A Linguistic Information Granulation Model and Its Penalty Function-Based Co-Evolutionary PSO Solution Approach for Supporting GDM with Distributed Linguistic Preference Relations

Abstract

This study focuses on linguistic information operational realization through information granulation in group decision-making (GDM) scenarios where the preference information offered by decision-makers over alternatives is described using distributed linguistic preference relations (DLPRs). First, an information granulation model is proposed to arrive at the operational realization of linguistic information in the GDM with DLPRs. The information granulation is formulated as a certain optimization problem where a combination of consistency degree of individual DLPRs and consensus degree among individuals is regarded as the underlying performance index. Then, considering that the proposed model is a constrained optimization problem (COP) with an adjustable parameter, which is difficult to be effectively solved using general optimization methods, we develop a novel approach towards achieving the optimal solution, referred to as penalty function-based co-evolutionary particle swarm optimization (PFCPSO). Within the PFCPSO setting, the designed penalty function is used to transform the COPs into unconstrained ones. Besides, the penalty factors and the adjustable parameter, as well as the decision variables of the optimization problems, are simultaneously optimized through the co-evolutionary mechanism of two populations in co-evolutionary particle swarm optimization (CPSO). Finally, a comprehensive evaluation problem about car brands is studied using the proposed model and the newly developed PFCPSO approach, which demonstrates their applicability. Two comparative studies are also conducted to show the effectiveness of the proposals. Overall, this study exhibits two facets of originality: the presentation of the linguistic information granulation model, and the development of the PFCPSO approach for solving the proposed model.