Objective Functions in Fuzzy Cognitive Maps: the Case of Time Series Modeling

Abstract

Modeling time series is a well investigated area for a long period. During last years fuzzy cognitive maps have been successfully employed for this purpose. Easy interpretation of relations and dependencies in an information space raised by time series is an important aspect of latest researches, which brought time series processing from an elementary, numerical, level to a space of concepts created by a given time series. In this paper we investigate time series modeling with fuzzy cognitive maps at a concept level. Discussion is focused on constructions of fuzzy cognitive maps for a given time series which is transformed to a level of concepts. Attention is payed on objective functions, which are employed to training and quality evaluating of fuzzy cognitive maps. Several types of objective functions are proposed, discussed and tested. Objective functions studied in this paper are based on mean square error and maximal square error.