System Diagnosis Using Fuzzy Cognitive Maps

Abstract

Fuzzy cognitive maps are an ideal tool for modeling multi-attribute systems, especially when they must incorporate such “soft” parameters as human factors, operator characteristics or societal concepts. Part of the utility of using a fuzzy cognitive map as the primary model of the system under consideration is that it can be constructed by merging submaps, with each submap prepared by a subject matter expert in the topic relevant to it. Piecing these submaps together to generate a complete map of the system often results in unexpected inferences because feedback can become present. Through feedback certain effects may get magnified or mitigated through causal chains that would not exist until the submaps are merged. A fuzzy cognitive map is a signed digraph that captures the essential cause/effect relationships in a system. (Zhou et al., 2006) The dynamics of the system are captured in the map by its nodal values and the web of directed edges in it indicating a cause/effect relationship. Nodes in the map represent attributes in a system that a subject matter expert believes important in understanding its changes. These nodes must represent changeable quantities, i.e. a characteristic of the attribute that can increase or decrease because the map is primarily a tool for understanding the changes that occur when inputs are perturbed. Nodes are normally assigned numeric values of +1, indicating an increase in the underlying concept, -1 indicating a decrease and 0, indicating no change. Note that the nodal values are crisp in the sense that there is no fuzziness associated with the change in value or its interpretation of the concept represented by it. (Kosko, 1992) Fuzziness enters the map through the value of the edge strengths. Nodes in the map are connected by a directed edge to indicate that the author of the map believes a causal relationship exists between the two nodes. The edge starts on the causal node and ends on the effect node, with an arrow used to identify the relationship. The edge strengths can be positive or negative. A positive value shows direct causality: an increase in Node A causes (results in) an increase in Node B. On the other hand, a negative value indicates inverse causality: an increase in Node A causes (results in) a decrease in Node B. The absence of an edge indicates that no causal relationship is thought to exist. (Kosko, 1987) Rather than assigning these edge strengths crisp values of +1 (direct causality) or -1 (inverse causality), they are given values on the interval [-1,1] to capture subtleties in the relationships that might exist. Thus, instead of A causes B, degrees of causality can be incorporated in the model that capture partial or imperfect relationships: A somewhat causes B, or A really causes B. As long as a consistent numeric scale is used for the adverbial modifiers, fuzziness in edge strength values can be incorporated. (Perusich & McNeese, 1997)