Decision-making based on probabilistic linguistic term sets without loss of information

Zhihong Yi

doi:10.1007/s40747-022-00656-2

Abstract

Probabilistic linguistic term set (PLTS) provides a much more effective model to compute with words and to express the uncertainty in the pervasive natural language by probability information. In this paper, to avoid loss of information, we redefine the classical probabilistic linguistic term sets (PLTSs) by multiple probability distributions from an ambiguity perspective and present some basic operations using Archimedean t-(co)norms. Different from the classical PLTSs, the reformulated PLTSs are not necessarily normalized beforehand for further investigations. Moreover, the multiple probability distributions based PLTSs facilitate the incorporation of the different attitudes of the DMs in their score values and the deviation, and thus the comparisons. Then the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is extended to the reformulated PLTS frame by incorporating probability information. With these newly developed elements in the reformulated PLTSs, a DEMATEL based multiple attributes decision-making is proposed. The illustrative example and comparison analysis show that the method over the reformulated PLTSs is feasible and valid, and has the advantage in processing without any information loss (i.e., without normalization) and fully exploration of the DMs-preference and knowledge.

Highlights

Decision-making is human-centered and has inborn uncertainty with vague information expressed by natural language
The series of fruitful theoretical and practical results [31] betray that HFLTS or hesitant fuzzy linguistic element (HFLE) provides an effective way to capture the uncertainty in natural languages
Throughout the paper, we focus on the reformulation the classical Probabilistic linguistic term set (PLTS), and introduce a Decision-Making Trial and Evaluation Laboratory (DEMATEL)-based multiple attributes decision-making (MADM)

Summary

Introduction

Decision-making is human-centered and has inborn uncertainty with vague information expressed by natural language. Compared to DEMATEL method based on the classical PLTS [9], or the linguistic term, or numerical expression, the method with the reformulated PLTS in this work has the advantage in effectively manifesting the experts-preference and knowledge, could lead to substantial improvement on the precision of decision-making. Ambiguity could be a point of departure to provide some new insights on PLTSs. 1, i.e., the PLTS has a set of linguistic terms with a probability distribution, which suggests people have an exact and complete knowledge of probabilistic information; for the case m i =1 pi.

Methods

Concluding remarks