Global fusion of multiple order relations and hesitant fuzzy decision analysis

Generally, when making decisions, decision makers always have their subjective opinions regarding attributes, alternatives or even themselves based on their experience and knowledge. Although some methods, such as weighted aggregation, preference analysis, and fuzzy decision-making, can be used to describe and fuse these opinions, these methods involve two limitations, specifically, inaccurate numerical presentation and stepwise aggregation method. To address these issues, in this paper, we define multiple order relations expressed as several inequalities to describe these subjective opinions, and then propose hesitant fuzzy global fusion models to simultaneously fuse the multiple order relations and make a decision. To this end, we first introduce the hesitant fuzzy envelopment rate and develop partial fusion models for single order relations; subsequently, multiple order relations and global fusion model are proposed. Moreover, to ensure computability, we further derive the linear forms of these models and summarize the improvement schedules for the nonoptimal alternatives. According to these calculations and results, a hesitant fuzzy decision analysis including subjective opinion fusion, evaluation presentation, decision-making calculation, alternative ranking and selection, and nonoptimal improvement, can be performed. Finally, an illustrative example based on a real background is considered to show the effectiveness of the models and decision analysis processes.

Automated summary

This paper introduces a method to describe subjective opinions using multiple equations, and proposes hesitant fuzzy global fusion models to address decision-making issues.