Abstract
In order to generalize the notions of a (∈,∈∨q)-fuzzy subring and various (∈,∈∨q)-fuzzy ideals of a ring, a (λ,μ)-fuzzy subring and a (λ,μ)-fuzzy ideal of a ring are defined. The concepts of (λ,μ)-fuzzy semiprime, prime, semiprimary and primary ideals are introduced, and the characterizations of such fuzzy ideals are obtained based on a (λ,μ)-cut set.MSC:16L99, 03E72.
Highlights
The concept of a fuzzy set introduced by Zadeh [ ] was applied to the group theory by Rosenfeld [ ] and the ring theory by Liu [ ]
In order to give more general concepts of a fuzzy subring and a fuzzy ideal of R, we introduce the following definitions
Proof We only prove the case of a (λ, μ)-fuzzy subring
Summary
The concept of a fuzzy set introduced by Zadeh [ ] was applied to the group theory by Rosenfeld [ ] and the ring theory by Liu [ ]. Definition [ ] A fuzzy subset A of R is said to be an (∈, ∈ ∨q)-fuzzy ideal of R if ( ) A is an (∈, ∈ ∨q)-fuzzy subring of R, ( ) xt ∈ A, y ∈ R =⇒ (xy)t, (yx)t ∈ ∨qA, ∀t ∈
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