Evolving fuzzy systems

Volatility forecasting is a challenging task that has attracted the attention of market practitioners, regulators and academics in recent years. This paper proposes an evolving fuzzy-GARCH approach to model and forecast the volatility of S&P 500 and Ibovespa indexes. The model comprises both the concept of evolving fuzzy systems and GARCH modeling approach in order to consider the principles of time-varying volatility and volatility clustering, in which changes are cataloged by similarity. Evolving fuzzy systems use data streams to continuously adapt the structure and functionality of fuzzy models to improve their performance, which is computationally efficient. The results show the high potential of the evolving fuzzy-GARCH model to forecast stock returns volatility, outperforming GARCH-type models in statistical terms.

An adaptive clustering procedure specifically designed for process monitoring, fault detection and isolation is presented in this paper. The key feature of the proposed procedure can be identified as its underlying capability to detect novelties in the system's mode of operation and, thus, to identify previously unseen functioning modes of the process. Once a novelty is detected, relevant informations are used to enrich the knowledge-base of the algorithm and as a result the proposed clustering procedure evolves and learns the new features of the monitored process in accordance with the available process data. The suggested clustering procedure is theoretically illustrated and its effectiveness has been investigated experimentally. Particularly, the on-line implementation of the algorithm and its integration with a fault detection expert system have been considered by making reference to a pneumatic process.

Equity assets volatility modeling and forecasting provide key information for risk management, portfolio construction, financial decision making and derivatives pricing. Realized volatility models outperform autoregressive conditional heteroskedasticity and stochastic volatility models in out-ofsample forecasting. Gain in forecasting performance is achieved when models comprise volatility jump components. This paper suggests evolving possibilistic fuzzy modeling to forecast realized volatility with jumps. The modeling approach is based on an extension of the possibilistic fuzzy c-means clustering and on functional fuzzy rule-based models. It employs memberships and typicalities to recursively update cluster centers. The evolving nature of the model allows adding or removing clusters using statistical distance-like criteria to update the model as dictated by input data. The possibilistic model improves robustness to noisy data and outliers, an essential requirement in financial markets volatility modeling and forecasting. Computational experiments and statistical analysis are done using Value-at-Risk estimates to evaluate and to compare the performance of the evolving possibilistic fuzzy modeling with the Heterogeneous Autoregressive, neural networks models and current state of the art evolving fuzzy methods. The experiments use actual data from S&P 500 and Nasdaq (United States), FTSE (United Kingdom), DAX (Germany), IBEX (Spain) and Ibovespa (Brazil), major equity market indexes in global markets. The results show that the evolving possibilistic fuzzy model is highly efficient to model realized volatility with jumps in terms of forecasting accuracy.

In this paper, we investigate on-line fuzzy modeling for predicting the prices of residential premises using the concept of evolving fuzzy models. These combine the aspects of incrementally updating the parameters and expanding the inner structure on demand with the concepts of uncertainty modeling in a possibilistic and linguistic manner (achieved through fuzzy sets and fuzzy rule bases). We use the FLEXFIS and eTS approaches as learning engines for evolving fuzzy (regression) models and compared them with a property valuating method employed by professional appraisers in reality as well as with a classical genetic fuzzy system. The comparison was based on a real-world data set taken from a cadastral system including prices of residential premises within the years 1998 to 2008.

Genetics-based machine learning (GBML) is one of the promising evolutionary algorithms for classifier design. It can construct rule-based classifiers from numerical data sets. These classifiers have comparable classification ability to those by other machine learning techniques and are more understandable than the others. Although GBML has high search ability, it needs long computation time especially for large data sets because a large number of patterns should be classified for string evaluation. We have already applied a parallel distributed implementation to our fuzzy GBML. In our method, we divide not only a population but also a training data set into subgroups. A sub-population and a training data subset are assigned to one CPU core. To avoid the overfitting to certain training data subset, the re-assignment of the training data subsets is periodically performed. The main advantage is that the speed-up rate of our method is larger than the number of used CPU cores without det...

