基于一族蕴涵算子的对偶三I算法

三I算法是一种新的模糊推理方法,是传统的模糊推理方法的修改和补充. 三I表达式取最小值时的最优解算法(即对偶三I算法)是三I算法思想的延伸和完善.本文针对蕴涵算子族Ip,讨论了FMP和FMT问题的对偶三I算法,给出了相应的计算公式,从而也进一步促进了对三I算法的研究.     

三I表达式取最小值时的最优解

在本文中，针对蕴涵算子$R_0$,我们给出了当$A\rightarrow B$与$A^*(B^*)$给定时,求使三I表达式$(A\rightarrow B)\rightarrow(A^*\rightarrow B^*)$取最小值的全体$B^*(A^*)$之集的上确界(下确界)算法.并将上确界算法推广到多维多重的模糊推理中.从三I表达式取最值时求最优的$B^*(A^*)$的角度来看,本文是三I算法思想的延伸和完善.     

FMT-泛三I算法的约束度理论

从先前提出的泛三I算法出发,面向FMT(fuzzy modus tollens)问题,提出模糊推理的FMT-泛三I约束算法。改进之前的三I约束FMT原则,给出泛三I约束解的存在条件,建立FMT-泛三I约束算法的统一形式的解。并且,针对9种具体的蕴涵算子,获得相应的泛三I约束解。最后,给出并改进FMT-三I约束算法的相关结论。     

一类Fisher方程的行波解

本文讨论了一类广义Fisher方程,得到了它的多个显式行波解.     

关于运输问题最优解的进一步讨论

首先给出了运输问题最优解的相关概念,将最优解扩展到广义范畴,提出狭义多重最优解和广义多重最优解的概念及其区别.然后给出了惟一最优解、多重最优解、广义有限多重最优解、广义无限多重最优解的判定定理及其证明过程.最后推导出了狭义有限多重最优解个数下限和广义有限多重最优解个数上限的计算公式,并举例验证了结论的正确性.     

参数Kleene系统的三Ⅰ算法与反向三Ⅰ支持算法

提出基于参数蕴涵算子θp模糊推理的思想,给出了在模糊推理的每一步都使用蕴涵运算pθ的三I算法与反向三I支持算法理论,得到了三I上确界算法、模糊取式算法(FM P)与模糊拒取式算法(FM T)的计算公式,这将有助于提高模糊推理结果的可靠性。     

第三种线性积分方程组的广义解

§1 引言近年来Bart等人讨论了单个第三种积分方程广义解的存在性,具有较明显的物理意义,受到广泛重视本文讨论下列第三种积分方程组广义解的存在性:     

无限维多目标规划的广义α-较多有效解和广义α-较多最优解

借助无限维线性空间的广义α-较多序,本文引进了无限维多目标规划问题的带参数的广义α-较多有效解和广义α-较多最优解.同时,研究了这些解类的有关性质,得到了α-较多有效解和α-较多最优解存在的充要条件.     

受迫二维广义KdV-Burgers方程的周期行波解

本文研究了受迫二维广义ＫｄＶ－Ｂｕｒｇｅｒｓ方程的周期行波解问题,讨论了解的有界性并给出了解的估计式,进而讨论了周期解的存在性及唯一性.     

一类两参数非线性反应扩散方程奇摄动问题的广义解

利用奇异摄动方法讨论了一类两参数广义奇摄动反应扩散方程问题.首先,在适当的条件下,对两个小参数进行幂级数展开,构造了问题的形式外部解.其次,在区域边界邻近,建立局部坐标系,利用多重尺度变量方法分别构造了问题解的第一、第二边界层校正项.最后,利用合成展开理论,得到了问题广义解的渐近表示式,并用泛函分析不动点原理,估计了渐近展开式的精度.该文得到问题的广义解在重叠区域内具有两个不同厚度的校正函数.它们分别对边界条件起着校正的作用,扩展了问题研究范围,同时还提供了构造这类在重叠区域上不同厚度的校正项的方法,因此具有广泛的研究前景.     

