Combining fuzzy cognitive maps and discrete random variables

Abstract

In this paper we propose an extension to the Fuzzy Cognitive Maps (FCMs) that aims at aggregating a number of reasoning tasks into a one parallel run. The described approach consists in replacing real-valued activation levels of concepts (and further influence weights) by random variables. Such extension, followed by the implemented software tool, allows for determining ranges reached by concept activation levels, sensitivity analysis as well as statistical analysis of multiple reasoning results. We replace multiplication and addition operators appearing in the FCM state equation by appropriate convolutions applicable for discrete random variables. To make the model computationally feasible, it is further augmented with aggregation operations for discrete random variables. We discuss four implemented aggregators, as well as we report results of preliminary tests.