Quotient FCMs - A Decomposition Theory for Fuzzy Cognitive Maps

Abstract

In this paper, we introduce a decomposition theory for fuzzy cognitive maps (FCMs). First, we partition the set of vertices of an FCM into blocks according to an equivalence relation, and by regarding these blocks as vertices we construct a quotient FCM. Second, each block induces a natural sectional FCM of the original FCM, which inherits the topological structure as well as the inference from the original FCM. In this way, we decompose the original FCM into a quotient FCM and some sectional FCMs. As a result, the analysis of the original FCM is reduced to the analysis of the quotient and sectional FCMs, which are often much smaller in size and complexity. Such a reduction is important in a..