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Abstract: In this paper, we derive a new application of fuzzy systems designed for a generalized autoregression conditional heteroscedasticity (GARCH) model. In general, stock market performance is time-varying and nonlinear, and exhibits properties of clustering. The latter means simply that certain large changes tend to follow other large changes, and in general small changes tend to follow other small changes. This paper shows results from using the method of functional fuzzy systems to analyze the clustering in the case of a GARCH model. The optimal parameters of the fuzzy membership functions and GARCH model are extracted using a genetic algorithm (GA). The GA method aims to achieve a global optimal solution with a fast convergence rate for this fuzzy GARCH model estimation problem. From the simulation results, we have determined that the performance is significantly improved if the leverage effect of clustering is considered in the GARCH model. The simulations use stock market data from the Taiwan weighted index (Taiwan) and the NASDAQ composite index (NASDAQ) to illustrate the performance of the proposed method. [Copyright &y& Elsevier]

The initial population of an evolutionary algorithm is an important factor which affects the convergence rate and ultimately its ability to find high quality solutions or satisfactory solutions for that matter. If composed of good individuals it may bias the search towards promising regions of the search space right from the beginning. Although, if no knowledge about the problem at hand is available, the initial population is most often generated completely random, thus no such behavior can be expected. This paper proposes a method for initializing the population that attempts to identify i.e., to get close to promising parts of the search space and to generate (relatively) good solutions in their proximity. The method is based on clustering and a simple Cauchy mutation. The results obtained on a broad set of standard benchmark functions suggest that the proposed method succeeds in the aforementioned which is most noticeable as an increase in convergence rate compared to the usual initialization approach and a method from the literature. Also, insight into the usefulness of advanced initialization methods in higher-dimensional search spaces is provided, at least to some degree, by the results obtained on higher-dimensional problem instances—the proposed method is beneficial in such spaces as well. Moreover, results on several very high-dimensional problem instances suggest that the proposed method is able to provide a good starting position for the search. [ABSTRACT FROM AUTHOR]

Abstract: Consistency and consensus measures are two important procedures employed in group decision making with multiplicative preference relations (MPRs). In this paper, we first establish the concept of individual consistency deviation degree between the original MPR and its optimal estimation. Then we develop a group consensus deviation degree optimization model (GCO Model) by minimizing the weighted arithmetic average of individual consistency deviation degrees. Our established theorems enlist the conditions for the existence of the optimal solution, the satisfactory solution, and non-inferior solution to the GCO Model. These results also provide an existence condition of redundant MPR in group decision making. Additionally, we show that the optimal value function of the GCO Model converges to 0, which implies that the consensus degree of DMs converges as the number of the decision makers increases indefinitely. [Copyright &y& Elsevier]