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.     

Robustness of fuzzy reasoning and δ-equalities of fuzzy sets

Fuzzy reasoning methods (or approximate reasoning methods) are extensively used in intelligent systems and fuzzy control. In this paper the author discusses how errors in premises affect conclusions in fuzzy reasoning, that is, he discusses the robustness of fuzzy reasoning. After reviewing his previous work (1996), he presents robustness results for various implication operators and inference rules. All the robustness results are formulated in terms of δ-equalities of fuzzy sets. Two fuzzy sets are said to be δ-equal if they are equal to an extent of δ     

A new approach to fuzzy reasoning

 Over the last years fuzzy control has become a very popular and successful control paradigm. The basic idea of fuzzy control is to incorporate human expert knowledge. This expert knowledge is specified in a rule based manner on a high and granular level of abstraction. By using vague predicates a fuzzy rule base neglects useless details and concentrates on important relations. Following L.A. Zadeh’s famous principle of incompatibility, this technique is most promising when applied to large and complex problems. Nevertheless, nowadays most fuzzy rule bases are small and represent simple knowledge. From our point of view this surprising and somewhat disappointing observation is due to a major lack of understanding how to handle a fuzzy rule base. In this paper we present a new theory for fuzzy reasoning. This theory is twofold. In general, a fuzzy rule base is both partially inconsistent and partially incomplete. This is the price to pay for abstraction and granularization. We show that if a fuzzy rule base maximizes consistency at the cost of completeness, the well-known possibilistic approach to fuzzy inference is the right choice. For a fuzzy rule base that maximizes completeness at the cost of consistency, we derive a new type of inference called σ-reasoning. Together, both mechanisms form an embracing theory for fuzzy reasoning in general. We propose a combined approach to be applied in order to manage complex rule bases.     

NEW METHODOLOGY TO FUZZY REASONING FOR RULE-BASED EXPERT SYSTEMS

Abstract

Much knowledge residing in the knowledge base of an expert system involves fuzzy concepts. A powerful expert system must have the capability of fuzzy reasoning. This paper presents a new methodology for dealing with fuzzy reasoning based on the matching function S. The single-input, single-output (SISO) fuzzy reasoning scheme and the multi-input, single-output (MISO) fuzzy reasoning schemes are discussed in detail. The proposed fuzzy reasoning methodology is conceptually clearer than the compositional rule of inference approach. It can provide an useful way for rule-based systems to deal with fuzzy reasoning.     

A generalised fuzzy reasoning algorithm for an object-oriented expert system tool

Abstract: A fuzzy reasoning algorithm is presented in this paper. It is based on the concept of a generalised fuzzy production rule that adds new conjunctions such as ADD and REL to the usual AND and OR conjunctions for the linkage of premises in conventional rules. A definition is given for weights and related factors, to express and measure a relation between the premises. A formal representation for fuzzy premises is presented, together with the introduction of a fuzzy match method. Multiple thresholds are used to convert the uncertainty measures of reasoning results into linguistic variables. We have applied the fuzzy reasoning algorithm to a frame-based hybrid expert system tool. An object-oriented approach is used in implementing the system. Some results of the application are presented and discussed.     

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.     

Genetic algorithm for the design of a class of fuzzy controllers:an alternative approach

A simple, easy to implement alternative method for designing fuzzy logic controllers (FLCs) with symmetrically distributed fuzzy sets in a universe of discourse is introduced. The design parameters include the parameters of the membership functions of the inputs and outputs and the rule base. The method is based on a network implementation of the FLC with real and binary weights with constraints. Due to the presence of the binary weights the backpropagation technique cannot be used. The learning problem is cast as a mixed integer constrained dynamic optimization problem and solved using the genetic algorithm (GA). The crossover and mutation are slightly disrupted in order to cope with the constraints on the binary weights. Training of the controller is carried out in a closed-loop simulation with the controller in the loop     

