正定关联BCI—代数

本文是作者［１］和［２］的继续，引入了正定关联ＢＣＩ－代数的概念，并证明了：正定关联ＧＢＣＫ－代数类和Ｐ－半单ＢＣＩ－代数类是正定关联ＢＣＩ－代数类的真子类。     

BCI代数的软关联理想和软正定关联理想

给出BCI代数的软关联理想和软正定关联理想的概念,讨论软理想、软关联理想和软正定关联理想三者之间的关系,研究了两个软关联理想(软正定关联理想)的扩展交、限制交、限制并和限制差分的性质。     

The Semigroup Characterizations of Nil BCI-Algebras

In this paper, some characterizations of nil BCI-algebras X are given by disscusing the adjoint semigroup of X. Moreover, the definition of generalized positive implicative BCI-algebras is introduced and some properties are obtained.AMS Subject Classification (1991): 03G25, 06F35.The subject supported by the Educational Committee of Hebei.     

The Semigroup Characterizations of Positive Implicative BCK—algebras

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＢｙａＢＣＩ－ａｌｇｅｂｒａｗｅｍｅａｎａｎａｌｇｅｂｒａ（Ｘ，，０）ｏｆｔｙｐｅ（２，０）ｗｉｔｈｔｈｅｆｏｌｌｏｗｉｎｇｃｏｎｄｉ－ｔｉｏｎｓ：（１）（（ｘｙ）（ｘｚ））（ｚｙ）＝０；（２）（ｘ（ｘｙ））ｙ＝０；（３）ｘｘ＝０；（４）ｘｙ＝ｙｘ＝０ｉｍｐｌｉｅｓｘ＝ｙ．ＩｆａＢＣＩ－ａｌｇｅｂｒａ（Ｘ，，０）ｓａｔｉｓｆｉｅｓ（５）０ｘ＝０．ｔｈｅｎｉｔｉｓｃａｌｌｅｄａＢＣＫ－ａｌｇｅｂｒａ．ＩｎａＢＣＩ－ａｌｇｅｂｒａ，ｔｈｅｆ…     

关于正关联BCK代数的一种扩张

在本文中，证明了每一个正关联ＢＣＫ－代数Ｘ均可嵌入于具有条件（Ｓ）的正关联ＢＣＫ－代数Ｘ^*，且Ｘ是Ｘ^*的一个子代数．特别地，当Ｘ是关联时，那么Ｘ^*也是关联的     

BCK-代数的Ω-模糊正定关联理想

给定一个集合Ω,引入了BCK-代数的Ω-模糊正定关联理想的概念,给出了一些恰当的例子,讨论了BCK-代数的Ω-模糊理想与Ω-模糊正定关联理想的关系.利用模糊正定关联理想,刻画了Ω-模糊正定关联理想.反之,模糊正定关联理想通过Ω-模糊正定关联理想来构造.证明了Ω-模糊正定关联理想(Ω-模糊理想)的同态原象仍是Ω-模糊理想(Ω-模糊理想).     

超*BCI-代数的商超代数

修改了超BCI-代数的定义,提出超*BCI-代数并对其性质作了研究.在此基础上,引入超*BCI-代数的左、右扩张、正定对换超*BCI-代数及其陪集等概念,给出了正定对换超*BCI-代数的商超代数定义,y并对其商超代数的性质作了研究.     

R_0代数的滤子理论

在R0代数中引入了正蕴涵滤子、奇异滤子、MV滤子的概念,讨论了这些滤子的性质及关系.得到了:在R0代数上,蕴涵滤子、正蕴涵滤子、布尔滤子是等价的;奇异滤子与MV滤子是等价的;正蕴涵滤子是奇异滤子,但反之不真.     

An answer to the Jun-Shim-Lele’s open problem on the fuzzy filters

In this note, a negative answer to the open problem of Jun, Shim and Lele on fuzzy filters of BCI-algebras is given, a necessary and sufficient condition, under which the open problem has a positive answer, is provided. Furthermore, we give two properties of fuzzy filters of BCI-algebras which generalize some results of Jun, Shim and Lele.     

