Fuzzy Reasoning as a Control Problem

Different from the dominant view of treating fuzzy reasoning as generalization of classical logical inference, in this paper fuzzy reasoning is treated as a control problem. A new fuzzy reasoning method is proposed that employs an explicit feedback mechanism to improve the robustness of fuzzy reasoning. The fuzzy rule base given a priori serves as a controlled object, and the fuzzy reasoning method serves as the corresponding controller. The fuzzy rule base and the fuzzy reasoning method constitute a control system that may be open loop or closed loop, depending on the underlying reasoning goals/constraints. The fuzzy rule base, the fuzzy reasoning method, and the corresponding reasoning goals/constraints define the three distinct ingredients of fuzzy reasoning. While various existing fuzzy reasoning methods are essentially a static mapping from the universe of single fuzzy premises to the universe of single fuzzy consequences, the new fuzzy reasoning method maps sequences of fuzzy premises to sequences of fuzzy consequences and is a function of the underlying reasoning goals/constraints. The Monte Carlo simulation shows that the new fuzzy reasoning method is much more robust than the optimal fuzzy reasoning method proposed in our previous work. The explicit feedback mechanism embedded in the fuzzy reasoning method does significantly improve the robustness of fuzzy reasoning, which is concerned with the effects of perturbations associated with given fuzzy rule bases and/or fuzzy premises on fuzzy consequences. The work presented in this paper sets a new starting point for various principles of feedback control and optimization to be applied in fuzzy reasoning or logical inference and to explore new forms of reasoning including robust reasoning and adaptive reasoning. It can be also expected that the new fuzzy reasoning method presented in this paper can be used for modeling and control of complex systems and for decision-making under complex environments.     

Construction of fuzzy knowledge bases incorporating feature selection

Constructing concise fuzzy rule bases from databases containing many features present an important yet challenging goal in the current researches of fuzzy rule-based systems. Utilization of all available attributes is not realistic due to the “curse of dimensionality” with respect to the rule number as well as the overwhelming computational costs. This paper proposes a general framework to treat this issue, which is composed of feature selection as the first stage and fuzzy modeling as the second stage. Feature selection serves to identify significant attributes to be employed as inputs of the fuzzy system. The choice of key features for inclusion is equivalent to the problem of searching for hypotheses that can be numerically assessed by means of case-based reasoning. In fuzzy modeling, the genetic algorithm is applied to explore general premise structure and optimize fuzzy set membership functions at the same time. Finally, the merits of this work have been demonstrated by the experiment results on a real data set     

A fuzzy reasoning design for fault detection and diagnosis of a computer-controlled system

A fuzzy reasoning and verification Petri nets (FRVPNs) model is established for an error detection and diagnosis mechanism applied to a complex fault-tolerant PC-controlled system. The inference accuracy can be improved through the hierarchical design of a two-level fuzzy rule decision tree and a Petri nets technique to transform the fuzzy rule into the FRVPNs model. Several simulation examples of the assumed failure events were carried out by using the FRVPNs and the Mamdani fuzzy method with MATLAB tools. The reasoning performance of the developed FRVPNs was verified by comparing the inference outcome to that of the Mamdani method. Both methods result in the same conclusions. Thus, the present study demonstrates that the proposed FRVPNs model is able to achieve the purpose of reasoning, and furthermore, determining of the failure event of the monitored application program.     

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.     

Decomposition of a fuzzy controller based on the inference break-up method

A concept called the decomposition of multivariable control rules is presented. Fuzzy control is the application of the compositional rule of inference and it is shown how the inference of the rule base with complex rules can be reduced to the inference of a number of rule bases with simple rules. A fuzzy logic based controller is applied to a simple magnetic suspension system. The controller has proportional, integral and derivative separate parts which are tuned independently. This means that all parts have their own rule bases. By testing it was found that the fuzzy PID controller gives better performance over a typical operational range then a traditional linear PID controller. The magnetic suspension system and the contact-less optical position measurement system have been developed and applied for the comparative analysis of the real-time conventional PID control and the fuzzy control.     

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.     

模糊控制的模糊推理分析

分析了使用RZ算子时推理合成规则(CRI)不具有还原性和不能正确进行模糊推理的原因,给出了正确应用CRI的条件;分析了全蕴涵3I算法的不足及其具有还原性的原因;对各种蕴涵算子的模糊推理进行分析比较,得到了正确的推理算法;对模糊推理在理论和实际应用中的矛盾作了具体说明.     

