Yuriy P. Zaychenko

Application of Fuzzy Logic Systems and Fuzzy Neural Networks in Forecasting Problems in Macroeconomy and Finance

This chapter is devoted to numerous applications of fuzzy neural networks in economy and financial sphere. In the Sect. 4.2 the problem of forecasting macroeconomic indicators of Ukraine with application of FNN is considered. The goal of this investigation was to estimate the efficiency of different fuzzy inference algorithms. Fuzzy algorithms of Mamdani, Tsukamoto and Sugeno were compared in forecasting Consumer Price Index (CPI) and GDP of Ukraine. As result of this investigation the best forecasting algorithm is detected.

Fuzzy Neural Networks in Classification Problems

The purpose of this chapter is consideration and analysis of fuzzy neural networks in classification problems, which have a wide use in industry, economy, sociology, medicine etc. In the Sect. 5.2 a basic fuzzy neural network for classification—NEFClass is considered, the learning algorithms of rule base and MF of fuzzy sets are presented and investigated. Advantages and lacks of the system NEFClass are analyzed and its modification FNN NEFClass M, free of lacks of the system NEFClass is described in the Sect. 5.3. The results of numerous comparative experimental researches of the basic and modified system NEFClass are described in Sect. 5.4. The important in a practical sense task of recognition of objects on electro-optical images (EOI) is considered and its solution with application of FNN NEFClass is presented in the Sect. 5.5. The comparative analysis of different learning algorithms of FNN NEFClass at the task of recognition of EOI objects in the presence of noise is carried out. Problem of hand-written mathematical expressions recognition is considered in the Sect. 5.6 and its solution with application of FNN NEFClass is presented.

Inductive Modeling Method (GMDH) in Problems of Intellectual Data Analysis and Forecasting

This chapter is devoted to the investigation and application of fuzzy inductive modeling method known as Group Method of Data Handling (GMDH) in problems of intellectual data analysis (Data Mining), in particularly its application in the forecasting problem in macroeconomy and financial sphere. The problem consists in forecasting models construction and finding unknown functional dependence between given set of macroeconomic indices and forecasted variable using experimental data. The advantage of inductive modeling method GMDH is a possibility of constructing adequate model directly in the process of algorithm run. The specificity of fuzzy GMDH is getting the interval estimates for forecasting variables. In this chapter the review of main results concerning GMDH and fuzzy GMDH is presented, analysis of application of various membership functions (MF) and perspectives of fuzzy GMDH application for forecasting in macroeconomy and financial sphere are estimated. The Sect. 6.2 contains the problem formulation. In the Sect. 6.3 main principles and ideas of GMDH are considered. In the Sect. 6.4 the generalization of GMDH in case of uncertainty—new method fuzzy GMDH suggested by authors is described which enables to construct fuzzy models almost automatically. The Sect. 6.5 contains the algorithm of fuzzy GMDH. In the Sect. 6.6 the fuzzy GMDH with Gaussian and bell-wise membership functions MF are considered and their similarity with triangular MF is shown. In the Sect. 6.7. fuzzy GMDH with different partial descriptions in particular orthogonal polynomials of Chebyshev and Fourier are considered. In the Sect. 6.8 the problem of adaptation of fuzzy models obtained by GMDH is considered and the corresponding adaptation algorithms are described. The Sect. 6.9 contains the results of numerous experiments of GMDH and fuzzy GMDH application for forecasting share prices and Dow Jones index at New York stock exchange (NYSE). The extension and generalization of fuzzy GMDH in case of fuzzy inputs is considered and its properties are analyzed in the Sect. 6.11.

Problem of Fuzzy Portfolio Optimization Under Uncertainty and Its Solution with Application of Computational Intelligence Methods

The problem of constructing an optimal portfolio of securities under uncertainty is considered in this chapter. The main objective of portfolio investment is to improve the investment environment, giving securities such investment characteristics that are only possible in their combination. The global market crisis of recent years has shown that the existing theory of investment portfolio optimization and forecasting stock indices exhausted and revision of the basic theory of portfolio management is needed. Therefore in this work the novel theory of investment portfolio optimization under uncertainty is presented based on fuzzy set theory and efficient forecasting methods.

Genetic Algorithms and Evolutionary Programing

The chapter is devoted to widely used genetic algorithms (GA) and deeply connected with them evolutionary programing. In Sect. 8.2 genetic algorithms are considered and their properties analyzed. The different variants of main GA operators: cross-over are considered, various presentations of individuals- binary and floating– point are considered and different cross-over operators for them are described. In the Sect. 8.3 various implementations of mutation operator are presented and their properties are discussed. Parameters of GA are considered, deterministic, adaptive and self-adaptive parameters modifications are described and discussed. In the Sect. 8.5 different selection strategies are considered and analyzed. In the Sect. 8.6 the application of GA for solution of practical problem of computer network structural synthesis is described. The Sect. 8.7 is devoted to detail description and analysis of evolutionary programing (EP). Main operators of EP: mutations and selection are considered and their properties analyzed. Different variants of algorithms EP are described. In the Sect. 8.8 differential evolution is considered, its properties discussed and the algorithm of DE is presented.

