41324764
Rule-based multi-FNN identification with the aid of evolutionary fuzzy granulation
Abstract In this paper, we introduce a category of Multi-Fuzzy-Neural Networks (Multi-FNNs) models, analyze the underlying architectures and propose a comprehensive identification framework. The proposed Multi-FNNs are based on a concept of fuzzy rule-based FNNs that use H ard C - M eans (HCM) clustering and evolutionary fuzzy granulation and exploit linear inference being treated as a generic inference mechanism of approximate reasoning. By this nature, this FNN model is geared toward capturing relationships between information granules–fuzzy sets. The form of the information granules themselves (in particular their distribution and a type of membership functions) becomes an important design feature of the FNN model that contributes to its structural and parametric optimization. The genetically guided global optimization is then augmented by more refined gradient-based learning mechanisms such as a standard back-propagation. The HCM algorithm, whose role is to carry out preprocessing of the experimental data, is utilized to determine the structure of Multi-FNNs. The detailed parameters of the Multi-FNN (such as apexes of membership functions, learning rates, and momentum coefficients) are adjusted using genetic algorithms. The proposed aggregate performance index helps achieve a sound balance between approximation and generalization (predictive) abilities of the model. To evaluate an effectiveness of the introduced model, several numeric data sets are experimented with. Those include a time-series data of gas furnace, NOx emission process of gas turbine power plant and some synthetic data.
9555956
Face recognition using fuzzy Integral and wavelet decomposition method
In this paper, we develop a method for recognizing face images by combining wavelet decomposition, Fisherface method, and fuzzy integral. The proposed approach is comprised of four main stages. The first stage uses the wavelet decomposition that helps extract intrinsic features of face images. As a result of this decomposition, we obtain four subimages (namely approximation, horizontal, vertical, and diagonal detailed images). The second stage of the approach concerns the application of the Fisherface method to these four decompositions. The choice of the Fisherface method in this setting is motivated by its insensitivity to large variation in light direction, face pose, and facial expression. The two last phases are concerned with the aggregation of the individual classifiers by means of the fuzzy integral. Both Sugeno and Choquet type of fuzzy integral are considered as the aggregation method. In the experiments we use n-fold cross-validation to assure high consistency of the produced classification outcomes. The experimental results obtained for the Chungbuk National University (CNU) and Yale University face databases reveal that the approach presented in this paper yields better classification performance in comparison to the results obtained by other classifiers.
44496446
THE GENETIC DESIGN OF HYBRID FUZZY CONTROLLERS
In this study, we introduce a comprehensive design methodology of hybrid fuzzy controllers (HFCs). The hybrid facet of the proposed architecture of the controller manifests in the form of a convex combination of a standard proportional integral derivative (PID) controller and a fuzzy controller. The design procedure dwells on the use of evolutionary computing (genetic algorithms) and an autotuning algorithm based on estimation modes. The tuning of the scaling factors of the HFC is an essential component of the entire optimization process. Numerical studies are presented and a detailed comparative analysis is included as well.
19471846
Fuzzy clustering with a knowledge-based guidance
Fuzzy clustering becomes a broadly accepted synonym of fundamental endeavors aimed at finding structures in multidimensional data. In essence, these methods operate in unsupervised mode. This means that they act upon data while being directed by some predefined objective function (criterion) for which they "discover" a structure (clusters) that yields a minimal value of this criterion. In this study, we discuss an issue of exploiting and effectively incorporating auxiliary problem dependent hints being available as a part of the domain knowledge associated with the pattern recognition problem at hand. As such hints are usually expressed by experts/data analysts at the level of clusters (information granules) rather than individual data (patterns), we refer to them as knowledge-based indicators and allude to a set of them as a knowledge-based guidance available to fuzzy clustering. The proposed paradigm shift in which fuzzy clustering incorporates this type of knowledge-based supervision is discussed and contrasted with the "pure" (that is data-driven) version of fuzzy clustering. Several fundamental categories of the guidance mechanisms are introduced and discussed, namely partial supervision, proximity-based guidance and uncertainty driven knowledge hints. The details on how the guidance machinery translates into updates of the partition matrices are presented. We also present a number of practical scenarios in which the role of knowledge hints becomes evident and highly justifiable. This concerns Web exploration, exploitation of labeled patterns, issues of incomplete feature spaces, and constraints of typicality of patterns, to name a few representative applications.
