Fuzzy Representation and Aggregation of Fuzzy Cognitive Maps

Typically, complex systems such as socio-ecological systems are ambiguous and ill-defined due to human-environment interactions. These systems could be participatory systems which involve many participants with different levels of knowledge and experience. The various perceptions of the participants may need to be combined to get a comprehensive understanding and useful knowledge of the system. Modelling these systems involves a high level of uncertainty and soft computing approaches based on the concept of fuzzy logic offer a way to deal with such uncertainty. Fuzzy cognitive map (FCM) incorporates fuzzy logic and has proven its efficiency in modelling and extracting knowledge from various qualitative complex systems. However, the literature shows a lack of appropriate ways to incorporate imprecise human perception in fuzzy form in FCM representation and to deal with these fuzzy values in aggregation of multiple FCMs into a group FCM. The aim of this paper is to provide adequate methods for both representation and aggregation of fuzzy values in FCMs. For FCM representaion, this paper utilizes a 2-tuple fuzzy linguistic representation model Herrera and Martinez (2000a) to represent the FCM connection values in a fuzzy way. This model can represent and deal with linguistic and numeric fuzzy values without any loss of information, and it keeps the consistency of these values throughout any subsequent computational processes. For FCM aggregation, which is the first step, this paper proposes a fuzzy method to combine linguistic and numeric fuzzy values at the same time. In the second step, it proposes a new calculation method to assess the different levels of knowledge of FCM designers (FCMs' credibility weights). These credibility weights of FCMs are then used in the proposed fuzzy aggregation method for a better representation of contrasts between participants resulting from their varied experiences and preferences. For the first step, the 2-tuple fuzzy model is used to represent the FCM connection values during the aggregation process, and therefore the connection values of the group FCM resulting from the aggregation process will be fuzzy values. For the second step, this paper utilizes the Consensus Centrality Measure (CCM) proposed in Obiedat et al. (2011) to calculate a credibility weight for each FCM.