An adaptive clustering procedure specifically designed for process monitoring, fault detection and isolation is presented in this paper. The key feature of the proposed procedure can be identified as its underlying capability to detect novelties in the system's mode of operation and, thus, to identify previously unseen functioning modes of the process. Once a novelty is detected, relevant informations are used to enrich the knowledge-base of the algorithm and as a result the proposed clustering procedure evolves and learns the new features of the monitored process in accordance with the available process data. The suggested clustering procedure is theoretically illustrated and its effectiveness has been investigated experimentally. Particularly, the on-line implementation of the algorithm and its integration with a fault detection expert system have been considered by making reference to a pneumatic process.

The NEFCLASS system makes it possible to learn fuzzy classi ers from data. Unfortunately, in some cases the derived rule bases are hard to interpret. We present modi ed learning and pruning strategies to derive simpli ed fuzzy classi cation rules from data. The usability of this approach is empirically shown on some real world data.

A methodology and experimental comparison of neuro-fuzzy structures, namely linguistic and zero and first-order Takagi-Sugeno, are developed. The implementation of the model is conducted through the training of a neuro-fuzzy network, i.e., a neural net architecture capable of representing a fuzzy system. In the first phase, the structure of the model is obtained by subtractive clustering, which allows the extraction of a set of relevant rules based on a set of representative input-output data samples. Membership functions with two-sided Gaussian functions are proposed and discussed. In the second phase, the model parameters are tuned via the training of a neural network. Furthermore, different fuzzy operators are compared, as well as regular and two-sided Gaussian functions.

A methodology for development of linguistically interpretable fuzzy models from data is developed. The implementation of the model is conducted through the training of a neuro-fuzzy network. Structure of the model is firstly obtained by subtractive clustering, allowing the extraction of a set of relevant rules from input-output data. The model parameters are then tuned via the training of a neural network through backpropagation. Interpretability goals are pursued through membership function merging and some constrains on the tuning of parameters. The assignment of linguistic labels to each of the membership functions is then possible. The model obtained for the system under analysis can be described, in this way, by a set of linguistic rules, easily interpretable.

The principal contribution of this work is to design a general framework for an intelligent system to extract one object of interest from ultrasound images. This system is based on reinforcement learning. The input image is divided into several sub-images, and the proposed system finds the appropriate local values for each of them so that it can extract the object of interest. The agent uses some images and their ground-truth (manually segmented) version to learn from. A reward function is employed to measure the similarities between the output and the manually segmented images, and to provide feedback to the agent. The information obtained can be used as valuable knowledge stored in the Q-matrix. The agent can then use this knowledge for new input images. The experimental results for prostate segmentation in trans-rectal ultrasound images show high potential of this approach in the field of ultrasound image segmentation.

An adaptive clustering procedure specifically designed for process monitoring, fault detection and isolation is presented in this paper. The key feature of the proposed procedure can be identified as its underlying capability to detect novelties in the system's mode of operation and, thus, to identify previously unseen functioning modes of the process. Once a novelty is detected, relevant informations are used to enrich the knowledge-base of the algorithm and as a result the proposed clustering procedure evolves and learns the new features of the monitored process in accordance with the available process data. The suggested clustering procedure is theoretically illustrated and its effectiveness has been investigated experimentally. Particularly, the on-line implementation of the algorithm and its integration with a fault detection expert system have been considered by making reference to a pneumatic process.

Fuzzy controllers are designed to work with knowledge in the form of linguistic control rules. But the translation of these linguistic rules into the framework of fuzzy set theory depends on the choice of certain parameters, for which no formal method is known. The optimization of these parameters can be carried out by neural networks, which are designed to learn from training data, but which are in general not able to pro t from structural knowledge. In this paper we discuss approaches which combine fuzzy controllers and neural networks, and present our own hybrid architecture where principles from fuzzy control theory and from neural networks are integrated into one system.

