Social Networks Based on Linguistic Z Numbers and Comparisons of Centrality Measures

Reliability of information is one of the most important and concerning factors in real-life decision-making problems. In reality, information is not perfect. This information is usually provided by using different languages. This information is not fully reliable. To avoid the inconsistency of information in decision-making problems, Lotfi Zadeh has provided the notion of the \(Z\) number. It plays a very important role in verifying the dependability of information or facts. \(Z\) -numbers are ordered pairs of two parts; the first part (fuzzy number) estimates the value of a random variable associated with it, and the second part estimates the authenticity of the first fuzzy number. Linguistic fuzzy numbers offer a host of benefits in decision-making and information representation. By allowing for the expression of imprecision and uncertainty using linguistic terms, they provide a human-centric and easily understandable way to convey complex information. Nowadays social network analysis is a very hot topic in research. Here we have developed a social network based on linguistic \(Z\) numbers. We have discussed an example of a students’ network formed based on linguistic \(Z\) numbers and discussed centrality measures for that social network and compared them. Then we have concluded the chapter with some future works.