Using Fuzzy c-Means for Weighting Different Fuzzy Cognitive Maps

Abstract

Currently, complex socio-ecological problems have increasingly prevailed with uncertainty that often dominates these domains. In order to better represent these problems, there is an urgent need to engage a wide range of different stakeholders' perspectives, regardless of their levels of expertise and knowledge. Then, these perspectives should be combined in an appropriate manner for a comprehensive and reasonable problem representation. Fuzzy cognitive map (FCM) has proven to be powerful and useful as a soft computing approach in addressing and representing such problem domains. By the FCM approach, the relevant stakeholders can represent their perspectives in the form of FCM system. Normally, relevant stakeholders have different levels of knowledge, and hence produce different representations (FCMs). Therefore, these FCMs should be weighted appropriately before the combination process. This paper uses fuzzy c-means clustering technique to assign different weights for different FCMs according to their importance in representing the problem. First, fuzzy c-means is used to compute the membership values of belonging of FCMs to the selected clusters based on the FCMs similarities that show how convergent and consistent they are. According to these membership values, the importance clusters' values are calculated, in which a cluster with a high membership value from all FCMs is the cluster with the high importance value, and vice versa. Next, the importance values for FCMs are derived from the importance values of the clusters by looking at the amount of contributions of FCMs memberships to the clusters. Finally, FCMs importance values are used to assign weight values to these FCMs, which are used when they are combined. The suitability of the proposed method is investigated using a real dataset that includes an appropriate number of FCMs collected from different stakeholders.