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Picture Fuzzy Einstein Hybrid-Weighted Aggregation Operator and Its Application to Multicriteria Group Decision Making
As an extension of intuitionistic fuzzy sets (IFSs), picture fuzzy sets (PFSs) can better model and represent the hesitancy and uncertainty of decision makers' preference information. In this study, we propose a multicriteria group decision making (MCGMD) method based on picture fuzzy sets. We...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Hindawi
2022
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9124077/ https://www.ncbi.nlm.nih.gov/pubmed/35607474 http://dx.doi.org/10.1155/2022/6925670 |
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author | Cao, Guo |
author_facet | Cao, Guo |
author_sort | Cao, Guo |
collection | PubMed |
description | As an extension of intuitionistic fuzzy sets (IFSs), picture fuzzy sets (PFSs) can better model and represent the hesitancy and uncertainty of decision makers' preference information. In this study, we propose a multicriteria group decision making (MCGMD) method based on picture fuzzy sets. We first define some basic picture Einstein operations with closed properties among PFSs on the basis of the Einstein t-norms and t-conorms. Then, utilizing the hybrid-weighted operator and the developed picture Einstein operations laws, we put forward a picture fuzzy Einstein hybrid-weighted aggregation operator for aggregating PFSs and discuss its several important properties. Furthermore, we present a new MCGMD method based on the proposed picture fuzzy Einstein hybrid-weighted aggregation operator. Finally, an example is conducted to validate the effectiveness of the proposed MCGMD method. |
format | Online Article Text |
id | pubmed-9124077 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Hindawi |
record_format | MEDLINE/PubMed |
spelling | pubmed-91240772022-05-22 Picture Fuzzy Einstein Hybrid-Weighted Aggregation Operator and Its Application to Multicriteria Group Decision Making Cao, Guo Comput Intell Neurosci Research Article As an extension of intuitionistic fuzzy sets (IFSs), picture fuzzy sets (PFSs) can better model and represent the hesitancy and uncertainty of decision makers' preference information. In this study, we propose a multicriteria group decision making (MCGMD) method based on picture fuzzy sets. We first define some basic picture Einstein operations with closed properties among PFSs on the basis of the Einstein t-norms and t-conorms. Then, utilizing the hybrid-weighted operator and the developed picture Einstein operations laws, we put forward a picture fuzzy Einstein hybrid-weighted aggregation operator for aggregating PFSs and discuss its several important properties. Furthermore, we present a new MCGMD method based on the proposed picture fuzzy Einstein hybrid-weighted aggregation operator. Finally, an example is conducted to validate the effectiveness of the proposed MCGMD method. Hindawi 2022-05-14 /pmc/articles/PMC9124077/ /pubmed/35607474 http://dx.doi.org/10.1155/2022/6925670 Text en Copyright © 2022 Guo Cao. https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
spellingShingle | Research Article Cao, Guo Picture Fuzzy Einstein Hybrid-Weighted Aggregation Operator and Its Application to Multicriteria Group Decision Making |
title | Picture Fuzzy Einstein Hybrid-Weighted Aggregation Operator and Its Application to Multicriteria Group Decision Making |
title_full | Picture Fuzzy Einstein Hybrid-Weighted Aggregation Operator and Its Application to Multicriteria Group Decision Making |
title_fullStr | Picture Fuzzy Einstein Hybrid-Weighted Aggregation Operator and Its Application to Multicriteria Group Decision Making |
title_full_unstemmed | Picture Fuzzy Einstein Hybrid-Weighted Aggregation Operator and Its Application to Multicriteria Group Decision Making |
title_short | Picture Fuzzy Einstein Hybrid-Weighted Aggregation Operator and Its Application to Multicriteria Group Decision Making |
title_sort | picture fuzzy einstein hybrid-weighted aggregation operator and its application to multicriteria group decision making |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9124077/ https://www.ncbi.nlm.nih.gov/pubmed/35607474 http://dx.doi.org/10.1155/2022/6925670 |
work_keys_str_mv | AT caoguo picturefuzzyeinsteinhybridweightedaggregationoperatoranditsapplicationtomulticriteriagroupdecisionmaking |