Przemyslaw Juszczuk

Predictive Capabilities of Adaptive and Evolutionary Fuzzy Cognitive Maps - A Comparative Study

Fuzzy cognitive maps (FCMs) represent the decision process in the form of a graph that is usually easy to interpret and, therefore, can be applied as a convenient decision-support tool. In the first part of this chapter, we explain the motivations for the research on FCMs and provide a review of the research in this area. Then, as stated in the title of the chapter, we concentrate our attention on the comparative study of adaptive and evolutionary FCMs. The terms adaptive and evolutionary refer to the type of learning applied to obtain a particular FCM. Despite many existing works on FCMs, most of them concentrate on one type of learning method. The purpose of our research is to learn FCMs using diverse methods on the basis of the same dataset and apply them to the same prediction problem. We assume the effectiveness of prediction to be one of the quality measures used to evaluate the trained FCMs. The contribution of this chapter is the theoretical and experimental comparison of adaptive and evolutionary FCMs. The final goal of our research is to determine which of the analyzed learning methods should be recommended for use with respect to the considered prediction problem. To illustrate the predictive capabilities of FCMs, we present an example of their application to the prediction of weather conditions.

Association ACDT as a tool for discovering the financial data rules

We present a novel approach based on the original idea of the Ant Colony Decision Tree (ACDT) algorithm used in the problem of building the decision trees. One of the crucial limitations of the canonical ACDT algorithm was its link to strict decision rules. In this paper we transform the algorithm in such way, that it is capable to manage complex association rules. Research is conducted on the various sets of financial data closely related with the swiss frank currency. Evaluation of results was possible on the basis of accuracy measure as well as the proposed fuzzy accuracy. These preliminary studies show, that the proposed algorithm is capable to maintain its effectiveness even in the problems with large number of attribute values.

Differential evolution as a new method of computing nash equilibria

The Nash equilibrium is one of the central concepts in game theory. Recently it was shown, that problems of finding Nash equilibrium and an approximate Nash equilibrium are PPAD-complete. In this article we present the Differential Evolution algorithm adapted to that problem, and we compare it with two well-known algorithms: the Simplicial Subdivision and the Lemke-Howson. The problem of finding the Nash equilibrium for two players games may be classified as a continuous problem, where two probability distributions over the set of pure strategies of both players should be found. Each deviation from the global optimum is interpreted as the Nash approximation and called the e-Nash equilibrium. We show that the Differential Evolution approach can be determined as a method, which in successive iterations is capable of obtaining e value close to the global optimum. We show, that the Differential Evolution may be succesfully used to obtain satisfactory results and it may be easily expanded into n-person games. Moreover, we present results for the problem of computing Nash equilibrium, when some arbitrary set strategies have a non-zero probability of being chosen.

A new evolutionary approach for computing Nash equilibria in bimatrix games with known support

In this paper, we present the application of the Differential Evolution (DE) algorithm to the problem of finding approximate Nash equilibria in matrix, non-zero sum games for two players with finite number of strategies. Nash equilibrium is one of the main concepts in game theory. It may be classified as continuous problem, where two probability distributions over the set of strategies of both players should be found. Every deviation from the global optimum is interpreted as Nash approximation and called ε-Nash equilibrium. The main advantage of the proposed algorithm is self-adaptive mutation operator, which direct the search process. The approach used in this article is based on the probability of chosing single pure strategy. In optimal mixed strategy, every strategy has some probability of being chosen. Our goal is to determine this probability and maximize payoff for a single player.

Approximate nash equilibria in bimatrix games

Nash equilibrium is one of the main concepts in the game theory. Recently it was shown, that problem of finding Nash equilibrium and an approximate Nash equilibrium is PPAD-complete. In this article we adapt Differential Evolution algorithm (DE) to the above problem. It may be classified as continuous problem, where two probability distributions over the set of pure strategies of both players should be found. Every deviation from the global optimum is interpreted as Nash approximation and called e-Nash equilibrium. We show, that the Differential Evolution approach can be determined as iterative method, which in successive iterations is capable to obtain e value close to the global optimum. The contribution of this paper is the experimental analysis of the proposed approach and indication of its strong features. We try to demonstrate, that the proposed method is very good alternative for the existing mathematical analysis of the mentioned Nash equilibrium problem.

