Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators
The partitioned Bonferroni mean (PBM) operator can efficiently aggregate inputs, which are divided into parts based on their interrelationships. To date, it has not been used to aggregate linguistic Pythagorean fuzzy numbers (LPFNs). In this paper, we extend the PBM operator and partitioned geometri...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/9531064 |
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| author | Mingwei Lin Jiuhan Wei Zeshui Xu Riqing Chen |
| author_facet | Mingwei Lin Jiuhan Wei Zeshui Xu Riqing Chen |
| author_sort | Mingwei Lin |
| collection | DOAJ |
| description | The partitioned Bonferroni mean (PBM) operator can efficiently aggregate inputs, which are divided into parts based on their interrelationships. To date, it has not been used to aggregate linguistic Pythagorean fuzzy numbers (LPFNs). In this paper, we extend the PBM operator and partitioned geometric Bonferroni mean (PGBM) operator to the linguistic Pythagorean fuzzy sets (LPFSs) and use them to develop a novel multiattribute group decision-making model under the linguistic Pythagorean fuzzy environment. We first define some novel operational laws for LPFNs, which take into consideration the interactions between the membership degree (MD) and nonmembership degree (NMD) from two different LPFNs. Based on these novel operational laws, we put forward the interaction PBM (LPFIPBM) operator, the weighted interaction PBM (LPFWIPBM) operator, the interaction PGBM (LPFIPGBM) operator, and the weighted interaction PGBM (LPFWIPGBM) operator. Then, we study some properties of these proposed operators and discuss their special cases. Based on the proposed LPFWIPBM and LPFWIPGBM operators, a novel multiattribute group decision-making model is developed to process the linguistic Pythagorean fuzzy information. Finally, some illustrative examples are introduced to compare our proposed methods with the existing ones. |
| format | Article |
| id | doaj-art-2f3fb416143442d294cdbae9d13daad1 |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-2f3fb416143442d294cdbae9d13daad12025-08-20T02:08:12ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/95310649531064Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation OperatorsMingwei Lin0Jiuhan Wei1Zeshui Xu2Riqing Chen3College of Mathematics and Informatics, Fujian Normal University, Fuzhou, Fujian 350117, ChinaDigital Fujian Internet-of-Things Laboratory of Environmental Monitoring, Fujian Normal University, Fuzhou, Fujian 350117, ChinaBusiness School, Sichuan University, Chengdu, Sichuan 610064, ChinaDigital Fujian Institute of the Big Data for Agriculture and Forestry, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, ChinaThe partitioned Bonferroni mean (PBM) operator can efficiently aggregate inputs, which are divided into parts based on their interrelationships. To date, it has not been used to aggregate linguistic Pythagorean fuzzy numbers (LPFNs). In this paper, we extend the PBM operator and partitioned geometric Bonferroni mean (PGBM) operator to the linguistic Pythagorean fuzzy sets (LPFSs) and use them to develop a novel multiattribute group decision-making model under the linguistic Pythagorean fuzzy environment. We first define some novel operational laws for LPFNs, which take into consideration the interactions between the membership degree (MD) and nonmembership degree (NMD) from two different LPFNs. Based on these novel operational laws, we put forward the interaction PBM (LPFIPBM) operator, the weighted interaction PBM (LPFWIPBM) operator, the interaction PGBM (LPFIPGBM) operator, and the weighted interaction PGBM (LPFWIPGBM) operator. Then, we study some properties of these proposed operators and discuss their special cases. Based on the proposed LPFWIPBM and LPFWIPGBM operators, a novel multiattribute group decision-making model is developed to process the linguistic Pythagorean fuzzy information. Finally, some illustrative examples are introduced to compare our proposed methods with the existing ones.http://dx.doi.org/10.1155/2018/9531064 |
| spellingShingle | Mingwei Lin Jiuhan Wei Zeshui Xu Riqing Chen Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators Complexity |
| title | Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators |
| title_full | Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators |
| title_fullStr | Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators |
| title_full_unstemmed | Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators |
| title_short | Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators |
| title_sort | multiattribute group decision making based on linguistic pythagorean fuzzy interaction partitioned bonferroni mean aggregation operators |
| url | http://dx.doi.org/10.1155/2018/9531064 |
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