DFNN及其在非线性动态系统中的应用

为了更好地辨识和控制非线性动态系统,在FNN基础上对其进行优化和改进,形成了动态模糊神经网络(DFNN)。给出了基于BP梯度算法的参数迭代学习算法,并应用于某非线性动态系统仿真试验中。仿真试验表明,该网络比单纯的FNN具有更强的辨识和控制能力,应用于非线性动态系统的控制中可以有效解决系统的非线性和不确定性,提高系统的跟踪性能,并且控制系统具有很强的鲁棒性。     

Lipschitz聚合算子的模糊推理鲁棒性研究

模糊推理中,输入和推理规则发生摄动时,内部连接算子的选择是影响推理输出的主要因素。给出了模糊Lipschitz聚合算子的定义,论证了满足Lipschitz条件的三角模算子和蕴涵算子,研究了一类稳定的Lipschitz聚合算子对模糊推理的鲁棒性影响,指出了当系统发生输入摄动和规则摄动时,内部连接算子为1-Lipschitz算子,能有效地抑制模糊推理的输出摄动,特别是当内部连接算子既是1-k∞-Lipschitz又是quasi-copulas时,模糊推理输出更稳定安全可行,模糊推理的鲁棒性得到更好调控;另外,从实验结果看,规则摄动对推理输出影响较大。实验部分既是对文中所提理论的很好验证,同时也是该理论在图像处理和人脸联想方面的具体应用。     

程度推理与程度控制

文章把语言值规则（模糊规则）视为语言值及其程度（隶属度）之间的一种对应关系,提出了程度函数和程度规则的概念,并由此建立了一种称为程度推理和程度控制的推理与控制方法。采用程度推理和程度控制,传统的模糊推理就变为简单的符号推演和函数计算,传统的模糊控制由数值／（语,度）转换、（语,度）变换和（语,度）／数值转换等三步来实现。     

基于证据推理的确定因子规则库推理方法

不确定性推理方法是人工智能领域的一个主要研究内容,If-then规则是人工智能领域最常见的知识表示方法. 文章针对实际问题往往具有不确定性的特点,提出基于证据推理的确定因子规则库推理方法.首先在If-then规则的基础上给出确定因子结构和确定因子规则库知识表示方法,该方法可以有效利用各种类型的不确定性信息,充分考虑了前提、结论以及规则本身的多种不确定性. 然后,提出了基于证据推理的确定因子规则库推理方法. 该方法通过将已知事实与规则前提进行匹配,推断结论并得到已知事实条件下的前提确定因子;进一步,根据证据推理算法得到结论的确定因子. 文章最后,通过基于证据推理的确定因子规则库推理方法在UCI数据集分类问题的应用算例,说明该方法的可行性和高效性.     

An improved robust fuzzy-PID controller with optimal fuzzy reasoning.

Many fuzzy control schemes used in industrial practice today are based on some simplified fuzzy reasoning methods, which are simple but at the expense of losing robustness, missing fuzzy characteristics, and having inconsistent inference. The concept of optimal fuzzy reasoning is introduced in this paper to overcome these shortcomings. The main advantage is that an integration of the optimal fuzzy reasoning with a PID control structure will generate a new type of fuzzy-PID control schemes with inherent optimal-tuning features for both local optimal performance and global tracking robustness. This new fuzzy-PID controller is then analyzed quantitatively and compared with other existing fuzzy-PID control methods. Both analytical and numerical studies clearly show the improved robustness of the new fuzzy-PID controller.     

Error Estimation of Perturbations Under CRI

The analysis of stability and robustness of fuzzy reasoning is an important issue in areas like intelligent systems and fuzzy control. An interesting aspect is to what extent the perturbation of input in a fuzzy reasoning scheme causes the oscillation of the output. In particular, when the error limits (restrictions) of the input values are given, what the error limits of the output values are. In this correspondence, we estimate the upper and lower bounds of the output error affected by the perturbation parameters of the input, and obtain the limits of the output values when the input values range over some interval in many fuzzy reasoning schemes under compositional rule of fuzzy inference (CRI)     

基于模糊推理的教学策略推理机的算法设计

详细阐述了模糊推理系统与实现模糊推理机工作流程设计的方法和算法,给出基于一定方式结合的框架与规则知识表示的推理机算法和规则推理机设计思想及实现方法,为学生选择学习内容和学习方法时对教学策略做出调整.     