闭模糊n级正关联理想

引入闭模糊n级正关联理想 ，刻划其结构和性质。     

Some types of filters in MTL-algebras

The aim of this work is to introduce the concepts of IMTL-filters and strong MTL-filters in MTL-algebras and show that these filters are related to IMTL-algebras and strong MTL-algebras, respectively. We also introduce the concepts of EIMTL and associative filters in MTL-algebras. The relationships between these filters and quotient algebras that are constructed via these filters are described. We clarify that EIMTL, IMTL and fantastic filters coincide in BL-algebras, whereas they have different properties in MTL-algebras; moreover, the relations between them are delineated. We prove that strong filters include some current filters such as implicative, positive implicative and fantastic filters.     

基于L~*-格值逻辑上的BCK-代数中直觉不分明化理想

在L~*-格值逻辑的语义框架下,以L~*-格值上的Lukasiewicz蕴涵算子为工具定义了L~*-格值逻辑上的直觉不分明化BCK-代数的概念,将用集论所刻画的BCK-代数中理想、正定蕴涵理想和蕴涵理想等概念在L~*-格值谓词演算下给予了新的刻画,讨论了它们的性质及其关系,研究了这些理想与其同态象、同态原象之间关系,获得了同类理想之积仍为该类理想.     

Positive set‐operators of low complexity

The powerset operator, ??, is compared with other operators of similar type and logical complexity. Namely we examine positive operators whose defining formula has a canonical form containing at most a string of universal quantifiers. We call them ?‐operators. The question we address in this paper is: How is the class of ?‐operators generated ? It is shown that every positive ?‐operator Γ such that Γ(??) ≠ ??, is finitely generated from ??, the identity operator Id, constant operators and certain trivial ones by composition, ∪ and ∩. This extends results of [3] concerning bounded positive operators.     

n ‐fold filters in BL‐algebras

In this paper we introduce n ‐fold (positive) implicative basis logic and the related algebras called n ‐fold (positive) implicative BL‐algebras. Also we define n ‐fold (positive) implicative filters and we prove some relations between these filters and construct quotient algebras via these filters. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fuzzyn-fold positive implicative filters in lattice implication algebras

The fuzzification of a positive implicative filter is considered, and some of properties are investigated. The relation among fuzzy filter, fuzzyn-fold implicative filter, and fuzzyn-fold positive implicative filter is discussed.     

划分图上的正影响数

一个社会网络中通常包括具有正面影响和负面影响的两类人员,为了研究这个社会网络中人们之间相互影响的某些规律,引入了一个新的概念. 用划分图G=(V,E),V=V⁺ \cup V^-表示这样的一个社会网络,其中V⁺和V^- 分别表示正面人员的集合和负面人员的集合. 图G的一个点子集D\subseteq V^-被称为G的一个正影响集,若G的每个点的至少一半的邻点在D\cup V⁺中. G的所有正影响集的最小基数称为G的正影响数. 给出G的正影响数的几个下界并证明了这些界是紧的. 此外,还证明了求正影响数问题在二部图和弦图上都是NP-完全的.     

Stability of Semilinear Delay Equations with Positive Solutions

We prove stability for a semilinear delay equation, whose nonlinearity is majorized by a linear positive operator. The key ingredients are a spectral condition, positivity of solutions to the linear problem, and lattice properties of the Banach space.     

关于实方阵的几个问题

本文讨论如下内容：１．把有关对称正定（半正定）的一些性质推广到广义正定（半正定）。２．给定ｘ∈Ｒｍ×ｍ，∧为对角阵，求ＡＸ＝ｘ∧在对称半正定矩阵类中解存在的充要条件及一般形式，并讨论了对任意给定的对称正定（半正定）矩阵Ａ，在上述解的集合中求得Ａ，使得     

Some Characterizations of Nil Ideals in BCI—algebras

51.IntrodcutionIn[1j,thenotionsofnilidealinBCI-algebrasandinlBCI-algebrawereintreduced.WeshowthatnilBCI-algebraisageneralizationofassociativeandquasi-associativeBCIalgebra([2J,[3j).lnthispaper,somecharacterizationsofnilidealsinBCI-algebraswereproved.Moreover,theBCI-algebrassatifyingO*x.=xwerediscussedandvariousproPertieswereproved.Werecallsomedefinitionsande1ementaryproperties.ThefollowingsaretrueinaBCI-al-gebra:(l)x o=x;(2)(x*y)*z=(x z) y;(3)x相似文献