Rule-Based FCM: A Relational Mapping Model

Abstract

Abstract. Rule-Based Fuzzy Cognitive Map (RBFCM) is proposed as an evolution of Fuzzy Causal Maps (FCM) to allow more complete and complex representation of cognition so that relations other than monotonic causality are made possible. This paper shows how RBFCM can be viewed in the context of relation algebra, and proposes a novel model for representing and reasoning causal knowledge relation. The mapping model and rules are introduced to infer three kinds of causal relations that FCM can't support. Capability analysis shows that our model is much better than FCM in emulating real world. MotivationFuzzy Conceptual Maps have become an important means for drawing a graphical representation of a system , and connecting the state concepts (variables) in the system by links that symbolize cause and effect relations, and have been used in simulating process, forecasting or decision support, etc. Though FCMs have many desirable properties, they have some major limitations [4]. For example, .FCMs can't provide the inference of sequential relations or time-delay causal relations because all the interaction of FCMs' concepts is synchronous, and can't provide the inference of conditional probabilistic causal relations. Their inference results in some intelligent systems are usually distorted.Some authors have tried to extend FCMs to include time, and they developed systems such as "Extended FCMs" (Hagiwara [2]) and rule-based FCMs (Carvalho [3]).But they can't support conditional probabilistic causal relations. Neural Cognitive Map (NCM [5]) are presented to solve complex causal relations, but NCM needs much training data that are difficult to be obtained in some intelligent systems, and time-delay causal relations as well as sequential relations are difficult to be found by neural networks.Our model proposes a novel model for representing and reasoning causal knowledge relation. The mapping model and rules are introduced to infer three kinds of causal relations including sequential relation, time-delay causal relations, and conditional probabilistic causal relations that FCM can't support. The Mathematical ModelIn our model, causal knowledge is in the form of concepts, relations, directional connections and weights. Fig.1 describes the cause-effect relation mapping about terror