups and investigate its different algebraic properties. We study the interrelation among (i-v) prime fuzzy ideals, (i-v) semiprime fuzzy ideals, and (i-v) irreducible fuzzy ideals and characterize regular semigroups by using these (i-v) fuzzy ideals.
Highlights
Zadeh [1] first introduced the concept of fuzzy sets in 1965
An idea of connecting the fuzzy sets and algebraic structures came first in Rosenfeld’s mind. He first introduced the notion of fuzzy subgroup [2] in 1971 and studied many results related to groups
After that fuzzification of any algebraic structures has become a new area of research for the researchers
Summary
Zadeh [1] first introduced the concept of fuzzy sets in 1965. After that it has become an important research tool in mathematics as well as in other fields. Let I be a semiprime ideal of a semigroup S and μan (i-v) fuzzy subset of S defined by μ (p) = {1[̃α, , β] , when p ∈ I; otherwise, (2) A nonconstant (i-v) fuzzy ideal μof a semigroup S is called an (i-v) completely semiprime fuzzy ideal of S if for any (i-v) fuzzy point xã of S xã ∘ xã ∈ μimplies xã ∈ μ. Let χI be an (i-v) completely semiprime fuzzy ideal of S.
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