CAJ | 학술논문

本文研究了半群中的广义模糊k-理想和(∈,∈∨q(λ,μ))-模糊k-理想.利用模糊集的截集及模糊集的性质,获得了(∈,∈∨q(λ,μ))-模糊k-理想的等价刻画,广义模糊特征化及广义模糊k-理想直积的基本性.最后还给出了半群S是左k-诺特的充要条件是对于S的任意广义模糊左k-理想A,Im(A)是[λ,μ]上的良序子集.这些结果有重要的理论价值.
본문연구료반군중적엄의모호k-이상화(∈,∈∨q(λ,μ))-모호k-이상.이용모호집적절집급모호집적성질,획득료(∈,∈∨q(λ,μ))-모호k-이상적등개각화,엄의모호특정화급엄의모호k-이상직적적기본성.최후환급출료반군S시좌k-낙특적충요조건시대우S적임의엄의모호좌k-이상A,Im(A)시[λ,μ]상적량서자집.저사결과유중요적이론개치.
This article studies generalized fuzzy k-ideals and (∈,∈ ∨q(λ,μ))-fuzzy k-ideals in semigroups.By using the axiom method,fuzzy cut sets and the properties of fuzzy sets,we obtain the equivalent characterization of (∈,∈ ∨q(λ,μ))-fuzzy k-ideals and the fundamental properties of generalized fuzzy characteristic and the direct product of generalized fuzzy k-ideals.Finally,we discuss the k-notherian semigroups and obtain that a semigroup S is left k-notherian iff Im(A) is a well-ordered subset of [λ,μ] for each generalized fuzzy left k-ideals A of S.