完备格Brouwer上伪t-模与蕴涵算子的注记(Ⅱ)

进一步研究完备Brouwer格上伪t-模与蕴涵算子,给出同二元算子生成的伪t-模与蕴涵算子的计算公式。     

完备Brouwer格上伪t-模与蕴涵算子的注记(I)

进一步研究完备Brouwer格上伪t-模和蕴涵算子,讨论完备Brouwer格上伪t-模和蕴涵算子的直积分解。     

关于《完备Brouwer格上伪t-模与蕴涵算子》的注记

举例说明关于伪t-模与蕴涵算子的文献[FSS 132(2002)113]中定理4.1是错误的,此定理还被接连用到[FSS 139(2003)673]及其它文献。本文进而给出此基础性定理成立的一个必要条件。注意,该必要条件是不能由无穷∨-分配伪t-模与无穷∧-分配蕴涵算子的定义引出的。     

广义单侧剩余广群

对吴氏左（右）剩余广群，给出一种新而且简化的定义，并详细地讨论其基本性质。用其主要结论得到完备格上的所有无穷∨-分配强伪t-模与所有无穷∧-分配强蕴涵算子之间的关系。     

强De Morgan代数上的广义R0 t-模

在De Morgan代数上引入广义R0算子,举例说明了一般De Morgan代数中的广义R0算子不能构成t-模。引入强De Morgan代数的概念,讨论它的基本性质,证明强De Morgan代数L上的广义R0算子构成t-模(称为广义R0t-模)。给出若干重要反例,并证明强De Morgan代数上的广义R0t-模是左连续的。     

伪统一模与剩余格之间的关系

讨论伪统一模与剩余格之间的关系,证明完备格上无穷∨-分配伪统一模和它的剩余蕴涵算子构成一个完备剩余格,并说明任给一个完备剩余格L=(L,∧,∨,*,e→,,*是无穷∨-分配的伪统一模,→和(?)是*的剩余蕴涵算子.     

模糊合取性质的进一步研究

本文进一步研究了模糊合取及其诱导模糊蕴涵的相关性质。在讨论了模糊合取的EP性质与结合性之间关系的基础上,得到了一个模糊合取成为一个t-模的条件;还研究了两个模糊合取各自诱导的模糊蕴涵取小(取大)与模糊合取取大(取小)诱导的模糊蕴涵之间的关系;最后给出了关于模糊合取诱导模糊蕴涵刻画的一个结果。     

直觉语言Hamacher加权集结算子及其应用

研究带参数的直觉语言Hamacher集结算子。基于Hamacher t-模与s-模定义直觉语言Hamacher运算法则。而后,利用所提Hamacher运算法则提出含参数的直觉语言Hamacher加权平均算子与几何算子,研究其基本性质。进一步地,剖析算子与参数之间的关系,如算子关于参数的单调性、算子关于参数的退化情况等。最后,基于所提出的集结算子构建出多属性决策方法,通过算例分析表明所提决策方法的可行性和实用性。     

关于左连续蕴涵算子的连续逼近问题

从阿基米德型t-范定义的剩余型蕴涵算子是连续的蕴涵算子出发，研究关于左连续的蕴涵算子Ro和Godel蕴涵算子心'的连续逼近问题，从而进一步为模糊推理寻求理论基础。     

max-zero t-模复合意义下的模糊矩阵幂序列的收敛性

主要讨论模糊矩阵在max-zro t-模(以下简称为max-t0)复合意义下的收敛性。证明了模糊矩阵在,max-t0复合意义下只有有限收敛,无限收敛,有限振荡及无限振荡这四种情况。并主要以一种特殊且重要的zero t-模：lukasiewice t-模为例,研究了max-lukasiewiez t模(以下简称为max-lu)复合意叉下的模糊矩阵的收敛性。证明了在max-lu复合意义下．模糊矩阵要么有限收敛要么有限振荡。且比较了在max-lu复合意义下以及在,max-product复合意义下,模糊矩阵收敛性的相同之处与不同之处,并揭示其原因。     

积格上蕴涵算子的直积分解

进一步讨论蕴涵算子的直积分解,描述积格上可以分解为两个蕴涵算子直积的蕴涵算子的特性,并研究积格上S-蕴涵、R-蕴涵、n-反演R-蕴涵和n-反演QL-蕴涵的可分解性。     

Equivalence after extension and Schur coupling coincide for inessential operators

In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is only known for special classes of operators, such as Fredholm operators with index zero and operators that can in norm be approximated by invertible operators. In this paper we prove that the implication EAE $?$ SC also holds for inessential Banach space operators. The inessential operators were introduced as a generalization of the compact operators, and include, besides the compact operators, also the strictly singular and strictly co-singular operators; in fact they form the largest ideal such that the invertible elements in the associated quotient algebra coincide with (the equivalence classes of) the Fredholm operators.     

Structuralist Logic: Implications, Inferences, and Consequences

On a structuralist account of logic, the logical operators, as well as modal operators are defined by the specific ways that they interact with respect to implication. As a consequence, the same logical operator (conjunction, negation etc.) can appear to be very different with a variation in the implication relation of a structure. We illustrate this idea by showing that certain operators that are usually regarded as extra-logical concepts (Tarskian algebraic operations on theories, mereological sum, products and negates of individuals, intuitionistic operations on mathematical problems, epistemic operations on certain belief states) are simply the logical operators that are deployed in different implication structures. That makes certain logical notions more omnipresent than one would think. Mathematics Subject Classification (2000): Primary 03B22; Secondary 03B20, 03B42, 03B60     

广义R0-代数

给出一种基于左连续的广义t-模的代数——广义R0-代数的定义和若干性质。     

模糊推理三Ⅰ算法的还原性

模糊推理算法的还原性是判断蕴涵算子与推理方法配合效果的一个重要标准,只有蕴涵算子与推理方法搭配适当,才能使模糊推理有一个好的效果。本文对模糊推理三I算法具备还原性的条件进行了研究。首先,当与蕴涵算子相伴随的三角模为连续三角模时,给出了FM P问题三I算法具有还原性的充要条件;其次,当蕴涵算子为连续的正则蕴涵算子时,给出了FM T问题的三I算法具有还原性的充要条件;最后,当正则蕴涵算子关于补运算满足对合律时,给出了FM T问题三I算法满足还原性的一个充分条件。     

Application of fuzzy implication to probe nonsymmetric relations: part I

Nine fuzzy implication operators were studied to determine their ability to identify nonsymmetric relations. The fuzzy degrees of the antecedent and consequent propositions of each implication were evaluated using the cumulative distribution function, which has the property that fuzzy degrees are uniformly distributed between 0 and 1 and hence are as fuzzy as possible.Under these conditions, average implications from the nine operators are confined to small subintervals of [0, 1]. For eight out of nine implication operators, the average implication largely duplicates information from the correlation coefficient. These points are explained theoretically.Confidence limits for fuzzy implication are also discussed.     

利用格蕴涵代数找出所有LI-理想的方法

利用格蕴涵代数中理想的定义未找出所有的理想需要花费大量的时间.给出了利用格蕴涵代数的蕴涵运算表找出格蕴涵代数所有理想的方法;再利用析取运算表找出格蕴涵代数中所有sl_理想的方法;最后,利用蕴涵否运算表找出格蕴涵代数中所有LI-理想的方法.