模糊推理在空调系统故障诊断中的应用

针对空调系统的故障诊断问题及其特点,提出了一种基于诊断知识的模糊描述和模糊推理方法,阐述了空调系统故障诊断专家系统中前向推理、后向推理以及正反向混台推理模糊断言可信度的计算方法,并且给出了相应的实例。     

Knowledge modeling based on interval-valued fuzzy rough set and similarity inference: prediction of welding distortion

Knowledge-based modeling is a trend in complex system modeling technology. To extract the process knowledge from an information system, an approach of knowledge modeling based on interval-valued fuzzy rough set is presented in this paper, in which attribute reduction is a key to obtain the simplified knowledge model. Through defining dependency and inclusion functions, algorithms for attribute reduction and rule extraction are obtained. The approximation inference plays an important role in the development of the fuzzy system. To improve the inference mechanism, we provide a method of similaritybased inference in an interval-valued fuzzy environment. larity based approximate reasoning, an inference result is Combining the conventional compositional rule of inference with simideduced via rule translation, similarity matching, relation modification, and projection operation. This approach is applied to the problem of predicting welding distortion in marine structures, and the experimental results validate the effectiveness of the proposed methods of knowledge modeling and similarity-based inference.     

Hybrid learning-based neuro-fuzzy inference system: a new approach for system modeling

In this article, a hybrid learning neuro-fuzzy inference system (HLNFIS) with a new inference mechanism is proposed for system modeling. In the HLNFIS, the incoming signal is fuzzified by the proposed improved Gaussian membership function (IGMF), which is derived from two standard Gaussian functions. With the premise construction with IGMFs, the system inference ability can be upgraded. The fuzzy inference processor, which involves both numerical and linguistic reasoning, is introduced in rule base construction. For effective parameter learning, the hybrid algorithm of random optimization (RO) and least square estimation (LSE) is exploited, where the premise and the consequence parameters of are updated by RO and LSE, respectively. To validate the feasibility and the potential of the proposed approach, three examples of system modeling are conducted. Through experimental results and comparisons the proposed HLNFIS shows excellent performance for complex modeling.     

Interpolation and extrapolation of fuzzy quantities revisited – an axiomatic approach

 This paper deals with the problem of rule interpolation and rule extrapolation for fuzzy and possibilistic systems. Such systems are used for representing and processing vague linguistic If-Then-rules, and they have been increasingly applied in the field of control engineering, pattern recognition and expert systems. The methodology of rule interpolation is required for deducing plausible conclusions from sparse (incomplete) rule bases. For this purpose the well-known fuzzy inference mechanisms have to be extended or replaced by more general ones. The methods proposed so far in the literature for rule interpolation are mainly conceived for the application to fuzzy control and miss certain logical characteristics of an inference. First, a set of axioms is proposed in this paper. With this, a definition is given for the notion of interpolation, extrapolation, linear interpolation and linear extrapolation of fuzzy rules. The axioms include all the conditions that have been of interest in the previous attempts and others which either have logical characteristics or try to capture the linearity of the interpolation. A new method for linear interpolation and extrapolation of compact fuzzy quantities of the real line is suggested and analyzed in the spirit of the given definition. The method is extended to non-linear interpolation and extrapolation as well.     

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.     

User profiles and fuzzy logic for web retrieval issues

 We present a study of the role of user profiles using fuzzy logic in web retrieval processes. Flexibility for user interaction and for adaptation in profile construction becomes an important issue. We focus our study on user profiles, including creation, modification, storage, clustering and interpretation. We also consider the role of fuzzy logic and other soft computing techniques to improve user profiles. Extended profiles contain additional information related to the user that can be used to personalize and customize the retrieval process as well as the web site. Web mining processes can be carried out by means of fuzzy clustering of these extended profiles and fuzzy rule construction. Fuzzy inference can be used in order to modify queries and extract knowledge from profiles with marketing purposes within a web framework. An architecture of a portal that could support web mining technology is also presented.     

An Inference Microprocessor Design

This paper is concerned with the design of an inference microprocessor for production rule systems.Its implementation is based on both exact and inexact (fuzzy logic) reasoning,so it can be used for building various production rule systems.The methods of translating linguistically expressed rules into numerical representations are described and the hardware implementations are discussed.Finally, a parallel architecture for the inference microprocessor is presented.     

A novel approach to guarantee good robustness of fuzzy reasoning

The analysis of internal connective operators of fuzzy reasoning is very significant and the robustness of fuzzy reasoning has been calling for study. An interesting and important question is that, how to choose suitable internal connective operators to guarantee good robustness of rule-based fuzzy reasoning? This paper is intended to answer it. In this paper, Lipschitz aggregation property and copula characteristic of t-norms and implications are discussed. The robustness of rule-based fuzzy reasoning is investigated and the relationships among input perturbation, rule perturbation and output perturbation are presented. The suitable t-norm and implication can be chosen to satisfy the need of robustness of fuzzy reasoning. In 1-Lipschitz operators, if both t-norm and implication are copulas, the rule-based fuzzy reasoning is much more stable and more reliable. In copulas, if both t-norm and implication are 1-l_∞-Lipschitz, they can guarantee good robustness of fuzzy reasoning. The experiments not only illustrate the ideas proposed in the paper but also can be regarded as applications of soft computing. The approach in the paper also provides guidance for choosing suitable fuzzy connective operators and decision making application in rule-based fuzzy reasoning.     