In this paper a methodology for development of linguistically interpretable fuzzy models is presented. The implementation of the model is conducted through the training of a neuro-fuzzy network, i.e., a neural net architecture capable of representing a fuzzy system. In the first phase the structure of the model is obtained by subtractive clustering, which allows the extraction of a set of relevant rules based on a set of representative input-output data samples. In the second phase, the model parameters are tuned via the training of a neural network through backpropagation. In order to attain interpretability goals, the method described imposes some restrictions on the tuning of parameters and performs membership function merging. In this way, it will be easy to assign linguistic labels to each of the membership functions used. Therefore, the model obtained for the system under analysis will be described by a set of linguistic rules, easily interpretable.

A methodology for development of linguistically interpretable fuzzy models from data is developed. The implementation of the model is conducted through the training of a neuro-fuzzy network. Structure of the model is firstly obtained by subtractive clustering, allowing the extraction of a set of relevant rules from input-output data. The model parameters are then tuned via the training of a neural network through backpropagation. Interpretability goals are pursued through membership function merging and some constrains on the tuning of parameters. The assignment of linguistic labels to each of the membership functions is then possible. The model obtained for the system under analysis can be described, in this way, by a set of linguistic rules, easily interpretable.

The efficiency of a fuzzy logic-based system is catalyzed by the system design. Fuzzy sets generalize classical crisp sets by incorporating concepts of membership for a fuzzy variable. Each fuzzy set is associated with linguistic concepts that are germane to a particular application. This paper presents an approach for evaluating the region of certainty and uncertainty represented in design of fuzzy linguistic variables. Fuzzy Resembler (FuzR) attempts to capture the goodness of a fuzzy system design using a geometric approach; it can be used for evaluating the design of fuzzy membership space. FuzR is the ratio between region of certainty to region of uncertainty. From the results, it can be inferred that FuzR presents meaningful observations of a fuzzy variable, characterized by trapezoidal, triangular, and gaussian membership functions. FuzR can be used as a design evaluation parameter for evolving fuzzy systems. Knowledge engineers can use it to optimize design of fuzzy systems in the absence of domain experts. Moreover, the level of abstraction provided by FuzR makes it an intuitive design parameter. The significance of this work lies more in its point-of-view than voracious results; the theory and formulation are still young and much more is yet to be conceptualized and tested.

La versión corta del código resume las aspiraciones a un alto nivel de abstracción; las cláusulas que se incluyen en la versión completa proporcionan ejemplos y detalles acerca de cómo estas aspiraciones modifican nuestra manera de actuar como profesionales de ingenieros en sistemas computacionales. Sin las aspiraciones los detalles pueden convertirse en tediosos y legalistas; sin los detalles las aspiraciones pueden convertirse en altisonantes pero vacías; juntas, las aspiraciones y los detalles forman un código cohesivo. Los ingenieros en Sistemas Computacionales deberán comprometerse a convertir el análisis, especificación, diseño, implementación, pruebas y mantenimiento de sistemas de información en una profesión respetada y benéfica. De acuerdo a su compromiso con la salud, seguridad y bienestar social, los ingenieros en Sistemas Computacionales deberán sujetarse a los ocho principios siguientes:

Current image segmentation techniques usually require that the user tune several parameters in order to obtain maximum segmentation accuracy, a computationally inefficient approach, especially when a large number of images must be processed sequentially in daily practice. The use of evolving fuzzy systems for designing a method that automatically adjusts parameters to segment medical images according to the quality expectation of expert users has been proposed recently (Evolving fuzzy image segmentation EFIS). However, EFIS suffers from a few limitations when used in practice mainly due to some fixed parameters. For instance, EFIS depends on auto-detection of the object of interest for feature calculation, a task that is highly application-dependent. This shortcoming limits the applicability of EFIS, which was proposed with the ultimate goal of offering a generic but adjustable segmentation scheme. In this paper, a new version of EFIS is proposed to overcome these limitations. The n...

