Genetic Algorithm Approach for the Identification Problem of the Discrete Possibilistic Dynamic System MIKHEIL KAPANADZE and GIA SIRBILADZE Department of Computer Sciences Iv.Javakhishvili Tbilisi State University 13, University st., Tbilisi 0186 GEORGIA mikheil@mikheil.com, gia.sirbiladze@tsu.ge Abstract: - This work deals with the problem of identification of Discrete Possibilistic Dynamic System (DPDS), using the technologies of Genetic Algorithmms (GA). Applying the results from [5-9,11-13,15,16,18-20], the fuzzy recurrent process with possibilistic uncertainty, the source of which is expert knowledge reflections on the states of evolutionary complex extremal system, is constructed. The dynamics of DPDS is described and the constructed model is converted to the finite model. Based on the fuzzy-integral model a genetic algorithm approach is developed for identifying the transition operation of the DPDS finite model. The DPDS transition operator is restored by means of expert data with possibilistic uncertainty. Obtained results are illustrated by the example for prediction and stopping problems for evaluations of the increasing business risks. Key-Words: - DPDS; identification of DPDS; genetic algorithm, solution regularization principle 1 Introduction In recent years, both the dynamics of fuzzy system and its modeling problem have attracted significant attention. Dynamics is an obvious problem in optimization. Applications of the dynamics of fuzzy systems and of the modeling of dynamic systems by fuzzy systems range from physics to biology, economics, pattern recognition and time series prediction. Evidence exists that fuzzy models can explain cooperative processes, such as in biology, chemistry, material sciences, or in economics. Relationships between dynamics of fuzzy systems and the performance of decision support systems were found, and chaotic processes in various classes of fuzzy systems were proved as a powerful tool in analyzing complex, weakly structurable systems, as abnormal and extremal processes. In alternative classical approaches of modeling of the complex systems the main accent is placed on the assumption of fuzziness. As the complexity of systems increases, our ability to define their behaviour exactly drops to a certain level, below which such characteristics of information as exactness and uncertainty become mutually excluding. In such situations an exact quantitative analysis of real complex systems is apt not to be quite plausible. Hence the system approach to constructing models of complex systems with fuzzy uncertainty guarantees the creation of computer-aided systems forming the instrumental basis of the intelligent technology solutions of expert-analytic problems. It is obvious that the source of fuzzy-statistical samples is the population of fuzzy characteristics of expert knowledge. For the decision-making process to be more effective in the framework of computer systems that support this process, we must solve analytical problems of optimization, state evaluation, model identification, complex dynamic system control, optimal control, filtering, and so on. In this paper we consider some problems of the identification of a discrete model of Fuzzy Dynamic System (DPDS) and application Genetic Algorithm Technologies in this domain. The basic approaches to the identification of fuzzy extremal process models that have been developed to this day [2-4,10,11,13,15,16,20-24 and others] can be divided into two groups – analytical and algorithmic – both of which are oriented to a fuzzy process model written in terms of fuzzy compositional or integro- differential equations or their modifications. Various analytical methods and algorithms were used in order to identify such models, i.e., the corresponding relation of spaces of inputs and outputs of fuzzy dynamic systems. These methods mainly imply the construction of some set-theoretic operation that is inverse to the composition operation and requires a subsequent smoothing of the results [3,4,24 and others]. In some works [,22,23 and others], fuzzy models of regression type were identified by means of analytical regularization methods that allowed one to obtain numerical estimators of model coefficients. In this paper, a new approach is proposed to Recent Researches in Applied Computer and Applied Computational Science ISBN: 978-960-474-281-3 122