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An approach to online identification of Takagi-Sugeno fuzzy models

An approach to the online learning of Takagi-Sugeno (TS) type models is proposed in the paper. It is based on a novel learning algorithm that recursively updates TS model structure and parameters by combining supervised and unsupervised learning. The rule-base and parameters of the TS model continually evolve by adding new rules with more summarization power and by modifying existing rules and parameters. In this way, the rule-base structure is inherited and up-dated when new data become available. By applying this learning concept to the TS model we arrive at a new type adaptive model called the Evolving Takagi-Sugeno model (ETS). The adaptive nature of these evolving TS models in combination with the highly transparent and compact form of fuzzy rules makes them a promising candidate for online modeling and control of complex processes, competitive to neural networks. The approach has been tested on data from an air-conditioning installation serving a real building. The results illustrate the viability and efficiency of the approach. The proposed concept, however, has significantly wider implications in a number of fields, including adaptive nonlinear control, fault detection and diagnostics, performance analysis, forecasting, knowledge extraction, robotics, behavior modeling.

Induced ordered weighted averaging operators

We briefly describe the Ordered Weighted Averaging (OWA) operator and discuss a methodology for learning the associated weighting vector from observational data. We then introduce a more general type of OWA operator called the Induced Ordered Weighted Averaging (IOWA) Operator. These operators take as their argument pairs, called OWA pairs, in which one component is used to induce an ordering over the second components which are then aggregated. A number of different aggregation situations have been shown to be representable in this framework. We then show how this tool can be used to represent different types of aggregation models.

Generation of Fuzzy Rules by Mountain Clustering

We develop, based upon the mountain clustering method, a procedure for learning fuzzy systems models from data. First we discuss the mountain clustering method. We then show how it could be used to obtain the structure of fuzzy systems models. The initial estimates of this model are obtained from the cluster centers. We then use a back propagation algorithm to tune the model.

Approximate clustering via the mountain method

We develop a simple and effective approach for approximate estimation of the cluster centers on the basis of the concept of a mountain function. We call the procedure the mountain method. It can be useful for obtaining the initial values of the clusters that are required by more complex cluster algorithms. It also can be used as a stand alone simple approximate clustering technique. The method is based upon a griding on the space, the construction of a mountain function from the data and then a destruction of the mountains to obtain the cluster centers. >

On the issue of obtaining OWA operator weights

We first investigate the issue of obtaining the weights associated with the OWA aggregation in the situation when we have observed data on the arguments and the aggregated value. We next introduce a family of OWA operators called exponential OWA operators. Finally, we look at a simple procedure for generating the weights given a required degree of orness.

Evolving Intelligent Systems: Methodology and Applications

From theory to techniques, the first all-in-one resource for EIS There is a clear demand in advanced process industries, defense, and Internet and communication (VoIP) applications for intelligent yet adaptive/evolving systems. Evolving Intelligent Systems is the first self- contained volume that covers this newly established concept in its entirety, from a systematic methodology to case studies to industrial applications. Featuring chapters written by leading world experts, it addresses the progress, trends, and major achievements in this emerging research field, with a strong emphasis on the balance between novel theoretical results and solutions and practical real-life applications. Explains the following fundamental approaches for developing evolving intelligent systems (EIS): the Hierarchical Prioritized Structure the Participatory Learning Paradigm the Evolving Takagi-Sugeno fuzzy systems (eTS+) the evolving clustering algorithm that stems from the well-known Gustafson-Kessel offline clustering algorithm Emphasizes the importance and increased interest in online processing of data streams Outlines the general strategy of using the fuzzy dynamic clustering as a foundation for evolvable information granulation Presents a methodology for developing robust and interpretable evolving fuzzy rule-based systems Introduces an integrated approach to incremental (real-time) feature extraction and classification Proposes a study on the stability of evolving neuro-fuzzy recurrent networks Details methodologies for evolving clustering and classification Reveals different applications of EIS to address real problems in areas of: evolving inferential sensors in chemical and petrochemical industry learning and recognition in robotics Features downloadable software resources Evolving Intelligent Systems is the one-stop reference guide for both theoretical and practical issues for computer scientists, engineers, researchers, applied mathematicians, machine learning and data mining experts, graduate students, and professionals.

Analytic properties of maximum entropy OWA operators

We discuss the maximum entropy approach to obtaining the weights associated with the ordered weighted averaging (OWA) aggregation operator. The resulting weights are called the MEOWA weights. Using the method of LaGrange multipliers, we obtain an analytic form for these weights and describe some of their properties. The concept of immediate probabilities is introduced as being a transformation of a probability distribution based on a decision makers degree of optimism. This transformation, which is affected by an OWA operator, is shown to result in a relationship between the transformed expected value and the degree of optimism that is monotone when the weights used are the MEOWA weights.

On the issue of defuzzification and selection based on a fuzzy set

Abstract We are concerned with the problem of selecting a crisp element based on information provided by a fuzzy set, a problem which manifests itself in the defuzzification step in fuzzy logic controllers. We provide a unifying approach to this selection process. Among other characteristics this unification puts the defuzzification methods of mean of maxima and center of gravity in the same framework. We show that this selection can be viewed as a three step operation: transformation of the decision fuzzy set; normalization to probability distribution; selection based on the probability distribution. A number of different procedures for selection are discussed.

Simpl_eTS: a simplified method for learning evolving Takagi-Sugeno fuzzy models

This paper deals with a simplified version of the evolving Takagi-Sugeno (eTS) learning algorithm - a computationally efficient procedure for on-line learning TS type fuzzy models. It combines the concept of the scatter as a measure of data density and summarization ability of the TS rules, the use of Cauchy type antecedent membership functions, an aging indicator characterizing the stationarity of the rules, and a recursive least square algorithm to dynamically learn the structure and parameters of the eTS model

PARAMETERIZED AND-UKE AND OR-LIKE OWA OPERATORS

We discuss the OWA (Ordered Weighted Averaging) operators which provide for aggregation operations lying between the and and the or, and the BADD (BAsic Defuzzification Distribution) transformation. This transformation plays a central role in the development of defuzzification procedures, the aggregation of elements in a fuzzy subset to obtain one representative element. We suggest the use of the BADD transformation to generate a class of OWA like aggregation operators, denoted BADD-OWA operators. We show that while these BADD-OWA operators have some interesting properties, they fail to be mono-tonic. We next use another family of defuzzification operators, called SLIDE, to generate another class of OWA operators. These S-OWA operators provide two subfamilies of OWA operators, one Or-like and the other And-Like.