*Article* **Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-Making**

**Huidong Wang 1,\*, Shifan He 1, Xiaohong Pan 1 and Chengdong Li 2**


Received: 20 October 2018; Accepted: 16 November 2018; Published: 2 December 2018

**Abstract:** For many multi-attribute decision-making (MADM) problems, linguistic variables are more convenient for people to express the attribute values. In this paper, a novel shadowed set-based method is proposed to deal with linguistic terms, where the linguistic term sets are symmetrical both in meaning and form. Firstly, to effectively express the linguistic variables, we develop a data-driven method to construct the shadowed set model for the linguistic terms. Secondly, the Pythagorean shadowed set is defined, and some theorems are subsequently explored. Thirdly, we propose the score function of the Pythagorean shadowed number and develop a new MADM method on the basis of the Pythagorean shadowed set. Finally, a case study of the supplier selection problem is provided to illustrate the effectiveness of the proposed method, and the superiority of our method is demonstrated by comparison analysis.

**Keywords:** Pythagorean fuzzy linguistic set; shadowed set; Pythagorean shadowed set; multi-attribute decision-making