The Cluster Analysis in Intellectual Systems

Term cluster analysis (introduced by Tryon, 1939 for the first time) actually includes a set of various algorithms of classification without teacher [1]. The general question asked by researchers in many areas is how to organize observed data in evident structures, i.e. to develop taxonomy. For example, biologists set the purpose to divide animals into different types that to describe distinctions between them. According to the modern system accepted in biology, the person belongs to primacies, mammals, vertebrate and an animal. Notice that in this classification, the higher is aggregation level, the less is the similarity between members in the corresponding class. The person has more similarity to other primacies (i.e. with monkeys), than with the “remote” members of family of mammals (for example, dogs), etc.The clustering is applied in the most various areas. For example, in the field of medicine the clustering of diseases, treatments of diseases or symptoms of diseases leads to widely used taksonomy. In the field of psychiatry the correct diagnostics of clusters of symptoms, such as paranoia, schizophrenia, etc., is decisive for successful therapy. In archeology by means of the cluster analysis researchers try to make taxonomy of stone tools, funeral objects, etc. Broad applications of the cluster analysis in market researches are well known. Generally, every time when it is necessary to classify “mountains” of information to groups, suitable for further processing, the cluster analysis is very useful and effective. In recent years the cluster analysis is widely used in the intellectual analysis of data (Data Mining), as one of the principal methods [1]. The purpose of this chapter is the consideration of modern methods of the cluster analysis, crisp methods(a method of C-means, Ward’s method, the next neighbor, the most distant neighbor), and fuzzy methods, robust probabilistic and possibilistic clustering methods. In the Sect. 7.2 problem of cluster analysis is formulated, main criteria and metrics are considered and discussed. In the Sect. 7.3 classification of cluster analysis methods is presented, several crisp methods are considered, in particular hard C-means method and Ward’s method. In the Sect. 7.4 fuzzy C-means method is described. In the Sect. 7.5 the methods of initial location of cluster centers are considered: peak and differential grouping and their properties analyzed.

Neural Networks with Feedback and Self-organization

In this chapter another classes of neural networks are considered as compared with feed-forward NN—NN with back feed and with self-organization. In Sect. 2.1 recurrent neural network of Hopfield is considered, its structure and properties are described. The method of calculation of Hopfield network weights is presented and its properties considered and analyzed. The results of experimental investigations for application Hopfield network for letters recognition under high level of noise are described and discussed. In the Sect. 2.2 Hamming neural network is presented, its structure and properties are considered, algorithm of weights adjusting is described. The experimental investigations of Hopfield and Hamming networks in the problem of characters recognition under different level of noise are presented. In the Sect. 2.3 so-called self-organizing networks are considered. At the beginning Hebb learning law for neural networks is described. The essence of competitive learning is considered. NN with self-organization by Kohonen are described. The basic competitive algorithm of Kohonen is considered/ its properties are analyzed. Modifications of basic Kohonen algorithm are described and analyzed. The modified competitive algorithm with neighborhood function is described. In the Sect. 2.4 different applications of Kohonen neural networks are considered: algorithm of neural gas, self-organizing feature maps (SOMs), algorithms of their construction and applications.

Fuzzy Inference Systems and Fuzzy Neural Networks

In recent years, the attention of many researchers in the field of artificial intelligence systems attracts the problem of decision making under uncertainty, the incompleteness of the initial data and quality criteria. There is a new trend in the theory of complex decision-making, which is rapidly developing—making decisions under uncertainty. A promising approach for solving many decision-making problems under uncertainty and incomplete information is based on fuzzy sets and systems theory created by Zadeh [1]. The introduction by L. Zadeh of the concept of linguistic variables described by fuzzy sets [2] gave rise to a new class of systems—fuzzy logic systems (FLS), which allows to formalize fuzzy expert knowledge. The use of fuzzy inference systems (FIS) and built on the their basis fuzzy neural networks (FNN) has allowed to solve many problems of decision-making under uncertainty, incompleteness and qualitative information—forecasting, classification, cluster analysis, pattern recognition. This chapter is devoted to the detailed consideration of FL systems. It discusses the basic algorithms of fuzzy inference Mamdani, Tsukamoto, Larsen and Sugeno (Sect. 3.2). In Sect. 3.3 the methods of defuzzification are described. In the Sect. 3.4 the important Fuzzy approximation theorem (FAT-theorem) is considered which is theoretical ground for wide applications of FNN. Further fuzzy controller (FC) Mamdani and Tsukamoto and classical learning algorithm on the basis of back-propagation are detailly considered. A new learning algorithm of FC Mamdani and Tsukamoto for Gaussian membership functions (MF) of gradient type is described (Sect. 3.6). Next FNN ANFIS is considered, its architecture and gradient learning algorithm are presented (Sect. 3.7). Then FNN TSK, the development of FNN ANFIS, is described and its hybrid training algorithm is reviewed (Sect. 3.8). In the Sect. 3.9 adaptive wavelet-neuro-fuzzy networks are considered and different learning algorithms in batch and on-line mode are presented. Cascade neo-fuzzy neural networks (CNFNN) are considered, training algorithms are presented and GMDH method for its structure synthesis is described and analyzed (Sect. 3.10).