Foundation of credibilistic logic

In this paper, credibilistic logic is introduced as a new branch of uncertain logic system by explaining the truth value of fuzzy formula as credibility value. First, credibilistic truth value is introduced on the basis of fuzzy proposition and fuzzy formula, and the consistency between credibilistic logic and classical logic is proved on the basis of some important properties about truth values. Furthermore, a credibilistic modus ponens and a credibilistic modus tollens are presented. Finally, a comparison between credibilistic logic and possibilistic logic is given.     

Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets

Two basic inference models of fuzzy reasoning are fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). The Triple I method is a very important method to solve the problems of FMP and FMT. The aim of this paper is to extend the Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets. In the paper, we first investigate the algebra operators' properties on the lattice structure of intuitionistic fuzzy information and provide the unified form of residual implications which indicates the relationship between intuitionistic fuzzy implications and fuzzy implications. Then we present the intuitionistic fuzzy reasoning version of the Triple I principles based on the models of intuitionistic fuzzy modus ponens (IFMP) and intuitionistic fuzzy modus tollens (IFMT) and give the Triple I method of intuitionistic fuzzy reasoning for residual implications. Moreover, we discuss the reductivity of the Triple I methods for IFMP and IFMT. Finally, we propose α-Triple I method of intuitionistic fuzzy reasoning.     

Symmetric implicational method of fuzzy reasoning

Fuzzy reasoning should take into account the factors of both the logic system and the reasoning model, thus a new fuzzy reasoning method called the symmetric implicational method is proposed, which contains the full implication inference method as its particular case. The previous full implication inference principles are improved, and unified forms of the new method are respectively established for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) to let different fuzzy implications be used under the same way. Furthermore, reversibility properties of the new method are analyzed from some conditions that many fuzzy implications satisfy, and it is found that its reversibility properties seem fine. Lastly, the more general α-symmetric implicational method is put forward, and its unified forms are achieved.     

Lattice BCK logics with Modus Ponens as unique rule

Lattice BCK logic is the expansion of the well known Meredith implicational logic BCK expanded with lattice conjunction and disjunction. Although its natural axiomatization has three rules named modus ponens, ∨‐rule and ∧‐rule, we show that we can give an equivalent presentation with just modus ponens and ∧‐rule, however it is impossible to obtain an equivalent presentation with modus ponens as unique rule. In this paper we study and characterize all axiomatic extensions of lattice BCK logic with modus ponens as unique rule. We obtain an infinite chain of proper axiomatic extensions with this property. Moreover, we prove that there is no weakest axiomatic extension of Lattice BCK‐logic admitting modus ponens as unique rule.     

F—fuzzy演绎系统

本文建立了一种演绎系统FFCS,在该演义系统中可以处理具有模糊性的推理过程,区别与其他对模糊推理进行形式化的逻辑系统,FFCS对模糊假言推理FMP做了完全形式化的处理。     

On the Coherence of Wittgensteinian Constructivism

Michael Dummett presents a modus tollens argument against a Wittgensteinian conception of meaning. In a series of papers, Dummett claims that Wittgensteinian considerations entail strict finitism. However, by a “sorites argument”, Dummett argues that strict finitism is incoherent and therefore questions these Wittgensteinian considerations.In this paper, I will argue that Dummett’s sorites argument fails to undermine strict finitism. I will claim that the argument is based on two questionable assumptions regarding some strict finitist sets of natural numbers. It will be shown that strict finitism entails none of these assumptions. Hence, the argument does not prove that the view is internally incoherent, and consequently, Dummett fails to undermine the Wittgensteinian conception of meaning.     

A Problem of Normal Form in Natural Deduction

Recently Ekman gave a derivation in natural deduction such that it either contains a substantial redundant part or else is not normal. It is shown that this problem is caused by a non‐normality inherent in the usual modus ponens rule.     

命题公式集F(S)的基于R0-算子的16类分划

利用R0-蕴涵算子对命题公式集F(S)进行分类,得出了F(S)的—个16类分划,并证明了这种分类关于非运算是同余分类.最后讨论了各类关于MP运算与HS运算的封闭性.     

Optimal control problems in hybrid systems with active singularities

The optimal control problem for systems with controlled unilateral phase constraints is considered. The definition of the generalized solutions is introduced, the transformation method for the original optimal control problem within the class of generalized solution to a standard optimal control problem is proposed, and the necessary optimality conditions are found.