积逻辑系统中的广义重言式

讨论积逻辑系统中的广义重言式理论 ,给出积逻辑系统中子代数和广义重言式的一系列性质。本文的主要结果表明 ,在几个重要的逻辑系统中 ,标准积逻辑系统具有最简单的广义重言式结构 ,而在推理过程中 ,它具有较差的真值传递性。     

A normal form which preserves tautologies and contradictions in a class of fuzzy logics

Most of the normal forms for fuzzy logics are versions of conjunctive and disjunctive classical normal forms. Unfortunately, they do not always preserve tautologies and contradictions which is important, for example, for automated theorem provers based on refutation methods.De Morgan implicative systems are triples like the De Morgan systems, which consider fuzzy implications instead of t-conorms. These systems can be used to evaluate the formulas of a propositional language based on the logical connectives of negation, conjunction and implication. Therefore, they determine different fuzzy logics, called implicative De Morgan fuzzy logics.In this paper, we will introduce a normal form for implicative De Morgan systems and we will show that for implicative De Morgan fuzzy logics whose t-norms are strict, this normal form preserves contradictions as well as tautologies.     

扰动模糊命题逻辑的代数结构及其广义重言式性质

着眼于扰动模糊命题逻辑的代数结构,为研究二维扰动模糊命题逻辑最大子代数I2R及其广义重言式提供了一些代数理论基础,最后研究了子代数间广义重言式的关系.     

区间值模糊命题逻辑系统的广义恒真式

建立区间值模糊命题逻辑系统F(∨，∧，σ┴，c)，其中，α^-θ┴b=(α^-)^c┴b^-,┴是I[0,1]中的t-余范；讨论系统F(∨，∧，σ┴，c)与对应的模糊命题逻辑系统F(∨，∧，σ┴，c)在广义恒真式方面的相互关系，得到定理：T^-[0,α]（F^-∨，∧，σ┴，c)=Tα(F(∨，∧，σ┴，c))。     

Fuzzy propositional logics

Fuzzy logic $\text{L}$_∞9 considered in connection with fuzzy sets theory, is a special theory, is a special many valued logic with truth-value sets [0, 1], which has been studied already by Lukasiewicz. We consider also his versions $\text{L}$_m for m ? 2 with finite truth-value sets. In all cases we add two further propositional connectives, one conjunction and one disjunction. For these logics we give a list of tautologies, consider relations between their sets of tautologies, prove their compactness, and mention some further results.     

模糊输入时滞系统的输出反馈控制及稳定性分析

针对一类状态不可测的模糊输入时滞系统,应用平行分布补偿算法(PDC),设计了模糊观测器,提出了基于模糊观测器的输出反馈控制方法,给出了保证模糊时滞系统渐近稳定的新的充分条件.应用广义Lyapunov函数和线性矩阵不等式方法,证明了模糊输入时滞系统的渐近稳定性,同时给出了控制和观测增益矩阵的分离设计算法.仿真结果进一步验证了所提出的方法和条件的有效性.     

Attribute reduction based on generalized fuzzy evidence theory in fuzzy decision systems

Attribute reduction is viewed as an important issue in data mining and knowledge representation. This paper studies attribute reduction in fuzzy decision systems based on generalized fuzzy evidence theory. The definitions of several kinds of attribute reducts are introduced. The relationships among these reducts are then investigated. In a fuzzy decision system, it is proved that the concepts of fuzzy positive region reduct, lower approximation reduct and generalized fuzzy belief reduct are all equivalent, the concepts of fuzzy upper approximation reduct and generalized fuzzy plausibility reduct are equivalent, and a generalized fuzzy plausibility consistent set must be a generalized fuzzy belief consistent set. In a consistent fuzzy decision system, an attribute set is a generalized fuzzy belief reduct if and only if it is a generalized fuzzy plausibility reduct. But in an inconsistent fuzzy decision system, a generalized fuzzy belief reduct is not a generalized fuzzy plausibility reduct in general.     

The Operators of Vector Logic

Vector logic is a mathematical model of the propositional calculus in which the logical variables are represented by vectors and the logical operations by matrices. In this framework, many tautologies of classical logic are intrinsic identities between operators and, consequently, they are valid beyond the bivalued domain. The operators can be expressed as Kronecker polynomials. These polynomials allow us to show that many important tautologies of classical logic are generated from basic operators via the operations called Type I and Type II products. Finally, it is described a matrix version of the Fredkin gate that extends its properties to the many-valued domain, and it is proved that the filtered Fredkin operators are second degree Kronecker polynomials that cannot be generated by Type I or Type II products. Mathematics Subject Classification: 03B05, 03B50.     

Distinguishing standard SBL‐algebras with involutive negations by propositional formulas

Propositional fuzzy logics given by a combination of a continuous SBL t‐norm with finitely many idempotents and of an involutive negation are investigated. A characterization of continuous t‐norms which, in combination with different involutive negations, yield either isomorphic algebras or algebras with distinct and incomparable sets of propositional tautologies is presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

EQ-algebras

We introduce a new class of algebras called EQ-algebras. An EQ-algebra has three basic binary operations (meet, multiplication and a fuzzy equality) and a top element. These algebras are intended to become algebras of truth values for a higher-order fuzzy logic (a fuzzy type theory, FTT). The motivation stems from the fact that until now, the truth values in FTT were assumed to form either an IMTL-, BL-, or MV-algebra, all of them being special kinds of residuated lattices in which the basic operations are the monoidal operation (multiplication) and its residuum. The latter is a natural interpretation of implication in fuzzy logic; the equivalence is then interpreted by the biresiduum, a derived operation. The basic connective in FTT, however, is a fuzzy equality and, therefore, it is not natural to interpret it by a derived operation. This defect is expected to be removed by the class of EQ-algebras introduced and studied in this paper. From the algebraic point of view, the class of EQ-algebras generalizes, in a certain sense, the class of residuated lattices and so, they may become an interesting class of algebraic structures as such.     

