L-fuzzy子格群乘积的刻画

借助L-fuzzy集的水平截集,给出L-fuzzy子格群乘积的若干等价刻画。     

L-fuzzy商群的L-fuzzy同构定理

给出了L-fuzzy群的L-fuzzy同态基本定理。同时建立了L-fuzzy商群的L-fuzzy同态和L-fuzzy同构定理。     

L-fuzzy矩形带

给出了L-fuzzy子矩形带的概念,并给出了L-fuzzy子半群与L-fuzzy子矩形带L-fuzzy同构的条件.     

共轭L-fuzzy子群的刻画

研究了共轭L-fuzzy集和共轭L-fuzzy子群的性质,借助于L-fuzzy集的四种水平截集,给出了关于它们的若干等价刻画。     

L-fuzzy子群乘积的刻画

借助于L-fuzzy集的四种水平截集,给出L-fuzzy子群乘积的若干等价刻画;作为其应用得到L-fuzzy子群乘积的共轭、L-fuzzy子群乘积的正规化子以及L-fuzzy子群乘积的同调的相关结果。     

L-fuzzy子群的L-fuzzy同态

给出了L-fuzzy子幺半群的概念及刻画．给出了一种真正的L-fuzzy子幺半群间的Lfuzzy同态和L-fuzzy同构等概念．最后证明了L-fuzzy子群在L-fuzzy同态映射和L-fuzzy同构逆映射下不变．     

L-fuzzy子域与L-fuzzy线性空间的新刻画

本文研究了L-fuzzy子域与L-fuzzy线性空间的性质.借助于Fuzzy集A的水平截集A(a),得到了若干新的等价刻画.且直接和方便于应用.     

基于群范畴的L-fuzzy结构提升范畴及其表示

引入群范畴上L-fuzzy结构提升范畴与格值结构提升范畴概念,L-fuzz结构是在逻辑层面表达群理论多值语义的有点化描述,也是Zermelo-Fr(a)nkel公理集合理论和各种代数形式理论的格值模型的语义赋值,而格值结构是在范畴层面表达群理论多值语义的无点化描述,本文建立了L-fuzzy结构与格值结构这两种不同数学结构之间的联系,证明了在范畴层面上述两种结构是同构的.给出了基于群范畴的L-fuzzy结构的格值结构表示.     

L-fuzzy向量空间的L-fuzzy线性映射

给出L-fuzzy向量空间的L-fuzzy线性映射等概念,并给出了它的一些等价刻画。     

L-fuzzy N-收敛空间

本文给出L-fuzzy N-收敛空间的定义,讨论L-fuzzy N-收敛空间范畴(L-fuzzyN-收敛空间和它们之间的连续映射构成的范畴)的若干范畴的性质,并且证明它的一个子范畴同构与L-fuzzy拓扑空间范畴.     

半环中带算子的L-模糊h-理想

The notions of M-hemirings and L-fuzzy left h-ideals with operators in M-hemirings are introduced,and some properties are investigated.Given an L-fuzzy left h-ideal with operators,a new L-fuzzy left h-ideal with operators is established. Using a collection of left M-h-ideals,L-fuzzy left h-ideais with operators are con- structed.Moreover,the concept of M-Notherian M-hemiring is introduced and its characterization is given.     

Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators

This paper proposes similarity of L-fuzzy relations based on L-topologies induced by L-fuzzy rough approximation operators. First, the notion L-fuzzy rough set is generalized and the relationship between generalized L-fuzzy rough sets and L-topologies on an arbitrary universe is investigated. It shows that Alexandrov L-topologies can be induced by L-fuzzy relations without any preconditions. Second, the concept of similarity of L-fuzzy relations is introduced and variations of an L-fuzzy relation are investigated. Third, algebraic structures on similarity of L-fuzzy relations are obtained. Finally, we prove that the subset of the transitive L-fuzzy relations similar to a fixed L-fuzzy relation is a complete distributive lattice.     

L—fuzzy Ring and L—fuzzy Module

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L-Fuzzy子环的L-Fuzzy同态的刻画

给出L-fuzzy子环的L-fuzzy同态和L-fuzzy子环的L-fuzzy模的L-fuzzy同构的一种新刻画。     

L-Fuzzy子群的L-Fuzzy直积的新刻画

研究L-fuzzy正规子群的性质,借助于L-fuzzy集A的水平截集A(a)和A[a],给出当L是完全分配格时L-fuzzy子群的L-fuzzy直积的若干等价刻画。     

On L-fuzzy systems

The concept of L-fuzzy systems is introduced. A universal structure of a special kind of L-fuzzy system and new constructions, based on a given L-fuzzy system, called the sup-quotient and inf-quotient L-fuzzy systems, respectively, are given. Problems of comparison and stabilities of L-fuzzy systems are discussed.