Abstract
In multiattribute group decision-making (MAGDM), due to quantity, fuzziness, and complexity of evaluation linguistic information on commodities, traditional distance measures need to be extended to the integration of evaluation information under a multigranular probabilistic linguistic environment. A more reasonable method is proposed to deal with the missing value in the evaluation information. On the basis of the generalized distance measures and filling in the missing evaluation information, some novel distance measures between two multigranular probabilistic linguistic term sets (PLTSs) are presented in this paper. Based on these distance measures, three extended decision-making (DM) algorithms based on TOPSIS, the extended TOPSIS, and VIKOR are proposed, which are MGPL-TOPSIS, MGPL-ETOPSIS, and MGPL-VIKOR, respectively. The case analyses on purchasing a car are provided to illustrate the application of the extended multiattribute group decision-making (MAGDM) algorithms. Then, sensitivity analyses based on PT are proposed as well. In particular, the extended TOPSIS method is presented. These results demonstrate the novelty, feasibility, and rationality of the distance measures between two multigranular PLTSs proposed in this paper.
Highlights
With the popularity of the Internet, online shopping has become an important way of daily shopping
The hesitant fuzzy set based on probability was proposed as the probability-based hesitant fuzzy set (PHFS) [8, 9], and probabilistic linguistic term set (PLTS) by Qi Pang et al is proposed to describe the object more effectively [10]. e probabilistic linguistic term sets (PLTSs) allow the DMs to give several linguistic terms, serving as the value of a linguistic
On the basis of the discussion above, we present a novel method to deal with the missing value in the evaluation information and generalized distance measures for the PLTSs with multigranular linguistic information. en, we apply it to solve the problems of multiattribute group decision-making (MAGDM) on the decisionmaking of purchasing a car
Summary
With the popularity of the Internet, online shopping has become an important way of daily shopping. En, how can two PLTSs with multigranular probabilistic linguistic information be measured? Zhang et al proposed a probabilistic linguistic method based on VIKOR to evaluate green supply chain initiatives [20]. Some researchers have applied the PLTS to solve some practical problems; for example, Hao et al presented a probabilistic dual-hesitant fuzzy set and its application in risk evaluation [23]. On the basis of the discussion above, we present a novel method to deal with the missing value in the evaluation information and generalized distance measures for the PLTSs with multigranular linguistic information. Based on the discussion above, this paper proposes distance measures for the PLTSs with multigranular linguistic information and applies them in MAGDM
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