Applications of fuzzy logic in the control of robotic manipulators

Fuzzy logic has been utilized at several hierarchical levels of a typical robotic control system. Four broad levels of application may be identified - task design, system monitoring (including self-tuning and self-organization), information filtering and preprocessing, and in-loop direct control. Even though the need for fuzzy logic is felt mostly at upper levels of the control system, the present applications are mainly concentrated within the lowest level, perhaps driven by convenience rather than necessity. This paper surveys several applications of fuzzy logic in the control of robotic manipulators. Applications are grouped into four hierarchical categories, broadly corresponding to an existing architecture of a robotic control system. Such a classification can be beneficial in ascertaining the appropriateness of fuzzy logic for the specific control task.     

Rule generation for hierarchical collaborative fuzzy system

A new method of rule generation for the hierarchical collaborative fuzzy system, HCFS, is proposed. This HCFS is structured like various parallel fuzzy subsystems and it overcomes the dimensionality problem and the lack of interpretability of most of the traditional fuzzy systems, when dealing with complex real-world problems. An association process of different fuzzy systems is presented in this work, through the use of a relevance concept of a fuzzy system. The result of this aggregation is a collaborative structure where all sub-models have the ability to gradually improve the overall accuracy of approximation by adding their own contributions. For this structure we propose a new algorithm to be used in the procedures of the three learning phases: the structure building, the parametric identification and the division of the learning data among the various levels of the hierarchical structure. This new fuzzy modelling technique automatically generates and tunes the sets of fuzzy rules in the hierarchical collaborative structure (HCS). The effectiveness of the proposed HCFS model in handling high-dimensional and complex problems is demonstrated through various numerical simulations.     

基于三Ι算法的模糊系统及其响应性能

给出了基于三Ⅰ算法和α-三Ⅰ算法的几种典型模糊系统的插值表达式．指出,基于三Ⅰ算法和α-三Ⅰ算法的模糊系统对于某些蕴涵算子具有函数逼近的泛性,而对于不少蕴涵算子只具有阶跃输出能力,而不具有函数逼近的泛性．此外,证明了基于三Ⅰ算法的模糊系统在一定条件下对于模糊逻辑系统中推理与聚合的次序交换无关．     

Bivalent and other solutions of fuzzy relational equations via linguistic hedges

We show that the well-known results regarding solutions of fuzzy relational equations and their systems can easily be generalized to obtain criteria regarding constrained solutions such as solutions which are crisp relations. When the constraint is empty, constrained solutions are ordinary solutions. The generalization is obtained by employing intensifying and relaxing linguistic hedges, conceived in this paper as certain unary functions on the scale of truth degrees. One aim of the paper is to highlight the problem of constrained solutions and to demonstrate that this problem naturally appears when identifying unknown relations. The other is to emphasize the role of linguistic hedges as constraints.     

粗糙模糊集与模糊粗糙集的截集性质

研究粗糙模糊集、模糊粗糙集、广义粗糙模糊集和广义模糊粗糙集的截集性质,并且还研究了基于逻辑算子的广义模糊粗糙集的基本性质。     

Long-range predictive adaptive fuzzy relational control

A class of long-range predictive adaptive fuzzy relational controllers is presented. The plant behavior is described over an extended time horizon by a fuzzy relational model which is identified based on input-output closed-loop observations of the plant variables. In this class of adaptive controllers the control law attempts to minimize a quadratic cost over an extended control horizon. When used with linear models, this approach has revealed a significant potential for overcoming the limitations of one-step ahead schemes, such as the stabilization of non-minimum phase plants. Here, a uniform framework is adopted for implementing both the fuzzy model and the fuzzy controller, namely distributed fuzzy relational structures gaining from their massive parallel processing features and from the learning capabilities typical of the connectivist approaches. Issues such as maintenance during the adaptation process of the meaning of linguistic terms used at both fuzzy systems interfaces are addressed, namely by introducing a new design methodology for on-line fuzzy systems interface adaptation. The examples presented reinforce the claim of the usefulness of this new approach.     

强正则剩余格值逻辑系统（L）N及其完备性

正则剩余格是一类重要的模糊逻辑代数系统,而常见的模糊逻辑形式系统大多数带有非联接词,并且相应的Lindenbaum代数都是正则剩余格.本文以强正则剩余格为语义,建立了一个一般的命题演算形式系统LN,并且证明了这个系统的完备性.几种常见的带有非联接词的模糊逻辑形式系统都是系统LN的扩张.     

Generalized valuations on MTL-algebras

In this paper, we study some kinds of generalized valuations on MTL-algebras, discuss the relationship between the cokernel of generalized valuations and types of filters on MTL-algebras. Then, we give some equivalent characterizations of positive implicative generalized valuations on MTL-algebras. Finally, we characterize the structure theory of quotient MTL algebras based on the congruence relation, which is constructed by generalized valuations. The results of this paper not only generalize related theories of generalized valuations, but also enrich the algebraic conclusion of probability measure, on algebras of triangular norm based fuzzy logic.     

强正则剩余格值逻辑系统L~N及其完备性

正则剩余格是一类重要的模糊逻辑代数系统,而常见的模糊逻辑形式系统大多数带有非联接词,并且相应的Lindenbaum代数都是正则剩余格.本文以强正则剩余格为语义,建立了一个一般的命题演算形式系统LN,并且证明了这个系统的完备性.几种常见的带有非联接词的模糊逻辑形式系统都是系统LN的扩张.