Probabilistic linguistic prospect outranking risk decision making method based on stochastic dominance and application in emergency plan evaluation

Abstract

In the decision-making process, probabilistic linguistic term sets (PLTSs) could represent decision-makers’ uncertain evaluation information. The combination of probabilistic and linguistic information assists decision-makers to depict their evaluation information more flexibly. In this paper, a prospect outranking decision-making method based on stochastic dominance is proposed for solving the multi-attribute risk decision-making problem under the probabilistic linguistic information environment. Firstly, to fully preserve the original probabilistic linguistic information, we give the definitions of the generalized probability distribution and the corresponding generalized cumulative distribution function of a PLTS for defining the distance measure between PLTSs. Secondly, based on the positive and negative ideal cumulative distribution functions, we propose the probabilistic linguistic prospect value functions. After that, considering the uncertainty of the relationship between alternatives, several kinds of novel prospect stochastic dominance and almost stochastic dominance relations are defined, which consider the decision makers’ distinction between gains and losses to measure the subtle relationship between alternatives. The stochastic dominance approach and the almost stochastic dominance approach under the probabilistic linguistic decision-making environment are put forward. Besides, we use the superiority and inferiority ranking method to solve the dominance ranking problem of the uncertainty relationship between any two alternatives. Finally, the proposed method is applied in the evaluation of emergency plans to show the accuracy and reliability, and comparative analyses are made to illustrate its availability.