GSETSK: a generic self-evolving TSK fuzzy neural network with a novel Hebbian-based rule reduction approach

Takagi–Sugeno–Kang (TSK) fuzzy systems have been widely applied for solving function approximation and regression-centric problems. Existing dynamic TSK models proposed in the literature can be broadly classified into two classes. Class I TSK models are essentially fuzzy systems that are limited to time-invariant environments. Class II TSK models are generally evolving systems that can learn in time-variant environments. This paper attempts to address the issues of achieving compact, up-to-date fuzzy rule bases and interpretable knowledge bases in TSK models. It proposes a novel rule pruning method which is simple, computationally efficient and biologically plausible. This rule pruning algorithm applies a gradual forgetting approach and adopts the Hebbian learning mechanism behind the long-term potentiation phenomenon in the brain. It also proposes a merging approach which is used to improve the interpretability of the knowledge bases. This approach can prevent derived fuzzy sets from expanding too many times to protect their semantic meanings. These two approaches are incorporated into a generic self-evolving Takagi–Sugeno–Kang fuzzy framework (GSETSK) which adopts an online data-driven incremental-learning-based approach.Extensive experiments were conducted to evaluate the performance of the proposed GSETSK against other established evolving TSK systems. GSETSK has also been tested on real world dataset using the high-way traffic flow density and Dow Jones index time series. The results are encouraging. GSETSK demonstrates its fast learning ability in time-variant environments. In addition, GSETSK derives an up-to-date and better interpretable fuzzy rule base while maintaining a high level of modeling accuracy at the same time.     

An approach to fuzzy default reasoning for function approximation

This paper discusses fuzzy reasoning for approximately realizing nonlinear functions by a small number of fuzzy if-then rules with different specificity levels. Our fuzzy rule base is a mixture of general and specific rules, which overlap with each other in the input space. General rules work as default rules in our fuzzy rule base. First, we briefly describe existing approaches to the handling of default rules in the framework of possibility theory. Next, we show that standard interpolation-based fuzzy reasoning leads to counterintuitive results when general rules include specific rules with different consequents. Then, we demonstrate that intuitively acceptable results are obtained from a non-standard inclusion-based fuzzy reasoning method. Our approach is based on the preference for more specific rules, which is a commonly used idea in the field of default reasoning. When a general rule includes a specific rule and they are both compatible with an input vector, the weight of the general rule is discounted in fuzzy reasoning. We also discuss the case where general rules do not perfectly but partially include specific rules. Then we propose a genetics-based machine learning (GBML) algorithm for extracting a small number of fuzzy if-then rules with different specificity levels from numerical data using our inclusion-based fuzzy reasoning method. Finally, we describe how our approach can be applied to the approximate realization of fuzzy number-valued nonlinear functions     

A fuzzy Petri net-based expert system and its application to damageassessment of bridges

In this paper, a fuzzy Petri net approach to modeling fuzzy rule-based reasoning is proposed to bring together the possibilistic entailment and the fuzzy reasoning to handle uncertain and imprecise information. The three key components in our fuzzy rule-based reasoning-fuzzy propositions, truth-qualified fuzzy rules, and truth-qualified fuzzy facts-can be formulated as fuzzy places, uncertain transitions, and uncertain fuzzy tokens, respectively. Four types of uncertain transitions-inference, aggregation, duplication, and aggregation-duplication transitions-are introduced to fulfil the mechanism of fuzzy rule-based reasoning. A framework of integrated expert systems based on our fuzzy Petri net, called fuzzy Petri net-based expert system (FPNES), is implemented in Java. Major features of FPNES include knowledge representation through the use of hierarchical fuzzy Petri nets, a reasoning mechanism based on fuzzy Petri nets, and transformation of modularized fuzzy rule bases into hierarchical fuzzy Petri nets. An application to the damage assessment of the Da-Shi bridge in Taiwan is used as an illustrative example of FPNES.     

Add-Mult型模糊神经网络

提出了一种Add-Mult型模糊神经网络模型(AMFNN)，给出了该模型的结构。根据梯度下降算法，给出了AMFNN模糊神经网络的误差反传学习算法。与6种极具代表性的模糊推理方法进行比较的结果表明，AMFNN模糊神经网络模型具有推理精度高、适用范围广、泛化能力强以及实现容易等特点，因而具有广阔的应用前景。     

Fuzzy interpolative reasoning via scale and move transformations

Interpolative reasoning does not only help reduce the complexity of fuzzy models but also makes inference in sparse rule-based systems possible. This paper presents an interpolative reasoning method by means of scale and move transformations. It can be used to interpolate fuzzy rules involving complex polygon, Gaussian or other bell-shaped fuzzy membership functions. The method works by first constructing a new inference rule via manipulating two given adjacent rules, and then by using scale and move transformations to convert the intermediate inference results into the final derived conclusions. This method has three advantages thanks to the proposed transformations: 1) it can handle interpolation of multiple antecedent variables with simple computation; 2) it guarantees the uniqueness as well as normality and convexity of the resulting interpolated fuzzy sets; and 3) it suggests a variety of definitions for representative values, providing a degree of freedom to meet different requirements. Comparative experimental studies are provided to demonstrate the potential of this method.