On incomplete matrix information completion methods and opinion evolution: Matrix factorization towards adjacency preferences

Abstract

Completeness and consistency are widely acknowledged as indispensable prerequisites for applying fuzzy preference relations in resolving real-world problems. Interactions between decision-makers in the field of group decision-making can have a profound effect on preference changes, especially in situations of incomplete information. However, preference matrices generated using existing models often suffer from low consistency during opinion evolution, which further increases the risk of wrong decisions. To cope with these problems, this paper proposes an opinion evolution method under incomplete information. The method consists of two main components: (1) A preference prediction model based on matrix factorization algorithm and social trust networks under incomplete information, and (2) A model for decision-makers’ preference evolution under dynamic trust scenarios. In Part (1), to simplify the preference collection method and reduce the occurrence of inconsistent information, this paper presents the concept of a consistent adjacency fuzzy preference matrix. To advance the utilization of machine learning algorithms for consistent preference relations, this paper employs the matrix factorization method with stochastic gradient descent to predict missing preferences in adjacency fuzzy preference matrix. In Part (2), to address the shortcomings in past opinion evolution models, this paper simulates the change of decision-makers’ opinions in different stages of interactions under variable trust weights by using alternative ranking similarity and trust thresholds. To illustrate the practical application of the proposed model, this article uses the enterprise supplier selection problem as a case study. The model’s effectiveness and feasibility are then validated through a comparative analysis with existing methods.