This paper introduces an original mathematical description for describing agents' decision-making process in the case of problems affected by both individual and collective behaviors in systems characterized by nonlinear, path dependent, and self-organizing interactions. An application to artificial financial markets is proposed by designing a multi-agent system based on the proposed formalization. In this application, agents' decision-making process is based on fuzzy logic rules and the price dynamics is purely deterministic according to the basic matching rules of a central order book. Finally, while putting most parameters under evolutionary control, the computational agent-based system is able to replicate several stylized facts of financial time series (distributions of stock returns showing a heavy tail with positive excess kurtosis, absence of autocorrelations in stock returns, and volatility clustering phenomenon).

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