Affiliations: [a] School of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, Henan, China
| [b] School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, Henan, China
Correspondence:
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Corresponding author. Hongbin Liu, School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, Henan 450046, China. E-mail: lhbnwpu@hotmail.com.
Abstract: The use of probabilistic linguistic term sets (PLTSs) means the process of computing with words. The existing methods computing with PLTSs mainly use symbolic model. To provide a semantic model for computing with PLTSs, we propose to represent a PLTS by using an interval type-2 fuzzy set (IT2FS). The key step is to compute the footprint of uncertainty of the IT2FS. To this aim, the upper membership function is computed by aggregating the membership functions of the linguistic terms contained in the PLTS, and the lower membership function is obtained by moving the upper membership function downward with the step being total entropy of the PLTS. The comparison rules, some operations, and an aggregation operator for PLTSs are introduced. Based on the proposed method of computing with PLTSs, a multi-criteria group decision making model is introduced. The proposed decision making model is then applied in green supplier selection problem to show its feasibility.
Keywords: Green supplier selection, interval type-2 fuzzy set, lower membership function, probabilistic linguistic term set, upper membership function
