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The Russian–Ukrainian conflict is considered as a dynamic system, whose variables are factors affecting the losses of the Russian army and the threat of the use of nuclear weapons. A fuzzy cognitive map (FCM) is used for modeling, that is, a directed graph whose vertices are model variables, and the weights of arcs are the degrees of positive and negative influences of variables on each other. The following factors influencing the losses of the Russian army and the threat of a nuclear strike were selected: resistance of the Ukrainian army, support of Ukraine with weapons, economic sanctions against Russia, opposition to the Russian government and its self-preservation instinct. The degrees of the influence of factors on each other and on the possibility of using nuclear weapons are evaluated by experts using fuzzy terms, which correspond to numeric values. To adjust the FCM, a genetic algorithm is used to select the degrees of influence of factors that minimize the discrepancy between the simulation results and expert estimations. The obtained FCM is used for scenario modeling of the conflict according to the "what if" scheme and ranking of factors according to their degree of influence on the level of nuclear threat. [ABSTRACT FROM AUTHOR]

This article offers a method for analyzing the reliability of a man–machine system (MMS) and ranking of influencing factors based on a fuzzy cognitive map (FCM). The ranking of influencing factors is analogous to the ranking of system elements the probabilistic theory of reliability. To approximate the dependence of "influencing factors—reliability," the relationship of variable increments is used, which ensures the sensitivity of the reliability level to variations in the levels of influencing factors. The novelty of the method lies in the fact that the expert values of the weights of the FCM graph edges (arcs) are adjusted based on the results of observations using a genetic algorithm. The algorithm's chromosomes are generated from the intervals of acceptable values of edge weights, and the selection criterion is the sum of squares of deviations of the reliability simulation results from observations. The method is illustrated by the example of a multifactor analysis of the reliability of the "driver–car–road" system. It is shown that the FCM adjustment reduces the discrepancy between the reliability forecast and observations almost in half. Possible applications of the method can be complex systems with vaguely defined structures whose reliability depends very much on interrelated factors measured expertly. [ABSTRACT FROM AUTHOR]

This paper presents a method of time series forecasting based on the integration of fuzzy logic and chaos theory. The proposed method has two stages. On the first stage, we consider the time series as a dynamic system and using the methods of mutual information and false nearest neighbors, as a part of applied chaos theory, we reconstruct the phase portrait corresponding to the original time series. On the second stage, we are learning the neuro fuzzy network as a model of time series forecasting using the vectors points of reconstructed phase portrait. We consider all the formalisms necessary for understanding the method and present the results of two computer experiments proving the ability of fuzzy inference accuracy increasing using the selection of optimal parameters of time delay and phase portrait dimension. [ABSTRACT FROM AUTHOR]

Fuzzy sets membership functions integrated with logistic map as the chaos generator were used to create reliability bifurcations diagrams of the system with redundancy of the components. This paper shows that increasing in the number of redundant components results in a postponement of the moment of the first bifurcation which is considered as most contributing to the loss of the reliability. The increasing of redundancy also provides the shrinkage of the oscillation orbit of the level of the system's membership to reliable state. The paper includes the problem statement of redundancy optimization under conditions of chaotic behavior of influencing parameters and genetic algorithm of this problem solving. The paper shows the possibility of chaos-tolerant systems design with the required level of reliability. [ABSTRACT FROM AUTHOR]

In this article, we propose the method of the multicriteria alternative selection under uncertainty. The basis of the method is the principle of the Bellman–Zadeh fuzzy measures intersection and nine-point linguistic rating scale of Saaty. The novelty of the method presented here consists of the fact that it does not require labor-intensive procedures, requiring arraying and array processing of paired comparisons matrix. Instead, special correlations are used, which are based on the comparison with the worst alternative and the least important criterion. As an example for the utilization of our method, we use the problem for choosing cars. © 2010 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

This paper deals with the restoration and the identification of the causes (diagnoses) through the observed effects (symptoms) on the basis of fuzzy relations and Zadeh's compositional rule of inference. We propose an approach for building fuzzy systems of diagnosis, which enables solving fuzzy relational equations together with design and tuning of fuzzy relations on the basis of expert and experimental information. The essence of tuning consists of the selection such membership functions for fuzzy causes and effects, and also fuzzy relations, which minimize the difference between model and experimental results of diagnosis. The genetic algorithm is used for solving the optimization problem. The proposed approach is illustrated by the computer experiment and the real example of diagnosis. [ABSTRACT FROM AUTHOR]