归结与调解方法的有效性和完备性——基于扩充模糊逻辑

模糊集与模糊逻辑是处理大量存在的不确定性与模糊性信息的重要数学工具,在近似推理等领域有着广泛的应用。该文将王家兵等人提出的真值取在[0,1]区间上的带有相似性关系的模糊逻辑,扩充到很一般的与滋可比的有余完全分配格值逻辑中,将王家兵等人的许多结论进行了推广。首先对带有相似性关系的模糊逻辑的语义描述进行了扩充,然后讨论了在这种模糊推理中归结式与调解式的有效性,最后通过证明一个子句集在扩充模糊逻辑中的不可满足性与它在带有相等关系的二值逻辑中的不可满足性是等价的,得到了基于归结与调解方法对这种广义模糊演算的完备性。     

逻辑等价度量下的模糊推理系统的鲁棒性

给出了基于模糊逻辑等价度量的模糊集的扰动的定义,讨论了模糊集扰动与模糊连接词及蕴涵算子扰动之间的关系,针对若干特殊的模糊连接词及蕴涵算子的扰动情形,给出了模糊推理系统的扰动的估计,并讨论了模糊推理系统的鲁棒性。     

广义λ—调解

本文提出了算子模糊逻辑中的广义λ－调解方法，证明了它和广义λ－归结的联合使用，对于λＥ－不可满足广义子句集是完备的。     

直觉模糊逻辑的（α,β）-广义锁归结方法

归结方法是定理自动证明的重要工具。为了简化直觉模糊命题逻辑的归结过程,基于直觉模糊命题逻辑归结原理的一般形式,提出了子句(αβ)-可满足和(αβ)-归结式的概念。研究了广义子句与其归结式的可满足性。在直觉模糊命题逻辑系统中给广义子句配锁,规定在做归结时各子句中被消去文字在该子句中的序号最小,由此建立了(αβ)-广义锁归结方法,并证明了该方法的可靠性和完备性。给出了直觉模糊逻辑的广义锁归结算法步骤,并通过实例说明了该方法的有效性。     

广义λ－调解

本文提出了算子模糊逻辑中的广义λ－调解方法，证明了它和广义λ－归结的联合使用，对于λＥ－不可满足广义子句集是完备的．     

直觉模糊集的模糊蕴含式运算方法

与经典模糊集相比,直觉模糊集具有更强的表达能力和灵活性.针对直觉模糊集的模糊推理,将经典的模糊集的模糊蕴含式拓展到直觉模糊集中,提出基于扩展二值逻辑的直觉模糊集下各种模糊蕴含式运算方法,通过实例验证直觉模糊集模糊蕴含式运算方法的有效性和正确性.     

语言真值直觉模糊逻辑的知识推理

针对格蕴涵代数、直觉模糊集及知识表示、基于语言真值直觉模糊代数的相关性质及运算方法,提出了六元语言真值直觉模糊代数的相关逻辑性质,并在六元语言真值直觉模糊知识表示的基础上,将模糊推理的CRI方法进行扩展,研究得出了六元语言真值直觉模糊推理的方法即6LTV-CRI算法。而后将直觉模糊推理与六元语言真值直觉模糊推理方法进行对比分析,验证了6LTV-CRI推理算法的合理性,并分析了其优缺点。     

一种广义直觉模糊粗糙集模型

Atanassov直觉模糊集是对Zadeh模糊集最有影响的一种扩充和发展。为进一步拓展Pawlak粗糙集对多重不确定性信息的处理能力,将直觉模糊集引入粗糙集,采用构造性方法提出了一种广义直觉模糊粗糙集模型。首先,介绍了直觉模糊集在一个特殊格上的等价定义,对直觉模糊近似空间的两个基本要素(直觉模糊逻辑算子和直觉模糊关系)进行了研究,证明了一些重要的性质定理;在此基础上,建立了等价关系下的直觉模糊粗糙集模型;最后,对所提模型的性质进行了分类验证与讨论。     

模糊推理算法的数学原理

模糊推理算法在自动控制等领域不断得到成功应用,但其理论基础却是贫弱的.从数学与逻辑的角度对模糊推理算法的基础进行研究分析,提出并证明了3个定理.结果表明在各种模糊推理模式中,前提与结论之间存在一个数学关系(有界实函数),模糊推理的各种算法都是这一函数的不同构造形式.所以,模糊推理的算法其基础是可靠的.     

基于2型模糊描述逻辑的知识描述与推理及其在信任管理系统中的应用

描述逻辑由于其强大的描述能力与成熟的推理算法而被广泛应用。然而，经典描述逻辑局限于处理确定的概念和关系，从而导致描述逻辑很难处理类似语义网等大型本体系统中的模糊知识。虽然1型模糊集可以一定程度上减轻不确定性带来的影响，但是其采用确定的隶属度值来决定模糊度的方法是不够精准的。与之相比，基于2型模糊集的系统能够利用隶属度区间更加精确地描述模糊信息。本文给出描述逻辑ALC的2型模糊扩展形式，并且给出并分析了2型模糊ALC的描述和推理方法。最后使用2型模糊ALC建立了一个基于模糊本体的信任管理系统FOntoTM。     

Fuzzy inference based on families of α-level sets

A fuzzy-inference method in which fuzzy sets are defined by the families of their α-level sets, based on the resolution identity theorem, is proposed. It has the following advantages over conventional methods: (1) it studies the characteristics of fuzzy inference, in particular the input-output relations of fuzzy inference; (2) it provides fast inference operations and requires less memory capacity; (3) it easily interfaces with two-valued logic; and (4) it effectively matches with systems that include fuzzy-set operations based on the extension principle. Fuzzy sets defined by the families of their α-level sets are compared with those defined by membership functions in terms of processing time and required memory capacity in fuzzy logic operations. The fuzzy inference method is then derived, and important propositions of fuzzy-inference operations are proved. Some examples of inference by the proposed method are presented, and fuzzy-inference characteristics and computational efficiency for α-level-set-based fuzzy inference are considered     

