Generalized （∈, ∈ ∨ q）-fuzzy Ideals in BCK-algebras

In this paper, as a generalization of the notion of(∈, ∈∨ q)-fuzzy ideals, we introduced the notion of(∈, ∈∨ qδ)-fuzzy ideals and investigated their properties in BCKalgebras. Several equivalent characterizations of(∈, ∈∨ qδ)-fuzzy ideals are obtained and relations between(∈, ∈∨ qδ)-fuzzy ideals and ideals are discussed in BCK-algebras.

Generalized fuzzy ideals of near-rings

The concept of（∈,∈∨q）-fuzzy subnear-rings（ideals） of a near-ring is introduced and some of its related properties are investigated.In particular,the relationships among ordinary fuzzy subnear-rings（ideals）,（∈,∈∨ q）-fuzzy subnear-rings（ideals） and（∈,∈∨q）-fuzzy subnear-rings（ideals） of near-rings are described.Finally,some characterization of [μ]t is given by means of（∈,∈∨ q）-fuzzy ideals.

Redefined generalized fuzzy ideals of near-rings

With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings, and discuss the relationship between strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals and prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings.

(∈,∈∨q)-Fuzzy带算子环

进一步讨论了Fuzzy环理论，给出(∈，∈Vq)-Fuzzy带算子环、(∈，∈Vq)-Fuzzy带算理想和(∈，∈Vq)-Fuzzy带算商环的定义，同时讨论了他们的一些初等性质．

(∈,∈∨_(q(,λμ)))-模糊子近环和理想

给出(∈,∈∨q(λ,μ))-模糊子近环和理想的全新概念及刻画,并获得一些充分必要条件。其中值得指出的是当λ=0,μ=0.5时可以得到Davvaz文章中的相关结论[B.Davvaz,(∈,∈∨q)-fuzzysubnear-rings and ideals,soft comput.,2006,10:206-211]。当λ=0,μ=1时可以得到Rosenfeld意义下的结论。

布尔代数的(∈,∈∨q_(λ,μ))-模糊理想

文中给出了布尔代数的(∈,∈∨q(λ,μ))-模糊理想及广义模糊理想的新概念,得到了(∈,∈∨q(λ,μ))-模糊理想的一些等价刻画及基本性质。

N(2，2，0)代数的(∈,∈∨q_（λ，μ）)-模糊理想

对N(2,2,0)代数(∈,∈∨q_(λ,μ))-模糊理想进行了详细的研究。给出了N(2,2,0)代数广义模糊理想和点态化(∈,∈∨q_(λ,μ))-模糊理想的概念,讨论了两者之间的等价关系。给出了(∈,∈∨q_(λ,μ))-模糊理想的一些等价刻画,并研究了其相关性质。讨论了(∈,∈∨q_(λ,μ))-模糊理想的同态像与同态原像的关系。最后研究了(∈,∈∨q_(λ,μ))-模糊理想的直积。

N(2,2,0)代数的(∈,∈∨q_((λ,μ)))-模糊素理想

在N(2,2,0)代数中引入了素理想的概念;利用模糊集理论,提出了点态化(∈,∈∨úq(λ,μ))-模糊素理想和广义模糊素理想的概念,讨论了两者之间的关系;得到了(∈,∈∨q(λ,μ))-模糊素理想的一些等价刻画及其相关性质;研究了(∈,∈∨q(λ,μ))-模糊素理想同态像与同态原像的基本性质。

Γ-半群的Fuzzy理想

给出了Γ-半群上的Fuzzy子半群和Fuzzy理想概念,并利用Fuzzy点重于一个Fuzzy集的关系,给出了Γ-半群的(∈,∈∨q)-Fuzzy理想定义,并对其特征和相关性质进行了讨论.

BCI-代数中的(s,t]-模糊理想和R-模糊理想

本文在O.G.Xi于BCI-代数中给出模糊理想概念的有成效的工作的基础上,在BCI-代数中又定义了两种新的模糊理想.首先,我们利用模糊点与模糊集的关系定义了(s,t]-模糊理想,(∈,∈Vq)-模糊理想与(|∈-|,|∈-|Vq-)-模糊理想是它的两种特例.其次,我们运用模糊逻辑中的蕴涵算子的概念给出了R-模糊理想的定义,并讨论了R-模糊理想与(s,t]-模糊理想之间的关系.