2312456
Two iterative methods of decomposition of a fuzzy relation for image compression/decompression processing
A decomposition problem of max–min type for a fuzzy relation is proposed. A fast method is derived by transforming slightly the derivatives in the traditional gradient algorithm and by updating simultaneously the prototype relation. The complexities of the proposed algorithm, with respect to the traditional gradient one, are decreased to approximately 1/c, where “c” denotes the Schein rank of the fuzzy relation involved. A dual decomposition problem of max–min type is also formulated and a similar fast method is presented. Both methods are applied to image compression/decompression processing.
125593703
Associations and rules in data mining: A link analysis
We discuss a problem of synthesis and analysis of rules based on experimental numeric data. Two descriptors of the rules that are viewed individually and en block are introduced. The coverage of the rules is quantified in terms of the data being covered by the antecedents and conclusions standing in the rule. Although this index describes each rule individually, the consistency of the rule deals with the quality of the rule viewed compared with other rules. It expresses how much the rule “interacts” with others in the sense that its conclusion is affected (distorted) by the conclusion parts coming from other rules. We propose a synthetic index of rule relevance that combines the two already introduced descriptors. We show how the rules are formed by means of fuzzy clustering and their quality is evaluated by means of the aforementioned indexes. Global characteristics of a set of rules also are discussed and related to the number of information granules formed in the space of antecedents and conclusions. Finally, we discuss the rules in the setting of granular modeling and express their performance in the design of numeric models. © 2004 Wiley Periodicals, Inc.
5269666
Conditional Fuzzy C-Means
A Fuzzy C-Means-based clustering method guided by an auxiliary (conditional) variable is introduced. The method reveals a structure within a family of patterns by considering their vicinity in a feature space along with the similarity of the values assumed by a certain conditional variable. The usefulness of the algorithm is exemplified in the problems of data mining.
34867589
Modeling temporal functions with granular regression and fuzzy rules
Modeling of temporal functions has been studied extensively in last few decades. Temporal functions or time series are found practically in the gamut of applications, ranging from engineering analysis to financial and commercial transactions.Numerous time series models been proposed, and they can be found in the relevant time series literature. Deterministic and stochastic models have dominated much of the research in this area. Nonetheless, these models have their limitations, and particularly specific models solve specific problem domains. Therefore, there is no general mechanism that can address the issues of modeling of temporal functions.Granular information is now being used to address a few of the problems in the theory of time series. This paper proposes two models that use the concepts of regression and interleaved information granules-intervals and fuzzy sets to identify the structure existing in a given time series. In brevity, we are attempting to combine regression and fuzzy rules to model temporal systems.
22511023
Fuzzy clustering with partial supervision
Presented here is a problem of fuzzy clustering with partial supervision, i.e., unsupervised learning completed in the presence of some labeled patterns. The classification information is incorporated additively as a part of an objective function utilized in the standard FUZZY ISODATA. The algorithms proposed in the paper embrace two specific learning scenarios of complete and incomplete class assignment of the labeled patterns. Numerical examples including both synthetic and real-world data arising in the realm of software engineering are also provided.
17239140
Granular clustering: a granular signature of data
The study is devoted to a granular analysis of data. We develop a new clustering algorithm that organizes findings about data in the form of a collection of information granules-hyperboxes. The clustering carried out here is an example of a granulation mechanism. We discuss a compatibility measure guiding a construction (growth) of the clusters and explain a rationale behind their development. The clustering promotes a data mining way of problem solving by emphasizing the transparency of the results (hyperboxes). We discuss a number of indexes describing hyperboxes and expressing relationships between such information granules. It is also shown how the resulting family of the information granules is a concise descriptor of the structure of the data-a granular signature of the data. We examine the properties of features (variables) occurring of the problem as they manifest in the setting of the information granules. Numerical experiments are carried out based on two-dimensional (2-D) synthetic data as well as multivariable Boston data available on the WWW.