prof. Wlodzislaw Duch, duch@phys.uni.torun.pl, http://www.phys.uni.torun.pl/~duch,
Department of Computer Methods, N. Copernicus University
prof. Danuta Rutkowska, drutko@kik.pcz.czest.pl,
Department of Computer Engineering, Technical University of Czestochowa
This paper concerns fuzzy neural networks and fuzzy inference neural networks, which are two different approaches to neuro-fuzzy combinations. The former is a direct fuzzification of artificial neural networks by introducing fuzzy signals and fuzzy weights. The latter is a representation of fuzzy systems in the form of multi-layer connectionist networks, similar to neural networks. Parameters of membership functions (centers and widths) play the role of neural network weights. In this paper, fuzzy inference neural networks with fuzzy parameters are considered. Neuro-fuzzy systems of this kind utilize both approaches: fuzzy neural networks and fuzzy inference neural networks. They also pertain to fuzzy systems of type 2 since membership functions with fuzzy parameters characterize type 2 fuzzy sets. Various architectures of these networks have been obtained for fuzzy systems based on different fuzzy implications. By analogy with fuzzy inference neural networks with crisp parameters, methods of learning fuzzy parameters and rule generation can be derived for neuro-fuzzy systems with fuzzy parameters. Fuzzy inference neural networks are studied in the framework of fuzzy granulation. In particular, fuzzy clustering as fuzzy information granulation is proposed to be applied in order to generate fuzzy IF-THEN rules. Applications of fuzzy inference neural networks are also outlined.
In this paper we present the Beta function and its main properties. A key feature of the Beta function, which is given by the central-limit theorem, is also given. We then introduce a new category of neural networks based on a new kernel: the Beta function. Next, we investigate the use of Beta fuzzy basis functions for the design of fuzzy logic systems. The functional equivalence between Beta-based function neural networks and Beta fuzzy logic systems is then shown with the introduction of Beta neuro-fuzzy systems. By using the SW theorem and expanding the output of the Beta neuro-fuzzy system into a series of Beta fuzzy-based functions, we prove that one can uniformly approximate any real continuous function on a compact set to any arbitrary accuracy. Finally, a learning algorithm of the Beta neuro-fuzzy system is described and illustrated with numerical examples.
The project deals with the application of computational intelligence (CI) tools for multispectral image classification. Pattern Recognition scheme is a global approach where the classification part is playing an important role to achieve the highest classification accuracy. Multispectral images are data mainly used in remote sensing and this kind of classification is very difficult to assess the accuracy of classification results. There is a feedback problem in adjusting the parts of pattern recognition scheme. Precise classification accuracy assessment is almost impossible to obtain, being an extremely laborious procedure. The paper presents simple neural networks for multispectral image classification, ARTMAP-like neural networks as more sophisticated tools for classification, and a modular approach to achieve the highest classification accuracy of multispectral images. There is a strong link to advances in computer technology, which gives much better conditions for modelling more sophisticated classifiers for multispectral images.
This paper uses the notion of relative sets in relation to fuzzy set theory to provide a mathematical framework to analyze communication among agents. Each relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Two orderings on relative sets are considered; one is an extension of the classical set inclusion ordering while the other is a new ordering of knowledge or information. According to these orderings, we can divide set theoretic problems into two major categories: reasoning problems and communicating problems. In the first category, an agent tries to extract a sound decision through granular reasoning. In this case, a granule represents a concept or a word. In the second category, each granule relates to an agent, and the problem is to compare agents' knowledge about concepts by their related granules, eg. a knowledge reduction problem. Then, we concentrate on the second category of problems and try to investigate this kind of problems in the context of fuzzy set theory. In this way, we could provide a basis for modeling and analyzing the relations among machines, which could communicate with each other using words and granules.
A sub-type of multi-agent systems (MAS) called evolutionary ones (EMAS), special in its features and field of application, needs a dedicated architecture that would be more adequate and easier in design and implementation. The proposed architecture uses the notion of a profile which models strategies and goals of an agent with respect to an aspect of its operation. To make a decision, an agent is equipped with an algorithm that coordinates premises determined in its profiles. The paper presents main ideas of the architecture illustrated with an actual realisation of an EMAS solving the multi-objective optimisation problem.
The paper presents a simulation study of the usefulness of a number of meta-heuristics used as optimisation methods for TSP problems. The five considered approaches are outlined: Genetic Algorithm, Simulated Annealing, Ant Colony System, Tabu Search and Hopfield Neural Network. Using a purpose-developed computer program, efficiency of the meta-heuritics has been studied and compared. Results obtained from about 40000 simulation runs are briefly presented and discussed.
A mathematical model of architecture and learning processes of multilayer artificial neural netwoks is discussed in the paper. Dynamical systems theory is used to describe the learning precess of networks consisting of linear, weakly nonlinear and nonlinear neurons. Conjugacy between a gradient dynamical system with a constant time step and a cascade generated by its Euler method theorem is applied as well.
A common task in speech processing for which neural networks are widely employed is text-to-phoneme conversion. In this paper we propose a novel solution to this problem by combining a multilayer neural network and a modular hybrid system that uses basic rules to subdivide the original problem into easier tasks which are then solved by dedicated neural networks. A hybrid solution can be more rapidly constructed than a single net solution, and is easily extendable. Input data representation is also discussed. A voting committee concept is used to enhance generalization abilities of the system. Efficiency of the proposed systems is compared.
A perception-based interpretation of evaluation systems is proposed in this paper. Thus, a perception-based approach to create intelligent systems is considered. The evaluation systems can be employed eg. in order to assess student exams, as well as to other applications. Evaluation marks used in these systems are given as perceptions expressed by words. The words play the role of labels of perceptions, and are represented by fuzzy sets. This means that the idea of perception-based systems, introduced by Zadeh, is applied. Various algorithms of overall assessment are suggested in this paper. Overall evaluation is produced as an aggregation of component evaluation marks. Systems of this kind can be obtained using fuzzy neurons, so fuzzy neural networks are also mentioned as a method of perception-based reasoning. The usefulness in artificial intelligence of both fuzzy sets and neural networks, and especially a combination of these, is shown.
The paper presents a new method of crisp and fuzzy interval comparison (ordering). The method is based on the probabilistic approach and the representation of fuzzy numbers as ordered a-level sets. It allows all the cases of interval location and overlapping to be taken into account, including the ordering of intervals and real numbers. Additionally, the method implicitly allows the widths of intervals to be used in ordering procedures. It should be noted that the probabilistic approach was employed only to infer the set of formulas needed to estimate quantitatively the degree to which one interval is less than or equal to another interval. However, the measure of this value may be treated as probability. Some simple examples are also presented to illustrate the technique's practical efficiency.
The aim of this paper is to present a constructive methodology and algorithms for operations with fuzzy sets of type 2. The need to elaborate this methodology came from practical problems of Decision Making. To realize the methodology, some simplifications of the problem have been introduced. Particularly, only the trapezium form of membership functions was used. To highlight the difference between the proposed approach and the classical theory of fuzzy sets of type 2, the terms "hyperfuzzy set" and "hyperfuzzy function" have been introduced. Some base situations of hyperfuzzy functions with real arguments and real functions of hyperfuzzy arguments are performed.
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