BL-代数的(∈,∈∨q)-模糊理想

在BL-代数中引入了(∈,∈∨q)-模糊理想的概念,给出了(∈,∈∨q)-模糊理想的性质和等价刻画;然后,通过模糊积和模糊上集概念的引入,给出了(∈,∈∨q)-模糊理想的一个新的等价刻画;最后,在模糊陪集的基础上构造了商BL-代数.

On Fuzzy Interior Ideals in Semigroups

The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set. With this new concept, the interval valued （∈, ∈ Vq）-fuzzy interior ideal in semigroups is introduced. In fact, this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups. In this paper, this kind of fuzzy interior ideals and related properties will be investigated. Moreover, the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.

ON FUZZY h-IDEALS OF HEMIRINGS

The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the quasi-coincidence of a fuzzy point in a fuzzy set. By using this new concept, the authors define the notion of interval valued （∈, ∈ Vq）fuzzy h-ideals of hemirings and study their related properties. In addition, the authors also extend the concept of a fuzzy subgroup with thresholds to the concept of an interval valued fuzzy h-ideal with thresholds in hemirings.

Generalized Fuzzy Lie Ideals of Lie Algebras

In this paper we introduce new generalized fuzzy Lie ideals of Lie algebras and study some of their important properties.We characterize these generalized Lie ideals of Lie algebras by their level subsets.Some characterization of the generalized fuzzy Lie ideals of Lie algebras are also established.

格蕴涵代数的区间值(∈,∈∨q)-fuzzy LI-理想(英文)

将区间值fuzzy集的思想和方法应用于格蕴涵代数,引入格蕴涵代数的区间值(∈,∈∨q)-fuzzy LI-理想的概念并讨论它们的性质。获得区间值(∈,∈∨q)-fuzzy LI-理想的若干等价刻画;并考察区间值(∈,∈∨q)-fuzzy LI-理想与LI-理想之间的关系。

N(2,2,0)代数的(∈,∈Vq_(λ,μ))-模糊关联理想若干性质

对N(2,2,0)代数(∈,∈∨q_((λ,μ)))-模糊关联理想若干性质进行了详细的研究.首先,运用点态化的方法证明了(∈,∈∨q_((λ,μ)))-模糊关联理想的同态像与同态原像的基本性质;其次,研究了(∈,∈∨q_((λ,μ)))-模糊关联理想的直积;最后,讨论了(∈,∈∨q_((λ,μ)))-模糊关联理想的直积的投影子集.

广义模糊子坡与(∈,∈∨q_((λ,μ)))-模糊子坡

给出广义模糊子坡(理想)的概念,并探讨了一些相关性质,得到了她们的若干等价刻画;接着讨论了广义模糊子坡(理想)的同态原像、同态像及直积等,得到了一些有意义的结果;然后给出了广义模糊特征子坡(理想)的定义,得到了其等价刻画;最后给出了(∈,∈∨q(λ,μ))-模糊子坡(理想)的概念并对其进行了一些研究,揭示了(∈,∈∨q(λ,μ))-模糊子坡(理想)与广义模糊子坡(理想)之间的关系。

N(2,2,0)代数的(∈,∈∨q_(λ,μ))-模糊关联理想

从以下几个方面对N(2,2,0)代数(∈,∈∨q_((λ,μ)))-模糊关联理想进行了详细的研究.首先,给出N(2,2,0)代数广义模糊关联理想概念和点态化(∈,∈∨q_((λ,μ)))-模糊关联理想概念,研究了两者之间的等价关系;其次,给出了(∈,∈∨q_((λ,μ)))-模糊关联理想若干等价刻画;再次,讨论了(∈,∈∨q_((λ,μ)))-模糊关联理想与(∈,∈∨q_((λ,μ)))-模糊理想之间的关系;最后,获得了(∈,∈∨q_((λ,μ)))-模糊关联理想交与并的相关性质.

正则剩余格上的广义模糊蕴涵理想

给出正则剩余格的(α,β)一模糊蕴涵理想的概念,初步讨论了它们的一些性质及其问的关系;与(∈,∈∨q)-模糊蕴涵理想对应的讨论了(∈,∈∨q)-模糊蕴涵理想的性质;最后将正则剩余格的(α,β)-模糊蕴涵理想作进一步拓展,得有限个(λ,μ)-模糊蕴涵理想的交集仍然是(λ,μ)-模糊蕴涵理想,并描述了(λ,μ),(∈,∈∨q_((λ,μ)))-模糊蕴涵理想的性质。

A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy