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A New Fuzzy Cognitive Map Structure Based on the Weighted Power Mean

We introduce a new structure for fuzzy cognitive maps (FCM) where the traditional fan-in structure involving an inner product followed by a squashing function to describe the causal influences of antecedent nodes to a particular consequent node is replaced with a weighted mean type operator. In this paper, we employ the weighted power mean (WPM). Through appropriate selection of the weights and exponents in the WPM operators, we can both account for the relative importance of different antecedent nodes in the dynamics of a particular node, as well as take a perspective ranging continuously from the most pessimistic (minimum) to the most optimistic (maximum) on the normalized aggregation of antecedents for each node. We consider this FCM structure to be more intuitive than the traditional one, as the nonlinearity involved in the WPM is more scrutable with regard to the aggregation of its inputs. We provide examples of this new FCM structure to illustrate its behavior, including its convergence, and compare it with a traditional FCM architecture on a scenario presented in previous works.