General type-2 fuzzy degree of nodes in multi-central social networks set NAFIPS co-authorship network

In this study, a new index is defined to measure a degree of node of the multi central complex network. The proposed index measures the belonging degree to the networks based on general type-2 fuzzy membership values. The proposed general type-2 fuzzy degree (GT2FD) consists of the primary degree, which indicates the similarity between nodes and central nodes; and the secondary degree, which indicated the position of the central node compared to other central nodes in the networks. We applied this index on co-authorships network of NAFIPS conferences to determine the authors' degree of belonging. All concepts and operations of general type-2 fuzzy sets could be applied for social network analysis by using GT2FD.

I. Introduction

One of the primary uses of graph theory in social network analysis is the determination of the level of importance nodes in a social network. There are many definitions and indices for importance in the literature. All of them attempts to describe and measure properties of node location in social network. Nodes who are the most important are usually located in strategic locations within the network. Among the definitions are those based on degree, closeness, betweenness and information are the number of these indices that determined the differential status or rank of the nodes. These definitions yield node indices which attempt to quantify the prominence of an individual nodes embedded in a network. The node indices can also be aggregated across nodes to obtain a single, group-level index which summarize how variable or differentiated the set of nodes is as a whole with respect to a given measure [1].