Social Network Analysis of Co-fired Fuzzy Rules

The popularity of modern online social networks has grown up so quickly in the last few years that, nowadays, social network analysis has become one of the hottest research lines in the world. It is important to highlight that social network analysis is not limited to the analysis of networks connecting people. Indeed, it is strongly connected with the classical methods widely recognized in the context of graph theory. Thus, social network analysis is applied to many different areas like for instance economics, bibliometrics, and so on. This contribution shows how it can also be successfully applied in the context of designing interpretable fuzzy systems. The key point consists of looking at the rule base of a fuzzy system as a fuzzy inference-gram (fingram), i.e., as a social network made of nodes representing fuzzy rules. In addition, nodes are connected through edges that represent the interaction between rules, at inference level, in terms of co-fired rules, i.e., rules fired at the same time by a given input vector. In short, fingram analysis consists of studying the interaction among nodes in the network for the purpose of understanding the structure and behavior of the fuzzy rule base under consideration. It is based on the basic principles of social network analysis which have been properly adapted to the design of fuzzy systems.