Geo-uninorm consistency control module for preference similarity network hierarchical clustering based consensus model

In order to avoid misleading decision solutions in group decision making (GDM) processes, in addition to consensus, which is obviously desirable to guarantee that the group of experts accept the final decision solution, consistency of information should also be sought after. For experts' preferences represented by reciprocal fuzzy preference relations, consistency is linked to the transitivity property. In this study, we put forward a new consensus approach to solve GDM with reciprocal preference relations that implements rationality criteria of consistency based on the transitivity property with the following twofold aim prior to finding the final decision solution: (A) to develop a consistency control module to provide personalized consistency feedback to inconsistent experts in the GDM problem to guarantee the consistency of preferences; and (B) to design a consistent preference network clustering based consensus measure based on an undirected weighted consistent preference similarity network structure with undirected complete links, which using the concept of structural equivalence will allow one to (i) cluster the experts; and (ii) measure their consensus status. Based on the uninorm characterization of consistency of reciprocal preferences relations and the geometric average, we propose the implementation of the geo-uninorm operator to derive a consistent based preference relation from a given reciprocal preference relation. This is subsequently used to measure the consistency level of a given preference relation as the cosine similarity between the respective relations' essential vectors of preference intensity. The proposed geo-uninorm consistency measure will allow the building of a consistency control module based on a personalized feedback mechanism to be implemented when the consistency level is insufficient. This consistency control module has two advantages: (1) it guarantees consistency by advising inconsistent expert(s) to modify their preferences with minimum changes; and (2) it provides fair recommendations individually, depending on the experts' personal level of inconsistency. Once consistency of preferences is guaranteed, a structural equivalence preference similarity network is constructed. For the purpose of representing structurally equivalent experts and measuring consensus within the group of experts, we develop an agglomerative hierarchical clustering based consensus algorithm, which can be used as a visualization tool in monitoring current state of experts' group agreement and in controlling the decision making process. The proposed model is validated with a comparative analysis with an existing literature study, from which conclusions are drawn and explained.