Finding Optimal Strategies in the Coordination Games

In this article we present a new algorithm which is capable to find optimal strategies in the coordination games. The coordination game refers to a large class of environments where there are multiple equilibria. We propose a approach based on the Differential Evolution where the fitness function is used to calculate the maximum deviation from the optimal strategy. The Differential Evolution (DE) is a simple and powerful optimization method, which is mainly applied to continuous problems. Thanks to the special operator of the adaptive mutation, it is possible to direct the searching process within the solution space. The approach used in this article is based on the probability of chosing the single pure strategy.

Investigating Patterns in the Financial Data with Enhanced Symbolic Description

In this article, we propose a novel approach to transforming financial time-series values into the symbolic representation based on value changes. Such approach seems to have a few advantages over existing approaches, while one of the most obvious is noise reduction in the data and possibility to find patterns which are universal for investigating different currency pairs. To achieve the goal we introduce the preprocessing method allowing the initial data transformation. We also define a text-based similarity measure which can be used as an alternative for methods allowing to find exact patterns in the historical data.

Ant Colony Optimization Algorithms in the Problem of Predicting the Efficiency of the Bank Telemarketing Campaign.

In this article, we analyze the effectiveness of the telemarketing campaign developed by the Portuguese bank. The main goal of this analysis was to estimate, is there existing ant colony algorithms are capable of building classifiers that lead to increasing the effectiveness of the telemarketing campaign. An additional question was related to the problem of adjusting the whole campaign to the actual needs of clients. Presented data include 17 attributes, including information about the efficiency of carried out conversations related to the bank deposit offer. The analysis presented in this article was developed on the basis of algorithms used for the decision trees construction such as CART and C4.5. As a result, a prediction allowing to estimate the result of the telemarketing conversation with a client was made. Conducted experiments allowed for the comparison of different classifiers. The comparison was made on the basis of different measures of classification efficiency. It is especially important in the case of the real-world data, where cardinality of decision classes is uneven. Conducted experiments allowed for the comparison of different classifiers. Initial evaluation confirms, that such an approach could be efficiently used for the dynamic data sets, like streams.

The procedure programming paradigm as a method of constructing automatic transaction systems based on moving averages

W artykule zostanie zaproponowane nowe podejście dotyczące generowania sygnalow transakcyjnych bazujących na klasycznym mechanizmie przeciecia średniej kroczącej z wykresem cenowym. Sam mechanizm doboru okresu wskaźnika uzalezniony bedzie od skuteczności wcześniejszych sygnalow. W przypadku trafności sygnalow liczba odczytow uwzglednianych przy wyznaczaniu wartości średniej kroczącej bedzie zmniejszona, co spowoduje zwiekszenie liczby otwartych zlecen. Z kolei duza liczba zlecen stratnych doprowadzi do zwiekszenia okresu średniej kroczącej, co wplynie na ograniczenie liczby sygnalow. Podejście to zostanie porownane z klasycznymi rozwiązaniami bazującymi na średnich kroczących. Mechanizm budowy systemu transakcyjnego zostanie przedstawiony jako zagadnienie związane z proceduralnym paradygmatem programowania, gdzie poszczegolne fragmenty kodu przygotowane zostaną w formie blokow – procedur. Takie podejście umozliwia elastyczne modyfikowanie istniejącego rozwiązania oraz rozszerzanie jego funkcjonalności poprzez dodawanie nowych elementow.

Multi-start Differential Evolution Approach in the Process of Finding Equilibrium Points in the Covariant Games

In this article we present the application of the Differential Evolution algorithm to the problem of finding optimal strategies in the covariant games. Covariant game is the class of games in the normal form, in which there is at least one Nash equilibrium, and some payoffs of players may be in some way correlated. We used the concept, that there is possibility, that the approximate solution of the game exists, when players use only the small subset of strategies. The Differential Evolution algorithm is presented as the multi-start method, in which sampling of the solution is used. If preliminary estimation of the solution is not satisfactory, the new subset of strategies for all players is selected and the new population of individuals is created.