R0代数的注记

讨论了R0代数与MV代数的关系，给出了R0代数的一种根。     

R0-代数(NM-代数)的布尔MP滤子与布尔MP理想

在R0-代数中引入布尔MP滤子与布尔MP理想的概念,给出其若干充要条件,研究了它们与素滤子、极大MP滤子的关系。通过反例指出了关于超MP滤了的一个错误结论,给出超MP滤子的一个充分必要条件。在此基础上研究了R0-代数的结构,用布尔MP滤子与布尔MP理想刻画了二部R0-代数、强二部R0-代数的特征。     

R_0代数的可证等价类

讨论了R0代数的滤子以及相应的可证等价类.在R0代数里给出了一些滤子的具体例子,得到:F是R0代数M的超滤当且仅当F是M的固执滤子;当F是R0代数的蕴涵滤子时,M/F是布尔代数;当F是R0代数的极大布尔滤子时,M/F是只有两个元的布尔代数.     

伪NM代数及其性质

本文提出了一类伪逻辑代数-伪NM代数,它是NM代数的非交换推广。详细地探讨了伪NM代数的基本性质,给出了伪NM代数的等价特征,这个特征恰好是Ro代数的非交换推广。证明了伪NM代数类形成一个簇。     

BR0-代数的无序表示形式及WBR0-代数性质

对BR0-逻辑代数进行了进一步研究,得到了BR0-逻辑代数的一种无序表示形式,使得BR0-代数中的序关系蕴涵于BR0-代数的基本运算⊕和→之中,并根据BR0-代数的无序表示形式提出了WBR0-代数理论,初步地讨论了其中的性质.     

代数系的Fuzzy理想

代数系的Fuzzy理想是Fuzzy代数理论中的重要内容之一,刘旺金、吴望名、Kuroki,N.等分别就某种代数系讨论了上述问题(参见[1]、[2]、[3])。本文在给出了Fuzzy代数的统一定义的基础上(刘文斌,科学通报,16(1986),1257)给出了代数系统的Fuzzy理想的统一定义和一个Fuzzy子代数系是一个Fuzzy理想的充要条件,它是Fuzzy正规子群,环的Fuzzy理想等概念的统一和推广。     

有界可换BCK-代数与MV-代数

在有界可换 BCK-代数〈X;*,0〉中定义 x′=N x,x + y =y*Nx,x× y =N ( Ny*x) ,1 MV=0 ,则 ( X,+ ,× ,′,0 MV,1 MV)是一个 MV-代数 ;而在 MV-代数 ( X,+ ,× ,′,0 MV,1 MV)中定义 x*y =x + y′,0 =1 MV,则〈X;*,0〉是一个有界可换 BCK-代数。     

R0-代数与BL-代数中的素滤子定理

R1-代数与BL-代数在模糊逻辑的研究中有重要作用,这与布尔代数在经典逻辑中的作用类似。本文通过一个特殊集x^-1F分别给出Ro-代数及BL-代数素滤子的一个等价条件,并给出BL-代数的一个新性质。应用这些结果分别得到Ro-代数与BL-代数的素滤子定理。     

预线性剩余格与逻辑代数

本文首先讨论了剩余格与FI代数之间、FI代数与MV代数之间的关系,对已有结果进行了改进。随后提出了预线性剩余格的概念,证明了预线性剩余格是BR_0代数与BL代数的基础,从而也就是著名的MV代数、R_0代数、G代数与Ⅱ代数的公共基础。     

间断区间的代数性质

讨论了区间的一些代数性质，证明了间断区间在与、或、非操作下是一个软代数。     

双交叉积Hopf代数上的辫子结构

本文讨论双交叉积Hopf代数B~β_αH的辫子结构。通过引进一些新的概念,给出并证明了双交叉积Hopf代数B~β_αH构成辫子Hopf代数的充分条件与必要条件,同时给出了其辫子结构的分解形式。     

有界Heyting代数的模糊LI-理想

理想是研究逻辑代数结构特征的重要工具性概念之一.本文综合运用代数学与模糊集的方法和原理,在有界Heyting代数中引入模糊LI-理想概念并研究其性质.进而讨论了模糊LI-理想与模糊格理想之间的关系,并给出了由一个模糊集生成的模糊LI-理想的表示定理,最后证明了一个给定有界Heyting代数的全体模糊LI-理想之集在模糊集合包含序下构成一个完备Heyting代数.     

