布尔代数的(∈,∈∨q)-Fuzzy子代数和(∈,∈∨q)-Fuzzy理想

引入了布尔代数的(∈,∈∨q)-Fuzzy子代数、(∈,∈∨q)-Fuzzy理想和(∈,∈∨q)-Fuzzy商布尔代数的概念,给出了布尔代数的Fuzzy子集是(∈,∈∨q)-Fuzzy子代数((∈,∈∨q)-Fuzzy理想)的充要条件,讨论了布尔代数的(∈,∈∨q)-Fuzzy子代数((∈,∈∨q)-Fuzzy理想)在布尔代数同态下的像和逆像,并证明了当I是布尔代数R的(∈,∈∨q)-Fuzzy真理想时,R/I是布尔代数。

区间集上非交换剩余格〈∈,∈■Q〉-fuzzy滤子的构造

以区间集和滤子理论作为研究区间集上非交换剩余格〈∈,∈■Q〉-fuzzy滤子的工具,通过引入区间集上非交换剩余格〈∈,∈■Q〉-fuzzy滤子的概念,讨论了生成〈∈,∈■Q〉-fuzzy滤子的几种方法,彰显模糊逻辑推演系统被视为代数滤子的镜像.

区间集上非交换剩余格〈∈,∈∪Q〉-Fuzzy滤子的特征刻画

基于区间集思想与滤子理论,讨论区间集上非交换剩余格与区间集上非交换剩余格Fuzzy滤子,给出了区间集上非交换剩余格〈∈,∈∪Q〉-Fuzzy滤子的代数结构及若干等价性特征刻画的表示定理.

泛逻辑学中UB代数系统的(∈,∈∨q)-fuzzy滤子

何华灿教授给出了理想状态下的泛逻辑学的形式演绎系统β,并证明了该系统的可靠性。并且提出了理想状态下的泛逻辑学对应的代数系统-UB代数,并讨论了它们的性质。在以上这些结果的基础上,引入UB代数的(∈,∈∨q)-fuzzy滤子和(∈,∈∨q)-fuzzy关联滤子的概念,获得了它们的若干等价刻画,证明了(∈,∈∨q)-fuzzy关联滤子的扩张定理。

(∈,∈∨q)-Fuzzy线性空间

提出了 (∈ ,∈∨q) -Fuzzy域及 (∈ ,∈∨q) -Fuzzy域上 (∈ ,∈∨q) -Fuzzy线性空间的概念 ,给出了一个Fuzzy集是 (∈ ,∈∨q) -Fuzzy线性空间的充分必要条件 ,讨论了 (∈ ,∈∨q)

M-(∈,∈∨q)-Fuzzy子群

给出了M-(∈,∈∨q)-Fuzzy子群及M-(∈,∈∨q)-Fuzzy正规子群的定义,并讨论了它们的一些初等性质.

区间集上非交换剩余格的〈∈,∈∪Q〉-fuzzy布尔滤子及其特征性质

基于区间集思想、滤子理论和广义Boole格概念,引入了区间集上非交换剩余格fuzzy布尔滤子及其相应的〈∈,∈∪Q〉-fuzzy布尔滤子的概念,给出构成区间集上非交换剩余格〈∈,∈∪Q〉-fuzzy布尔滤子的充要条件,以及I(2U)上的〈∈,∈∪Q〉-fuzzy布尔滤子的特征性质.

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.

Fuzzy环上的(∈,∈Vq)—Fuzzy模

本文提出了(∈,∈V_q)—Fuzzy模的概念,给出了一个Fuzzy集是(∈,∈V_q)—Fuzzy模在模同态下的象及逆象。

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.

关于格蕴涵代数的(∈,∈∨q[k])-fuzzy LI-理想的注记

运用fuzzy集的思想和方法对格蕴涵代数的（∈，∈∨q[k]）-fuzzy LI-理想概念作进一步研究．引入了格蕴涵代数的（∈-，∈-∨q[k]-）-fuzzy LI-理想的概念并给出了它的一个等价刻画．讨论了（∈，∈∨q[k]）-fuzzy LI-理想和（∈-，∈-∨q[k]-）-fuzzy LI-理想与LI-理想的关系，建立并证明了相应的关系定理．

区间集上非交换剩余格的〈∈,∈凵 Q〉-fuzzy布尔滤子特征表示定理

基于区间集思想、滤子理论、广义布尔代数与Boole格,引入区间集上非交换剩余格fuzzy布尔滤子和区间集上非交换剩余格的〈∈,∈凵 Q〉-fuzzy布尔滤子的概念,讨论了〈∈,∈凵 Q〉-fuzzy布尔滤子的等价性特征表示定理。

ON (∈,∈ ∨q)-FUZZY FILTERS OF BL-ALGEBRAS

The authors introduce the notions of （∈, ∈ ∨q）-fuzzy Boolean （implicative, positive implicative, and fantastic） filters in BL-algebras, present some characterizations on these generalized fuzzy filters, and describe the relations among these generalized fuzzy filters. It is proved that an （∈, ∈ ∨q）fuzzy filter in a BL-algebra is Boolean （implicative） if and only if it is both positive implicative and fantastic.

GENERALIZED FUZZY FILTERS OF BL-ALGEBRAS

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued （∈,∈ ∨q）-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investigated. In particular, the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-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.

Interval Valued (∈,∈ ∨q)-Fuzzy Filters of MTL-Algebras

The concepts of interval valued （∈,∈ ∨q）-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships between these fuzzy filters in an MTL-algebra are investigated.

The characterization of Γ-modules in terms of fuzzy soft Γ-submodules

In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.

(∈,∈∨q)模糊素理想与(λ,μ)模糊子格(理想)

定义了格上的(∈,∈∨q)-f uzzy素理想,并且得到了相应的性质,同时定义了格上的(λ,μ)-f uzzy子格和f uzzy理想,进一步探讨了其上的一些性质,得出(∈,∈∨q)-模糊素理想的若干充要条件,讨论了(λ,μ)-f uzzy子格与(λ,μ)-f uzzy理想之间的关系。

泛逻辑学中UB代数系统的广义fuzzy滤子

将区间值fuzzy集的概念应用于理想状态(广义相关系数h=0.5,广义自相关系数k=0.5)下泛逻辑学所对应的代数系统——UB代数,引入区间值(∈,∈∨q)-fuzzy滤子和区间值(∈,∈∨q)-fuzzy关联滤子的概念并研究它们的性质。获得了UB代数的这两类广义fuzzy滤子的若干等价刻画,证明了区间值(∈,∈∨q)-fuzzy关联滤子的扩张定理。