Probabilistic linguistic distance measures and their applications in multi-criteria group decision making

Abstract

The probabilistic linguistic term sets can express not only the decision makers’ several possible linguistic assessment values, but also the weight of each linguistic assessment value, so they can preserve the original decision information and then have become an efficient tool for solving multi-criteria group decision making problems. To promote the wide applicability of probabilistic linguistic term sets in various fields, this chapter focuses on the distance measures for probabilistic linguistic term sets and their applications in multi-criteria group decision making. This chapter first defines the distance between two probabilistic linguistic term elements. Based on this, a variety of distance measures are proposed to calculate the distance between two probabilistic linguistic term sets. Then, these distance measures are further extended to compute the distance between two collections of probabilistic linguistic term sets by considering the weight information of each criterion. After that, the concept of the satisfaction degree of an alternative is given and utilized to rank the alternatives in multi-criteria group decision making. Finally, a real example is given to show the use of these distance measures and then compare the probabilistic linguistic term sets with hesitant fuzzy linguistic term sets.