Linguistic stochastic dominance to support consensus reaching in group decision making with linguistic distribution assessments

Abstract

The complexity of linguistic distribution assessments increases the difficulty for the decision makers dealing with them. Recently, stochastic dominance has been varied to be a useful tool to compare two stochastic variables. Inspired by this, in this paper we dedicate to utilizing the stochastic dominance to compare the linguistic distribution assessments and further discuss the consensus reaching issue in GDM with linguistic distribution assessments. First, we introduce three types of individuals’ semantic sensitivity. Based on this, we define the linguistic stochastic dominances respectively under different semantic sensitivity contexts, and then provide several desirable properties. Then, we design a consensus reaching resolution framework based on linguistic stochastic dominance (CRRF-LSD). Finally, a case study is provided to show the application value of the CRRF-LSD, and two comparison analyses are further conducted to show the advantages of the linguistic stochastic dominance and the CRRF-LSD. The comparison results show that the proposed linguistic stochastic dominances method has clear advantages over several classical existing methods in comparing two linguistic distribution assessments. Meanwhile, the comparison results show that only the CRRF-LSD method takes the PIS and semantic sensitivity into account, which is helpful to determine more accurate individual ranking results.