Distribution Linguistic Trust Propagation and Aggregation Based on Numerical Scale and Archimedean t−norm

Trust network analysis has been widely applied in various fields, such as group recommendation, group decision-making and other related areas. In this paper, we focus on obtaining the complete trust network in which experts express their trust relationships for another with a single linguistic term or distribution assessments of a linguistic term set. We first discuss the conditions of obtaining the complete trust network, and the propagation and aggregation of the trust relationships with a single linguistic term. Since the linguistic term set may be symmetric and uniform, symmetric and non-uniform, or asymmetric and non-uniform, we translate linguistic terms into numerical indexes and define the propagation operator based on the semantics of the linguistic term and the Archimedean t-norm. The propagation result is translated to 2−tuple linguistic model because it may not exist in the initial linguistic term set. Some properties are proposed to verify that the proposed operator is compatible with human thought. Then the 2−tuple distribution assessments on a linguistic term set are defined, and the other aggregation operator is proposed to propagate linguistic distribution assessment trust relationships. The second aggregation operator focuses on both the aggregation of linguistic terms and symbolic proportions of linguistic terms and is a generalization of the first operator. Finally, a numerical example of CouchSurfing comparative analyses further demonstrates that the proposed operators are effective and reasonable, and can consider the different semantics of a linguistic term in practical application.