Algebras difusas

Resumen En este trabajo se propone una estructura de álgebra difusa (borrosa) basada en la distinción entre difusidad extensiva y comprehensiva, desarrollando y conectando los trabajos de Nahmias sobre variables difusas, de Klement sobre medibilidad difusa y de Nowakowska sobre estructuras de conceptos.      

Computing representations for radicals of finitely generated differential ideals

This paper deals with systems of polynomial differential equations, ordinary or with partial derivatives. The embedding theory is the differential algebra of Ritt and Kolchin. We describe an algorithm, named Rosenfeld–Gröbner, which computes a representation for the radical ${\mathfrak p}This paper deals with systems of polynomial differential equations, ordinary or with partial derivatives. The embedding theory is the differential algebra of Ritt and Kolchin. We describe an algorithm, named Rosenfeld–Gr?bner, which computes a representation for the radical of the differential ideal generated by any such system Σ. The computed representation constitutes a normal simplifier for the equivalence relation modulo (it permits to test membership in ). It permits also to compute Taylor expansions of solutions of Σ. The algorithm is implemented within a package (the package (diffalg) is available in MAPLE standard library since MAPLE VR5) in MAPLE. A part of this work (in particular the MAPLE diffalg package) was realized while the first author was a postdoctoral fellow at the Symbolic Computation Group of the University of Waterloo, N2L 3G6 ON, Canada.     

Kronecker algebra for series–parallel multi-state systems reliability evaluation

Multi-state systems (MSS) are systems whose stochastic degradation process is characterised by several performance levels varying from nominal functioning to complete failure. MSS arise naturally in many application areas. MSS reliability evaluation and estimation has received much attention from researchers and a wide range of papers dealing with MSS have been published. In this paper, an approach based on Kronecker algebra combined with stochastic processes is proposed to evaluate the reliability of a series–parallel MSS. The main advantage of the proposed approach is that the mathematical expressions of the MSS reliability indices are derived from data of individual elementary components without generating the whole, possibly huge, MSS state space. Furthermore, the approach is well formalised and easy to implement thanks to Kronecker algebra operators. Examples are given to illustrate the proposed approach.     

广义近似空间与粗糙分类代数

提出了广义近似空间、粗近似公理、干扰集公理、粗糙集的分类原则、粗选原则、不确定偶集原则、精选原则、对策分类、量子逻辑分类、bit量子对称分类、不可比集、bit空间集、协议关系、粗糙集函数、粗糙分类代数和粗糙单代数等基本概念，并提出了一个猜想；展示了一些新观点；基于协议关系构造了粗糙商代数和粗糙子代数，给出了回避-归并算法及算例。     

Intelligently deciphering unintelligible designs: algorithmic algebraic model checking in systems biology

Systems biology, as a subject, has captured the imagination of both biologists and systems scientists alike. But what is it? This review provides one researcher''s somewhat idiosyncratic view of the subject, but also aims to persuade young scientists to examine the possible evolution of this subject in a rich historical context. In particular, one may wish to read this review to envision a subject built out of a consilience of many interesting concepts from systems sciences, logic and model theory, and algebra, culminating in novel tools, techniques and theories that can reveal deep principles in biology—seen beyond mere observations. A particular focus in this review is on approaches embedded in an embryonic program, dubbed ‘algorithmic algebraic model checking’, and its powers and limitations.