A hybrid frequency—time domain adaptive fuzzy control scheme for flexible link manipulators

This paper addresses the implementation of an adaptive fuzzy controller for flexible link robot arms. The design technique is a hybrid scheme involving both frequency and time domain techniques. The eigenvalues of the open loop plant can be estimated through application of a frequency domain based identification algorithm. The region of the eigenvalue space, within which the system operates, is partitioned into fuzzy cells. Membership function are assigned to the fuzzy sets of the eigenvalue universe of discourse. The degree of uncertainty on the estimated eigenvalues is encountered through these membership functions. The knowledge data base consists of feedback gains required to place the closed loop poles at predefined locations. A rule based controller infers the control input variable weighting each with the value of the membership functions at the identified eigenvalue. The afore-mentioned controller is compared through simulation with conventional techniques, namely pole placement and gain scheduling.     

模糊推理的合成规则及其合成运算的选择研究

本文首先提出当知识库中含有多条取自于同论域上的模糊推理规则时，应用通常的六条合成推理规则所推得的结论将随着模糊推理规则数的增多而越来越偏离真实度这一问题。本文针对该问题对通常的六条合成推理规则及其三角模下的六条推广合成推理规则进行了理论比较研究，并对合成运算进行了比较研究。研究表明：合成推理规则（或Ｒ￣４）以合成运算ｍａｘ－Ｔ０是克服上述问题的最佳选择。这一重要结果对于模糊知识库的设计具有指导意义。     

一种改进的三级倒立摆变论域模糊控制器设计

在传统变论域模糊控制系统中, 论域随着输入的变化实时改变, 论域的反复调整降低了控制的实时性, 同时伸缩因子的函数结构和参数也不易确定. 基于上述问题本文设计了基于改进型变论域算法的三级倒立摆模糊控制器: 首先提出了相对变论域控制思想, 然后采用模糊逻辑推理器构造了伸缩因子, 实时调整输入变量, 从而相对性地改变论域大小, 避免了传统伸缩因子的函数结构和参数不易确定的问题, 并根据系统闭环响应曲线设计了控制 器输出调整因子. 最后采用极点配置方法对状态变量进行综合, 避免了规则爆炸问题. 三级倒立摆的仿真结果表明了该方法具有较好的控制效果.     

Incorporation, characterization, and conversion of negative rulesinto fuzzy inference systems

This paper considers the incorporation of negative examples into fuzzy inference systems (FIS). A new method of defuzzification called dot attenuation is presented. This is a generalization of conventional defuzzification that has the ability to incorporate negative examples into the FIS reasoning process. Several variations of dot attenuation including dot product attenuation (DPA), dot minimum attenuation, and dot difference attenuation (DDA), are presented and incorporated into the center of gravity and center average defuzzification. DPA is illustrated with an inverted pendulum controller, which has a negative rule added to its rule base. The modification of the control surface due to the introduction of the negative rule is investigated. Simple steering control of a robot in the presence of obstructions using DDA is demonstrated. A method of conversion from a mixed positive/negative rule base into a standard rule base using modus tollens is introduced. Expert and automated creation of negative rules is discussed     

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality.

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.     

Fuzzy Interpolative Reasoning for Sparse Fuzzy Rule-Based Systems Based on ${bm alpha}$-Cuts and Transformations Techniques

In sparse fuzzy rule-based systems, the fuzzy rule bases are usually incomplete. In this situation, the system may not properly perform fuzzy reasoning to get reasonable consequences. In order to overcome the drawback of sparse fuzzy rule-based systems, there is an increasing demand to develop fuzzy interpolative reasoning techniques in sparse fuzzy rule-based systems. In this paper, we present a new fuzzy interpolative reasoning method via cutting and transformation techniques for sparse fuzzy rule-based systems. It can produce more reasonable results than the existing methods. The proposed method provides a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy rule-based systems.