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《模糊系统与数学》2014,(2)
伪BCK-代数是非可换模糊逻辑(蕴涵片段)的基本代数框架,伪BCI-代数是伪BCK-代数的推广,本文研究伪BCI-代数的结构。首先,借助BZ-代数(又称弱BCC-代数)给出伪BCI-代数的一个特征性质;其次,通过引入群逆伪BCI-代数的概念,研究了伪BCI-代数与(非可换)群之间的关系;接着,引入群逆滤子、优滤子和正规滤子的概念,并通过它们给出伪BCI-代数成为群逆伪BCI-代数(以及滤子成为p-滤子)的充要条件;最后,证明了如下结论:(1)平均伪BCI-代数等价于p-半单BCI-代数;(2)伪BCI-代数的每一个滤子是p-滤子,当且仅当它是群逆的且其伴随群的每一个子群是正规子群。 相似文献
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引入了BCK-代数的范数与距离的概念,给出了赋范BCK-代数的一些基本性质,证明了赋范BCK-代数的同构(同态)像和原像仍是赋范BCK-代数,研究了BCK-代数与BCK-代数笛卡儿之间的赋范性质关系.并且引入了赋范BCK-代数的点列极限概念,研究了极限的相关性质.讨论了有界赋范BCK-代数的与模糊BCK-代数的关系. 相似文献
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应用模糊点和模糊集间的关系,给出BCK-代数(∈,∈)((∈,∈∨q),(∈-),(∈- ∨(q-))-模糊蕴涵理想的定义,描述了BCK-代数的(∈,∈)-模糊蕴涵理想与模糊理想,模糊子代数间的关系,研究了BCK-代数的模糊子集为(∈,∈)((∈,∈∨q),((∈-,(∈- ∨(q-))-模糊蕴涵理想的充要条件. 相似文献
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一个BCK-代数叫做关联的,如果它满足 (1).x*(y*x)=x K.Is’eki[2]证明了满足(1)的BCI-代数是一个BCK-代数。于是为了引入关联BCI-代数概念,先给出关联BCK-代数的等价条件。本文将不加说明地引用[1]中的记号和结论。 相似文献
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伪BCI-代数是一类非经典逻辑代数,它是伪BCK-代数的推广,而伪BCK-代数与各种非可换模糊逻辑代数有密切关系。本文从任意伪BCI-代数出发,构造了两种加法运算,进而得到两个导出半群。同时,本文引入强伪BCI-代数、伪BCI-代数的T-部分等概念,给出伪BCI-代数的T-部分成为伪BCI-滤子的一些等价条件。 相似文献
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通过对MV代数和Lukasiewicz命题演算系统的研究,我们对MV代数的定义进行了简化,并讨论了MV代数和其它代数之间的关系。主要结果是:(1)从蕴涵角度出发,给出了MV代数的两种简化定义;(2)提出了弱格蕴涵代数的概念,并证明了它与BR0代数等价;(3)证明了弱格蕴涵代数是正则Fuzzy蕴涵代数。 相似文献
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研究元素个数不超过6的真伪BCK-代数的计数问题.首先,证明了在元素个数不超过3的偏序集上不存在真伪BCK-代数.其次,引入NP-型偏序集(不存在真伪BCK-代数的含重大元的偏序集)、偏序集的层、次余原子等概念,证明了在一个层数n≤3的NP-型偏序集上添加孤立余原子(或孤立次余原子或上邻元的个数n≥3的极小次余原子)后得到的偏序集也是NP-型偏序集,由此得到26种NP-型偏序集(元素个数n≤6).最后,借助Matlab软件编程计算得出所有非同构的元素个数不超过6的真伪BCK-代数,其中元素个数为4的真伪BCK-代数2个,元素个数为5的真伪BCK-代数34个,元素个数为6的真伪BCK-代数631个. 相似文献
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§1. IntroductionByaBCI-algebrawemeananalgebra(X,,0)oftype(2,0)withthefollowingcondi-tions:(1)((xy)(xz))(zy)=0;(2)(x(xy))y=0;(3)xx=0;(4)xy=yx=0impliesx=y.IfaBCI-algebra(X,,0)satisfies(5)0x=0.thenitiscalledaBCK-algebra.InaBCI-algebra,thef… 相似文献
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格蕴涵代数与BCK代数的关系 总被引:2,自引:1,他引:2
本文给出了有界可换的BCK代数的分配性的一些等价条件,指出了格蕴涵代数与有界可换分配的BCK代数以及格H蕴涵代数与有界关联的BCK代数之间的对偶关系 相似文献
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FI代数,BCK代数与关联半群 总被引:7,自引:3,他引:4
文献[1]讨论了Fuzzy蕴涵代数(简称为FI代数)与MV代数、格蕴涵代数之间的关系,本文进一步讨论了FI代数与有界关联BCK代数、关联半群的联系,并应用FI代数方法简化了BCK代数中某些定理的证明。 相似文献
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Jie Meng 《Semigroup Forum》1995,50(1):89-96
Chan and Shum [2] introduced the notion of implicative semigroups and obtained some of its important properties. BCK algebras
with condition (S) were introduced by Iséki [4] and extensively investigated by several authors. In this note, we prove that
implicative commutative semigroups are equivalent to BCK algebras with condition (S), that is, given an algebra <S;≤,·,*,1> of type (2,2,0), define ⊗ by stipulatingx⊗y=y*x and ≺ by puttingx≺y if and only ify≤x, then <S≤,·,*,1> is an implicative commutative semigroup if and only if <S;≺,·,⊗, 1> is a BCK algebra with condition (S); a nonempty subsetF ofS is an ordered filter of <S;≤,·,*, 1> if and only ifF is an ideal of <S;≺,·, ⊗, 1>.
The author would like to thank the referee for his valuable comments which helped in the modification of this paper. 相似文献
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Shaoxian Xu 《Southeast Asian Bulletin of Mathematics》2003,26(3):535-540
