Belief interval interpretation of probabilistic linguistic term sets and a visual method for solving the preference problem in multicriteria group decision making

For the application of probabilistic linguistic term sets (PLTSs) in multicriteria group decision making (MCGDM), this paper aims to develop an approach to solve the preference problem. First, a belief interval interpretation of PLTSs is presented, which makes it possible to represent the mathematical operations on PLTSs as the operations on belief intervals. This can reduce the uncertainty degree of information caused by the differentiated knowledge and cognitions of decision makers. Then, two methods of belief interval measure are proposed. One is the distance measure, which is utilized to obtain the criteria weights of each decision maker, so as to recognize the preferences for criteria. The other is the probability degree, which is used to get the partial order relation for alternatives of each decision maker, and to recognize the preferences for alternatives. Next, employing Dempster's rule of combination and graph theory, a visual algorithm is constructed to solve the MCGDM preference problem in the application of PLTSs. Finally, an illustrative example for the selection of emergency materials deployment scheme and the comparative analyses are shown to demonstrate the effectiveness of the proposed method.

Automated summary

This paper proposes an approach to solve the preference problem in multicriteria group decision making using probabilistic linguistic term sets (PLTSs). By presenting a belief interval interpretation of PLTSs and two methods of belief interval measure, as well as constructing a visual algorithm based on Dempster's rule of combination and graph theory, the preference problem in MCGDM is effectively addressed. An illustrative example is provided to demonstrate the effectiveness of the proposed method.