Triangular fuzzy number representation of relations in Fuzzy Cognitive Maps

Abstract

In this paper, the conventional Fuzzy Cognitive Maps (FCMs), which has already achieved success in many fields, are extended by using triangular fuzzy numbers (TFNs). The advantage of FCMs is that they are relatively easy to construct and parameterize and are capable of handling the full range of system feedback structure, including density-dependent effects. However, it is a well-known fact that there are some limitations inherent in FCM, such as lack of adequate capability to handle uncertain information and lack of enough ability to aggregate the information from different sources. Triangular fuzzy numbers which are represented by a triplet has the capacity to represent the uncertain relations between the concepts. In this context, the weight matrix representing the causal relations are enhanced to a fuzzy weight matrix that has TFNs as element. As a result of this improvement, the dynamic reasoning algorithm of the conventional FCM is improved for the use of the proposed novel FCM. The proposed FCM is presented via four simulations and the results are discussed. The results of the simulation study shows how easily the uncertain information can be represented and interpreted by the proposed FCM design methodology.