Diverse forms of the concept of opposition are already existent in philosophy, linguistics, psychology and physics. The inter- play between entities and opposite entities is apparently fundamental for balance maintenance in almost a universal manner. However, it seems that we have failed to incorporate oppositional thinking in en- gineering, mathematics and computer science. Especially, the set theory in general, and fuzzy set theory in particular, do not offer a formal framework to incorporate opposition in inference engines. Considering sets along with their opposites can establish a new com- puting scheme with a wide range of applications. In this work, pre- liminary definitions for opposite fuzzy sets will be established. The underlaying idea of opposition-based computing is the simultaneous consideration of guess and opposite guess, and estimate and opposite estimate, in order to accelerate learning, search and optimization. To demonstrate the applicability and usefulness of op...

Current image segmentation techniques usually require that the user tune several parameters in order to obtain maximum segmentation accuracy, a computationally inefficient approach, especially when a large number of images must be processed sequentially in daily practice. The use of evolving fuzzy systems for designing a method that automatically adjusts parameters to segment medical images according to the quality expectation of expert users has been proposed recently (Evolving fuzzy image segmentation EFIS). However, EFIS suffers from a few limitations when used in practice mainly due to some fixed parameters. For instance, EFIS depends on auto-detection of the object of interest for feature calculation, a task that is highly application-dependent. This shortcoming limits the applicability of EFIS, which was proposed with the ultimate goal of offering a generic but adjustable segmentation scheme. In this paper, a new version of EFIS is proposed to overcome these limitations. The n...

Opposition-based computing is the paradigm for incorporating entities along with their opposites within the search, optimization and learning mechanisms. In this work, we introduce the notion of "opposite fuzzy sets" in order to use the entropy difference between a fuzzy set and its opposite to carry out object discrimination in digital images. A quasi-global scheme is used to execute the calculations, which can be employed by any other existing thresholding technique. Results for prostate ultrasound images have been provided to verify the performance whereas expert's markings have been used as gold standard.

In this note we clarify some issues with respect to the central opposition theorem as formulated in [1]. We slightly reformulate the theorem to more plausibly highlight its proof. As well, we provide some general remarks to better understand the scope of that theorem. ß

Abstract— Diverse forms of the concept of opposition are already existent in philosophy, linguistics, psychology and physics. The inter-play between entities and opposite entities is apparently fundamental for balance maintenance in almost a universal manner. However, it seems ...

The study presents methods for classification of applicants into different categories of credit risk using four different computational intelligence techniques. The selected methodologies involved in the rule-based categorization task are (1) feedforward neural networks trained with second order methods (2) inductive machine learning, (3) hierarchical decision trees produced by grammar-guided genetic programming and (4) fuzzy rule based systems produced by grammar-guided genetic programming. The data used are both numerical and linguistic in nature and they represent a realworld problem, that of deciding whether a loan should be granted or not, in respect to financial details of customers applying for that loan, to a specific private EU bank. We examine the proposed classification models with a sample of enterprises that applied for a loan, each of which is described by financial decision variables (ratios), and classified to one of the four predetermined classes. Attention is given to the comprehensibility and the ease of use for the acquired decision models. Results show that the application of the proposed methods can make the classification task easier and -in some cases-may minimize significantly the amount of required credit data. We consider that these methodologies may also give the chance for the extraction of a comprehensible credit management model or even the incorporation of a related decision support system in banking.

Industrial monitoring of complex processes with hundreds or thousands of variables is a hard task faced in this work through evolving fuzzy systems. The Visbreaker process of the Sines Oil Refinery is the case studied. Firstly dimension reduction is performed by multidimensional scaling, obtaining the process evolution in a three dimensional space. Then an evolving fuzzy system (eFS) is developed to detect eventual malfunction of sensors. This eFS takes the data in the three reduced dimensions as antecedents and classifies the process state into normal and abnormal states. A software platform-the eFSLab (Evolving Fuzzy Systems Laboratory) -, with which this work has been developed, is presented and discussed. Several strategies for rule creation and evolution of rules, for Takagi-Sugeno (and for Mamdani system obtained from these) , are implemented in eFSLab. The obtained eFS shows a promising performance in the case studied, classifying in some simulations the state of the process into abnormal-normal condition in about 95% of the cases, with a number of rules between 5 and 8.

