Novel case-based distance sorting methods for PLTSs considering the consistency of preferences of decision-makers

The multiple criteria decision-making (MCDM) problem is a significant issue in various aspects of social life. In many practical cases, decision makers (DMs) care not only about the ranking results but also the sorting results, and they may provide holistic estimations for decision-making problems. To leverage these holistic estimations effectively and address both the sorting and ranking results, in this paper, we design three novel case-based distance sorting (CBDS) methods for ranking alternatives and clustering them into predefined categories using probabilistic linguistic information within the MCDM framework. First, to determine the optimal alternative, we propose a new method based on the comparison rules for probabilistic linguistic term sets (PLTSs). Then, we introduce a method of checking the consistency of DMs’ preferences and establish a mathematical programming model to identify the consistent preference subsets, thereby maintaining the consistency. Furthermore, we develop an algorithm to identify all consistent preference subsets of a DM and establish three novel CBDS methods that explicitly account for DMs’ preference inconsistencies and the number of alternatives. Finally, we apply our methods in a case study that clusters disabled elders into three categories to demonstrate both the effectiveness and practicability of the proposed approaches. A robust test shows that the framework preserves the best and worst alternatives while yielding highly consistent rankings.