Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-Making
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 an...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2018-12-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/10/12/688 |
| _version_ | 1817995127974526976 |
|---|---|
| author | Huidong Wang Shifan He Xiaohong Pan Chengdong Li |
| author_facet | Huidong Wang Shifan He Xiaohong Pan Chengdong Li |
| author_sort | Huidong Wang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T02:02:28Z |
| format | Article |
| id | doaj.art-71035e78c74047d48cd680f08f8d6c3a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T02:02:28Z |
| publishDate | 2018-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-71035e78c74047d48cd680f08f8d6c3a2022-12-22T02:18:48ZengMDPI AGSymmetry2073-89942018-12-01101268810.3390/sym10120688sym10120688Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-MakingHuidong Wang0Shifan He1Xiaohong Pan2Chengdong Li3School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, ChinaSchool of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, ChinaSchool of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, ChinaSchool of Information and Electrical Engineering, Shandong Jianzhu University, Jinan 250101, ChinaFor 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.https://www.mdpi.com/2073-8994/10/12/688Pythagorean fuzzy linguistic setshadowed setPythagorean shadowed setmulti-attribute decision-making |
| spellingShingle | Huidong Wang Shifan He Xiaohong Pan Chengdong Li Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-Making Symmetry Pythagorean fuzzy linguistic set shadowed set Pythagorean shadowed set multi-attribute decision-making |
| title | Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-Making |
| title_full | Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-Making |
| title_fullStr | Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-Making |
| title_full_unstemmed | Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-Making |
| title_short | Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-Making |
| title_sort | shadowed sets based linguistic term modeling and its application in multi attribute decision making |
| topic | Pythagorean fuzzy linguistic set shadowed set Pythagorean shadowed set multi-attribute decision-making |
| url | https://www.mdpi.com/2073-8994/10/12/688 |
| work_keys_str_mv | AT huidongwang shadowedsetsbasedlinguistictermmodelinganditsapplicationinmultiattributedecisionmaking AT shifanhe shadowedsetsbasedlinguistictermmodelinganditsapplicationinmultiattributedecisionmaking AT xiaohongpan shadowedsetsbasedlinguistictermmodelinganditsapplicationinmultiattributedecisionmaking AT chengdongli shadowedsetsbasedlinguistictermmodelinganditsapplicationinmultiattributedecisionmaking |