La versión corta del código resume las aspiraciones a un alto nivel de abstracción; las cláusulas que se incluyen en la versión completa proporcionan ejemplos y detalles acerca de cómo estas aspiraciones modifican nuestra manera de actuar como profesionales de la ingeniería de software. Sin las aspiraciones los detalles pueden convertirse en tediosos y legalistas; sin los detalles las aspiraciones pueden convertirse en altisonantes pero vacías; juntas, las aspiraciones y los detalles forman un código cohesivo.

A methodology for the encoding of the chromosome of a genetic algorithm (GA) is described in the paper. The encoding procedure is applied to the problem of automatically generating fuzzy rule-based models from data. Models generated by this approach have much of the flexibility of black-box methods, such as neural networks. In addition, they implicitly express information about the process being modelled through the linguistic terms associated with the rules. They can be applied to problems that are too complex to model in a first principles sense and can reduce the computational overhead when compared to established first principles based models. The encoding mechanism allows the rule base structure and parameters of the fuzzy model to be estimated simultaneously from data. The principle advantage is the preservation of the linguistic concept without the need to consider the entire rule base. The GA searches for the optimum solution given a comparatively small number of rules compared to all possible. This minimises the computational demand of the model generation and allows problems with realistic dimensions to be considered. A further feature is that the rules are extracted from the data without the need to establish any information about the model structure a priori. The implementation of the algorithm is described and the Information Sciences 150 17-31 www.elsevier.com/locate/ins * Corresponding authors. (P.P. Angelov), r.a.buswell@lboro.ac.uk (R.A. Buswell).

A methodology for development of linguistically interpretable fuzzy models from data is developed. The implementation of the model is conducted through the training of a neuro-fuzzy network. Structure of the model is firstly obtained by subtractive clustering, allowing the extraction of a set of relevant rules from input-output data. The model parameters are then tuned via the training of a neural network through backpropagation. Interpretability goals are pursued through membership function merging and some constrains on the tuning of parameters. The assignment of linguistic labels to each of the membership functions is then possible. The model obtained for the system under analysis can be described, in this way, by a set of linguistic rules, easily interpretable.

Industrial monitoring of complex processes with hundreds or thousands of variables is a hard task faced in this work through evolving fuzzy systems. The Visbreaker process of the Sines Oil Refinery is the case studied. Firstly dimension reduction is performed by multidimensional scaling, obtaining the process evolution in a three dimensional space. Then an evolving fuzzy system (eFS) is developed to detect eventual malfunction of sensors. This eFS takes the data in the three reduced dimensions as antecedents and classifies the process state into normal and abnormal states. A software platform-the eFSLab (Evolving Fuzzy Systems Laboratory) -, with which this work has been developed, is presented and discussed. Several strategies for rule creation and evolution of rules, for Takagi-Sugeno (and for Mamdani system obtained from these) , are implemented in eFSLab. The obtained eFS shows a promising performance in the case studied, classifying in some simulations the state of the process into abnormal-normal condition in about 95% of the cases, with a number of rules between 5 and 8.

Industrial monitoring of complex processes with hundreds or thousands of variables is a hard task faced in this work through evolving fuzzy systems. The Visbreaker process of the Sines Oil Refinery is the case studied. Firstly dimension reduction is performed by multidimensional scaling, obtaining the process evolution in a three dimensional space. Then an evolving fuzzy system (eFS) is developed to detect eventual malfunction of sensors. This eFS takes the data in the three reduced dimensions as antecedents and classifies the process state into normal and abnormal states. A software platform-the eFSLab (Evolving Fuzzy Systems Laboratory) -, with which this work has been developed, is presented and discussed. Several strategies for rule creation and evolution of rules, for Takagi-Sugeno (and for Mamdani system obtained from these) , are implemented in eFSLab. The obtained eFS shows a promising performance in the case studied, classifying in some simulations the state of the process into abnormal-normal condition in about 95% of the cases, with a number of rules between 5 and 8.

