关于BL-代数的模糊滤子与模糊理想

在BL-代数中引入模糊超滤子和模糊固执滤子的概念,证明了如下条件对于BL-代数的非常数模糊滤子f来说是等价的:(1)f是布尔的和素的,(2)f是蕴涵的和素的,(3)f是超的,(4)f是固执的。应用模糊正蕴涵滤子给出G-代数的若干特征性质。提出BL-代数模糊理想的概念,给出一些重要例子,并通过例子说明在BL-代数中模糊理想一般不能由模糊滤子导出。同时,从模糊理想出发构造了商BL-代数,并建立了相应的同态基本定理。最后,研究了BL-代数的几类模糊理想及其相互关系,给出模糊布尔理想、模糊素理想、模糊超理想的特征性质。     

R_0代数中素滤子的拓扑性质

首先讨论了R_0代数M中MP滤子、素滤子的基本性质,然后通过自然的方式在M的全体素滤子之集PF_(IL)(M)上构造拓扑,证明了PF_(IL)(M)是紧致的T_0空间.最后把PF_(IL)(M)上的拓扑限制在M的全体极大滤子之集MF_(IL)(M)上,得到MF_(IL)(M)是紧致的Hausdorff空间.     

Fuzzy Weak Regular,Strong and Preassociative Filters in Residuated Lattices

In this paper, the notions of fuzzy weak regular, strong and preassociative filters are introduced with some properties of them investigated. In particular, under the context of Glivenko algebras, fuzzy weak regular filters and regular ones are equivalent and characterizations of Glivenko algebras are concluded by characterizations of fuzzy strong filters. At last the notion of fuzzy preassociative filters are defined, which are proved to coincide with fuzzy Boolean filters, and then some new alternative definitions of Boolean algebras are obtained by this type of filters.     

Spectrum topology of a residuated lattice

In this paper, given a non-commutative residuated lattice L, a topological space is constructed using certain fuzzy subsets of L. Indeed, we show that the set of all prime fuzzy filters of a non-commutative residuated lattice L forms a topological space. Particularly, we show that this space is compact and a T ₀-space and its certain subspaces are Hausdorff spaces. Finally, we show that the set of all prime filters of L is also a Hausdorff space.     

偏序集中的弱理想和弱滤子

在偏序集上利用上集算子和下集算子引入了弱理想,弱滤子,弱素理想,弱素滤子,弱极大理想和弱极大滤子等概念,研究了它们的若干性质,同时给出了偏序集上的(DPI),(BPI),(DMI),(BUF)公理并建立了它们与Zorn引理之问的相互关系.     

Fuzzy prime Boolean filters and their operations in IMT L-algebras

Some characterizations of fuzzy prime Boolean filters of IMT L-algebras are given. The lattice operations and the order-reversing involution on the set PB(M) of all fuzzy prime Boolean filters of IMT L-algebras are defined. It is showed that the set PB(M) endowed with these operations is a complete quasi-Boolean algebra (a distributive complete lattice with an order-reversing involution). It is derived that the algebra M=F, which is the set of all cosets of F, is isomorphic to the Boolean algebra {0; 1} if F is a fuzzy prime Boolean filter. By introducing an adjoint pair on PB(M), it is proved that the set PB(M) is also a residuated lattice.     

Some kinds of falling fuzzy filters of lattice implication algebras

In this paper, the concepts of falling fuzzy(implicative, associative) filters of lattice implication algebras based on the theory of falling shadows and fuzzy sets are presented at first. And then the relations between fuzzy(implicative, associative) filters and falling fuzzy(implicative, associative) filters are provided. In particular, we put forward an open question on a kind of falling fuzzy filters of lattice implication algebras. Finally, we apply falling fuzzy inference relations to lattice implication algebras and obtain some related results.     

On fuzzy fantastic filters of lattice implication algebras

Fuzzification of a fantastic filter in a lattice implication algebra is considered. Relations among a fuzzy filter, a fuzzy fantastic filter, and fuzzy positive implicative filter are stated. Conditions for a fuzzy filter to be a fuzzy fantastic filter are given. Using the notion of level set, a characterization of a fuzzy fantastic filter is considered. Extension property for fuzzy fantastic filters is established. The notion of normal/maximal fuzzy fantastic filters and complete fuzzy fantastic filters is introduced, and some related properties are investigated.     