Fuzzy operator logic and fuzzy resolution

There have been only few attempts to extend fuzzy logic to automated theorem proving. In particular, the applicability of the resolution principle to fuzzy logic has been little examined. The approaches that have been suggested in the literature, however, have made some semantic assumptions which resulted in limitations and inflexibilities of the inference mechanism. In this paper we present a new approach to fuzzy logic and reasoning under uncertainty using the resolution principle based on a new operator, the fuzzy operator. We present the fuzzy resolution principle for this logic and show its completeness as an inference rule.     

A Fuzzy Inference Network Model for Search Strategy Using Neural Logic Network

In this paper, a fuzzy inference network model for search strategy using neural logic network is presented. The model describes search strategy, and neural logic network is used to search. Fuzzy logic can bring about appropriate inference results by ignoring some information in the reasoning process. Neural logic networks are powerful tools for the reasoning process but not appropriate for the logical reasoning. To model human knowledge, besides the reasoning process capability, the logical reasoning capability is equally important. Another new neural network called neural logic network is able to do the logical reasoning. Because the fuzzy inference is a fuzzy logical reasoning, we construct a fuzzy inference network model based on the neural logic network, extending the existing rule inference network. And the traditional propagation rule is modified.     

Complex fuzzy logic

A novel framework for logical reasoning, termed complex fuzzy logic, is presented in this paper. Complex fuzzy logic is a generalization of traditional fuzzy logic, based on complex fuzzy sets. In complex fuzzy logic, inference rules are constructed and "fired" in a manner that closely parallels traditional fuzzy logic. The novelty of complex fuzzy logic is that the sets used in the reasoning process are complex fuzzy sets, characterized by complex-valued membership functions. The range of these membership functions is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane, thus providing a method for describing membership in a set in terms of a complex number. Several mathematical properties of complex fuzzy sets, which serve as a basis for the derivation of complex fuzzy logic, are reviewed in this paper. These properties include basic set theoretic operations on complex fuzzy sets - namely complex fuzzy union and intersection, complex fuzzy relations and their composition, and a novel form of set aggregation - vector aggregation. Complex fuzzy logic is designed to maintain the advantages of traditional fuzzy logic, while benefiting from the properties of complex numbers and complex fuzzy sets. The introduction of complex-valued grades of membership to the realm of fuzzy logic generates a framework with unique mathematical properties, and considerable potential for further research and application.     

S-模糊逻辑系统中积分相似度及算子连续性

与通常相似度定义在真度基础上不同,在S-蕴涵模糊逻辑系统中提出了基于S-蕴涵算子的积分相似度。讨论了积分相似与逻辑等价的关系,给出了积分相似度的推理性质,提出了与积分相似度对应的伪距离。论证了伪距离空间中逻辑算子都是连续的。     

The construction of a fuzzy inference network by extension of the rule inference network

Fuzzy logic can bring about inappropriate inferences as a result of ignoring some information in the reasoning process. Neural networks are powerful tools for pattern processing, but are not appropriate for the logical reasoning needed to model human knowledge. The use of a neural logic network derived from a modified neural network, however, makes logical reasoning possible. In this paper, we construct a fuzzy inference network by extending the rule–inference network based on an existing neural logic network. The propagation rule used in the existing rule–inference network is modified and applied. In order to determine the belief value of a proposition pertaining to the execution part of the fuzzy rules in a fuzzy inference network, the nodes connected to the proposition to be inferenced should be searched for. The search costs are compared and evaluated through application of sequential and priority searches for all the connected nodes.     

Simplification of fuzzy-neural systems using similarity analysis

This paper presents a fuzzy neural network system (FNNS) for implementing fuzzy inference systems. In the FNNS, a fuzzy similarity measure for fuzzy rules is proposed to eliminate redundant fuzzy logical rules, so that the number of rules in the resulting fuzzy inference system will be reduced. Moreover, a fuzzy similarity measure for fuzzy sets that indicates the degree to which two fuzzy sets are equal is applied to combine similar input linguistic term nodes. Thus we obtain a method for reducing the complexity of a fuzzy neural network. We also design a new and efficient on-line initialization method for choosing the initial parameters of the FNNS. A computer simulation is presented to illustrate the performance and applicability of the proposed FNNS. The result indicates that the FNNS still has desirable performance under fewer fuzzy logical rules and adjustable parameters.     

A fuzzy logic approach to experience‐based reasoning

Experience‐based reasoning (EBR) is a reasoning paradigm that has been used in almost every human activity such as business, military missions, and teaching activities since early human history. However, EBR has not been seriously studied from either a logical or mathematical viewpoint, although case‐based reasoning (CBR) researchers have paid attention to EBR to some extent. This article will attempt to fill this gap by providing a unified fuzzy logic‐based treatment of EBR. More specifically, this article first reviews the logical approach to EBR, in which eight different rules of inference for EBR are discussed. Then the article proposes fuzzy logic‐based models to these eight different rules of inference that constitute the fundamentals for all EBR paradigms from a fuzzy logic viewpoint, and therefore will form a theoretical foundation for EBR. The proposed approach will facilitate research and development of EBR, fuzzy systems, intelligent systems, knowledge management, and experience management. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 867–889, 2007.