A methodology for development of linguistically interpretable fuzzy models from data is developed. The implementation of the model is conducted through the training of a neuro-fuzzy network. Structure of the model is firstly obtained by subtractive clustering, allowing the extraction of a set of relevant rules from input-output data. The model parameters are then tuned via the training of a neural network through backpropagation. Interpretability goals are pursued through membership function merging and some constrains on the tuning of parameters. The assignment of linguistic labels to each of the membership functions is then possible. The model obtained for the system under analysis can be described, in this way, by a set of linguistic rules, easily interpretable.

In this paper we introduce an application of intervalvalued systems to the segmentation of prostate ultrasound images. The system classifies each pixel as prostate or background. The input variables are the values of each pixel in different processed images as proximity, edginess and enhanced image. The system has 20 rules and is trained with ideal images segmented by an expert. Interval-valued fuzzy systems have been used due to their potential to capture uncertainty in a more robust way compared to ordinary fuzzy systems.

Every segmentation algorithm has parameters that
need to be adjusted in order to achieve good results. Evolving
fuzzy systems for adjustment of segmentation parameters have
been proposed recently (Evolving fuzzy image segmentation –
EFIS [1]). However, similar to any other algorithm, EFIS too
suffers from a few limitations when used in practice. As a major
drawback, EFIS depends on detection of the object of interest for feature calculation, a task that is highly application-dependent.
In this paper, a new version of EFIS is proposed to overcome
these limitations. The new EFIS, called self-configuring EFIS
(SC-EFIS), uses available training data to auto-configure the
parameters that are fixed in EFIS. As well, the proposed SCEFIS
relies on a feature selection process that does not require
the detection of a region of interest (ROI).

An adaptive clustering procedure specifically designed for process monitoring, fault detection and isolation is presented in this paper. The key feature of the proposed procedure can be identified as its underlying capability to detect novelties in the system's mode of operation and, thus, to identify previously unseen functioning modes of the process. Once a novelty is detected, relevant informations are used to enrich the knowledge-base of the algorithm and as a result the proposed clustering procedure evolves and learns the new features of the monitored process in accordance with the available process data. The suggested clustering procedure is theoretically illustrated and its effectiveness has been investigated experimentally. Particularly, the on-line implementation of the algorithm and its integration with a fault detection expert system have been considered by making reference to a pneumatic process.

We developed two GA-based schemes for the design of fuzzy rule-based classification systems. One is genetic rule selection and the other is genetics-based machine learning (GBML). In our genetic rule selection scheme, first a large number of promising fuzzy rules are extracted from numerical data in a heuristic manner as candidate rules. Then a genetic algorithm is used to select a small number of fuzzy rules. A rule set is represented by a binary string whose length is equal to the number of candidate rules. On ...

Abstract—Two conflicting goals are often involved in the design of fuzzy rule-based systems: Accuracy maximization and interpretability maximization. A number of approaches have been proposed for finding a fuzzy rule-based system with a good accuracy-interpretability tradeoff. Formulation of the accuracy maximization is usually straightforward in each application area of fuzzy rule-based systems such as classification, regression and forecasting. Formulation of the interpretability maximization, however, is not so easy. This ...