半环上的模糊素理想和模糊素根

引入了半环的模糊素理想的概念,给出了它的几种刻画方式,得到了它的一些性质;进一步定义了模糊素理想的模糊素根,获得了一些漂亮结果。     

Some Properties of Fuzzy Filter and Its Category

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S-fuzzy Version of Stone's Theorem for Distributive Lattices

In this paper,we initiate a study of S-fuzzy ideal(filter) of a lattice where S stands for a meet semilattice.A S-fuzzy prime ideal(filter) of a lattice is defined and it is proved that a S-fuzzy ideal(filter) of a lattice is S-fuzzy prime ideal(filter) if and only if any non-empty α-cut of it is a prime ideal(filter).Stone's theorem for a distributive lattice is extended by considering S-fuzzy ideals(filters).     

Fuzzy半群中的Fuzzy素理想

探讨Fuzzy半群中Fuzzy素理想,Fuzzy 完全理想与Fuzzy理想的根的一些代数性质,证明Fuzzy半群中每一个Fuzzy理想是Fuzzy完全半素理想当且仅当它可表为一族Fuzzy完全素理想之交。     

Quantale中的模糊滤子

在Quantale中引入模糊滤子的概念,研究了它的一系列性质,得到了若干等价刻画,讨论了Quantale中滤子和模糊滤子之间的相互确定关系,证明了Quantale态射既保模糊滤子又反射模糊滤子。给出了模糊滤子在Quantale态射下的像的具体结构。     

关于剩余格中滤子的格结构

This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice. Also, the concept of prime filter in residuated lattice was proposed and some equivalent conditions about prime filter were given.     

On (∈, ∈ ∨ q)‐fuzzy filters of R0‐algebras

In this paper, we introduce the notions of (∈, ∈ ∨ q)‐fuzzy filters and (∈, ∈ ∨ q)‐fuzzy Boolean (implicative) filters in R₀‐algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that a fuzzy set in R₀‐algebras is an (∈, ∈ ∨ q)‐fuzzy Boolean filter if and only if it is an (∈, ∈ ∨ q)‐fuzzy implicative filter. Finally, we consider the concepts of implication‐based fuzzy Boolean (implicative) filters of R₀‐algebras (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

蕴涵格的同余关系及熵蕴涵格

在蕴涵格中引入了蕴涵滤子的概念 ,讨论了蕴涵滤子的一些基本性质 ,并由此建立了由素蕴涵滤子决定的同余关系及其商蕴涵格 ,以便为Fuzzy推理建立严格的逻辑基础作些必要的准备 .     

A Note on Closed Degrees of Difficulty of the Medvedev Lattice

We consider some nonprincipal filters of the Medvedev lattice. We prove that the filter generated by the nonzero closed degrees of difficulty is not principal and we compare this filter, with respect to inclusion, with some other filters of the lattice. All the filters considered in this paper are disjoint from the prime ideal generated by the dense degrees of difficulty. Mathematics Subject Classification: 03D30.     

阿基米德序半群的链的若干刻画

本文首先引入了一个序半群$S$的准素模糊理想的概念,通过序半群$S$上的一些二元关系以及它的理想的模糊根给出了该序半群是阿基米德序子半群的半格的一些刻画.进一步地借助于序半群$S$的模糊子集对该序半群是阿基米德序子半群的半格进行了刻画.尤其是通过序半群的模糊素根定理证明了序半群$S$是阿基米德序子半群的链当且仅当$S$是阿基米德序子半群的半格且$S$的所有弱完全素模糊理想关于模糊集的包含关系构成链.     

蕴涵格的滤子及同余关系

在蕴涵格中引和了蕴涵滤子的概念，讨论了蕴涵滤子的一些基本性质，并由此建立了由素蕴涵滤子决定的同余关系及其商蕴涵格，以便为Fuzz推理建立了严格的逻辑基础作些必要的准备。     

${R}_{0}$代数中的滤子格

Abstract In the present paper, some basic properties of MP filters of Ro algebra M are investigated. It is proved that（FMP（M）,包含,′∧^-∨^-,{1},M）is a bounded distributive lattice by introducing the negation operator ′, the meet operator ∧^-, the join operator ∨^- and the implicati on operator → on the set FMP（M） of all MP filters of M. Moreover, some conditions under which （FMP（M）,包含,′∨^-,→{1},M）is an Ro algebra are given. And the relationship between prime elements of FMP （M） and prime filters of M is studied. Finally, some equivalent characterizations of prime elements of .FMP （M） are obtained.