Fuzzy cognitive maps in multi-agent environments

Abstract

In the last years we have seen a large development about fuzzy cognitive maps (FCMs). The theoretical base of FCM is connected with the neural networks theory (differential hebbian learning) and fuzzy sets and systems theory. There are applications of the FCM in the following fields of research: adaptive network cognitive processor, analyze and extend graph theoretical behavior, plant control, information requirement analysis, analysis electrical circuit, model gastric-appetite behavior and popular political development. Our interest in this work is to show the importance of combination of FCM with the multi-agent modal logic of knowledge and belief to model structures of complex design in multiagent environments. We make an application to plant control. The model that we introduce can be used to model popular political development, social systems, and military strategy, and others. In Goto and Yamaguchi [1991] is shown as FCMs can model plant control. In our point of view an ideal model of plant control must not involve the opinion of an expert about a plant control, but the opinion of a group of experts. If each expert of a group makes a FCM on a plant control, it is interesting to investigate what signifies the common knowledge of group about this plant control. Moreover is interesting to know what each agent of group knows about the FCM made by others agents. This can be much important in the design of plant control and to build political model, social systems, and military strategy. With reference to multi-agent modal logic of knowledge and belief, we make a generalization of work of Friedman and Halpern [1994a], Friedman and Halpern [1994b], by using of fuzzy measures. The multi-agent modal logic of knowledge and belief with fuzzy measures allows interpret fuzzy statements with linguistic fuzzy quantifiers such as developed in FCM.