The idea of opposition-based learning was introduced 10 years ago. Since then a noteworthy group of researchers has used some notions of oppositeness to improve existing optimization and learning algorithms. Among others, evolutionary algorithms, reinforcement agents, and neural networks have been reportedly extended into their ``opposition-based'' version to become faster and/or more accurate. However, most works still use a simple notion of opposites, namely linear (or type-I) opposition, that for each $x\in[a,b]$ assigns its opposite as $\breve{x}_I=a+b-x$. This, of course, is a very naive estimate of the actual or true (non-linear) opposite $\breve{x}_{II}$, which has been called type-II opposite in literature. In absence of any knowledge about a function $y=f(\mathbf{x})$ that we need to approximate, there seems to be no alternative to the naivety of type-I opposition if one intents to utilize oppositional concepts. But the question is if we can receive some level of accuracy increase and time savings by using the naive opposite estimate $\breve{x}_I$ according to all reports in literature, what would we be able to gain, in terms of even higher accuracies and more reduction in computational complexity, if we would generate and employ \textbf{true opposites}? This work introduces an approach to approximate type-II opposites using evolving fuzzy rules when we first perform ``opposition mining''. We show with multiple examples that learning true opposites is possible when we mine the opposites from the training data to subsequently approximate $\breve{x}_{II}=f(\mathbf{x},y)$.

In this paper, a stable backpropagation algorithm is used to train an online evolving radial basis function neural network. Structure and parameters learning are updated at the same time in our algorithm, we do not make difference in structure learning and parameters learning. It generates groups with an online clustering. The center is updated to achieve the center is near to the incoming data in each iteration, so the algorithm does not need to generate a new neuron in each iteration, i.e., the algorithm does not generate many neurons and it does not need to prune the neurons. We give a time varying learning rate for backpropagation training in the parameters. We prove the stability of the proposed algorithm.

Initialization and structure learning in fuzzy neural networks for data-driven rule-based modeling are discussed. Gradient-based optimization is used to fit the model to data and a number of techniques are developed to enhance transparency of the generated rule base: data-driven initialization, similarity analysis for redundancy reduction, and evaluation of the rules contributions. The initialization uses flexible hyper-boxes to avoid redundant and irrelevant coverage of the input space. Similarity analysis detects redundant terms while the contribution evaluation detects irrelevant rules. Both are applied during network training
for early pruning of redundant or irrelevant terms and rules,  excluding them from further parameter learning (training). All steps of the modeling method are presented, and the method is illustrated on an example from the literature.

An approach to on-line design of fuzzy controllers of Takagi-Sugeno type with gradually evolving structure is treated in the paper. Fuzzy rules, representing the structure of the controller are generated based on data collected during the process of control using newly introduced technique for on-line identification of Takagi-Sugeno systems. The output of the plant under control (including its dynamic) and the respective control signal has been memorised and stored in on-line mode. These data has been used to train in a non-iterative, recursive way the fuzzy controller. The indirect adaptive control approach has been used in combination with the novel on-line identification technique. This approach exploits the quasi-linear nature of Takagi-Sugeno models and builds-up the control rule-base structure and adapts it in on-line mode with recursive, non-iterative learning. The method is illustrated with an example from airconditioning systems, though it has wider potential applications.

A methodology for the development of linguistically interpretable fuzzy models from data is presented. The implementation of the model is conducted through the training of a neuro-fuzzy network, i.e., a neural net architecture capable of representing a fuzzy system. In the first phase, the structure of the model is obtained by means of subtractive clustering, which allows the extraction of a set of relevant rules based on a set of representative input–output data samples. In the second phase, the parameters of the model are tuned via the training of a neural network through backpropagation. In order to attain interpretability goals, the method proposed imposes some constraints on the tuning of the parameters and performs membership function merging. In this way, it will be easy to assign linguistic labels to each of the membership functions obtained, after training. Therefore, the model obtained for the system under analysis will be described by a set of linguistic rules, easily interpretable.

Finding an optimal threshold in order to segment digital images is a difficult task in image processing. Numerous approaches to image thresholding already exist in the literature. In this work, a reinforced threshold fusion for image binarization is introduced which aggregates existing thresholding techniques. The reinforcement agent learns the optimal weights for different thresholds and segments the image globally. A fuzzy reward function is employed to measure object similarities between the binarized image and the original gray-level image, and provide feedback to the agent. The experiments show that promising improvement can be obtained. Three well-established thresholding techniques are combined by the reinforcement agent and the results are compared using error measurements based on ground-truth images.