Rule Based Fuzzy Cognitive Maps: Fuzzy Causal Relations

TLDR

The main challenge in implementing RBFCM is that traditional fuzzy operations cannot capture causality as defined in causal maps. This paper introduces RBFCM and a method to implement fuzzy causal relations, extending FCM to represent non‑monotonic causal links. RBFCM are built on traditional fuzzy systems with feedback, featuring a flexible structure for adding and removing concepts and links, and a new Fuzzy Carry Accumulation operation that models the accumulative property of causal relations.

Abstract

Rule Based Fuzzy Cognitive Maps (RBFCM) are proposed as an evolution of Fuzzy Causal Maps (FCM) that allow a more complete representation of cognition, since relations other than monotonic causality are made possible. Their structure is based on traditional fuzzy systems with feedback. The main problem to solve while trying to implement a RBFCM is the causal relation itself, since traditional fuzzy operations can not implement causality as it is usually defined in causal maps. This paper introduces Rule Based Fuzzy Cognitive Maps and presents a method to implement Fuzzy Causal Relations. This method allows a great flexibility in the addition and removal of concepts and links among concepts, and introduces a new Fuzzy Operation that simulates the “accumulative” property of causal relations – the Fuzzy Carry Accumulation (FCA).