Abstract
The traditional multi-attribute group decision making (MAGDM) method needs to be improved to the integration of assessment information under multi-granular probabilistic linguistic environments. Some novel distance measures between two multi-granular probabilistic linguistic term sets (PLTSs) are proposed, and distance measures are proved to be reasonable. To calculate the weights of the alternative attributes, the extended cross-entropy method for multi-granular probabilistic linguistic term sets is proposed. Then, a novel extended MAGDM algorithm based on prospect theory (PT) is proposed. Two case studies of decision making (DM) on purchasing a car is provided to illustrate the application of the extended MAGDM algorithm. The case analyses are proposed to illustrate the novelty, feasibility, and application of the proposed MAGDM algorithm by comparing the other three algorithms based on TOPSIS, VIKOR, and Pang Qi et al.’s method. The analyses results demonstrate that the proposed algorithm based on PT is superior.
Highlights
multi-attribute group decision making (MAGDM) is a hot issue, which aims at finding the optimal alternative with multi-attributes [1]
Because the decision making (DM) may hesitate in several possible values in DM, Rodriguez et al [23] proposed the definitions of hesitant fuzzy linguistic term sets (HFLTSs) as follows
A MAGDM problem with multi-granular probabilistic linguistic information is described as follows
Summary
MAGDM is a hot issue, which aims at finding the optimal alternative with multi-attributes [1]. In practical DM problems, the DMs express their preferences on the considered alternatives by linguistic terms, such as “bad”, “medium”, or “good”, and so on They make the optimal decision by some appropriate. The basic distance measures of probabilistic linguistic term sets (PLTSs) with multi-granular probabilistic linguistic information are proposed firstly. In the problems of both individual DM and GDM, the DMs can prefer some of the possible linguistic terms leading to the set of possible values with different importance degrees. We can get accurate preference information of the DMs under the probabilistic linguistic term sets (PLTSs). Some methods have been proposed with multi-granularity linguistic information in GDM [32,33]. In order to solve these problems, distance measures of PLTSs with multi-granular linguistic information are proposed. A novel algorithm for MAGDM based on PT is proposed
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