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.
Highlights
Multi-attribute decision-making (MADM) aims to select the best alternative solution(s) from multiple alternatives and has been widely used in various fields [1,2,3]
To express the fuzziness and uncertainty of linguistic terms, we introduce shadowed set method to cope with linguistic term, and further put forward a new Pythagorean shadowed set
MADM Method Based on the Pythagorean Shadowed Set
Summary
Multi-attribute decision-making (MADM) aims to select the best alternative solution(s) from multiple alternatives and has been widely used in various fields [1,2,3]. Yu [6] proposed an extended TODIM method with unbalanced hesitant fuzzy linguistic term sets for MADM problems. As distinct from the linguistic 2-tuple and scale function, shadowed sets [13,14] can effectively construct linguistic terms using a data-driven method, and have recently been attracting more and more attention [15,16]. The limitation of IFS is that the sum of membership degree and non-membership degree must be no more than 1, which makes it difficult to sufficiently express the ideas of the DMs. Yager [18] defined the Pythagorean fuzzy set (PFS), which can effectively express the certainty and uncertainty of experts. Inspired by the idea of the shadowed set and PFS, we propose a new approach to solve MADM problems under linguistic set environment.
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