We give some semigroup characterizations for implicative BCK-algebras, and prove that the adjoint semigroups of implicative BCK-algebras are residualed semigroups.AMS Subject Classification (2000): 03G25, 06F35 相似文献
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Umberto Rivieccio 《Algebra Universalis》2014,71(2):155-186
The twist-structure construction is used to represent algebras related to non-classical logics (e.g., Nelson algebras, bilattices) as a special kind of power of better-known algebraic structures (distributive lattices, Heyting algebras). We study a specific type of twist-structure (called implicative twist-structure) obtained as a power of a generalized Boolean algebra, focusing on the implication-negation fragment of the usual algebraic language of twist-structures. We prove that implicative twist-structures form a variety which is semisimple, congruence-distributive, finitely generated, and has equationally definable principal congruences. We characterize the congruences of each algebra in the variety in terms of the congruences of the associated generalized Boolean algebra. We classify and axiomatize the subvarieties of implicative twist-structures. We define a corresponding logic and prove that it is algebraizable with respect to our variety. 相似文献
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The purpose of this paper is to prove that every semigroup with the zero is an orthogonal sum of orthogonal indecomposable
semigroups. We prove that the set of all 0-consistent ideals of an arbitrary semigroup with the zero forms a complete atomic
Boolean algebra whose atoms are summands in the greatest orthogonal decomposition of this semigroup.
Supported by Grant 0401A of RFNS through Math. Inst. SANU. 相似文献
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The main purpose of this paper is to exhibit the decisive role that order continuity plays in the structure of locally compact Boolean algebras as well as in that of atomic topological Boolean algebras. We prove that the following three conditions are equivalent for a topological Boolean algebra B: (1) B is compact; (2) B is locally compact, Boolean complete, order continuous; (3) B is Boolean complete, atomic and order continuous. Note that under the discrete topology any Boolean algebra is locally compact. 相似文献
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We investigate a new class of Boolean algebra, called initial chain algebras on pseudotrees. We discuss the relationship between this class and other classes of Boolean algebras. Every interval algebra, and hence every countable Boolean algebra, is an initial chain algebra. Every initial chain algebra on a tree is a superatomic Boolean algebra, and every initial chain algebra on a pseudotree is a minimally-generated Boolean algebra.We show that a free product of two infinite Boolean algebras is an initial chain algebra if and only if both factors are countable. 相似文献
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We prove that each computable Boolean algebra has a computable presentation in which for every computable family of automorphisms the set of atoms moved by at least one of its members is finite. This implies that each computable atomic Boolean algebra has a computable presentation in which its every computable family of automorphisms is finite. The priority argument is not used in the proof. 相似文献