Methods for Multiple-Attribute Group Decision Making with q-Rung Interval-Valued Orthopair Fuzzy Information and Their Applications to the Selection of Green Suppliers
In the practical world, there commonly exist different types of multiple-attribute group decision making (MAGDM) problems with uncertain information. Symmetry among some attributes’ information that is already known and unknown, and symmetry between the pure attribute sets and fuzzy attrib...
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doaj-06f52630b18d4f35a1a78b85c455e1312020-11-25T00:45:52ZengMDPI AGSymmetry2073-89942019-01-011115610.3390/sym11010056sym11010056Methods for Multiple-Attribute Group Decision Making with q-Rung Interval-Valued Orthopair Fuzzy Information and Their Applications to the Selection of Green SuppliersJie Wang0Hui Gao1Guiwu Wei2Yu Wei3School of Business, Sichuan Normal University, Chengdu 610101, ChinaSchool of Business, Sichuan Normal University, Chengdu 610101, ChinaSchool of Business, Sichuan Normal University, Chengdu 610101, ChinaSchool of Finance, Yunnan University of Finance and Economics, Kunming 650221, ChinaIn the practical world, there commonly exist different types of multiple-attribute group decision making (MAGDM) problems with uncertain information. Symmetry among some attributes’ information that is already known and unknown, and symmetry between the pure attribute sets and fuzzy attribute membership sets, can be an effective way to solve this type of MAGDM problem. In this paper, we investigate four forms of information aggregation operators, including the Hamy mean (HM) operator, weighted HM (WHM) operator, dual HM (DHM) operator, and the dual-weighted HM (WDHM) operator with the q-rung interval-valued orthopair fuzzy numbers (q-RIVOFNs). Then, some extended aggregation operators, such as the q-rung interval-valued orthopair fuzzy Hamy mean (q-RIVOFHM) operator; q-rung interval-valued orthopairfuzzy weighted Hamy mean (q-RIVOFWHM) operator; q-rung interval-valued orthopair fuzzy dual Hamy mean (q-RIVOFDHM) operator; and q-rung interval-valued orthopair fuzzy weighted dual Hamy mean (q-RIVOFWDHM) operator are presented, and some of their precious properties are studied in detail. Finally, a real example for green supplier selection in green supply chain management is provided, to demonstrate the proposed approach and to verify its rationality and scientific nature.http://www.mdpi.com/2073-8994/11/1/56multiple attribute group decision making (MAGDM)Pythagorean fuzzy set (PFSs)q-rung orthopair fuzzy sets (q-RIVOFSs)q-RIVOFWHM operatorq-RIVOFWDHM operatorgreen suppliers selection |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jie Wang Hui Gao Guiwu Wei Yu Wei |
spellingShingle |
Jie Wang Hui Gao Guiwu Wei Yu Wei Methods for Multiple-Attribute Group Decision Making with q-Rung Interval-Valued Orthopair Fuzzy Information and Their Applications to the Selection of Green Suppliers Symmetry multiple attribute group decision making (MAGDM) Pythagorean fuzzy set (PFSs) q-rung orthopair fuzzy sets (q-RIVOFSs) q-RIVOFWHM operator q-RIVOFWDHM operator green suppliers selection |
author_facet |
Jie Wang Hui Gao Guiwu Wei Yu Wei |
author_sort |
Jie Wang |
title |
Methods for Multiple-Attribute Group Decision Making with q-Rung Interval-Valued Orthopair Fuzzy Information and Their Applications to the Selection of Green Suppliers |
title_short |
Methods for Multiple-Attribute Group Decision Making with q-Rung Interval-Valued Orthopair Fuzzy Information and Their Applications to the Selection of Green Suppliers |
title_full |
Methods for Multiple-Attribute Group Decision Making with q-Rung Interval-Valued Orthopair Fuzzy Information and Their Applications to the Selection of Green Suppliers |
title_fullStr |
Methods for Multiple-Attribute Group Decision Making with q-Rung Interval-Valued Orthopair Fuzzy Information and Their Applications to the Selection of Green Suppliers |
title_full_unstemmed |
Methods for Multiple-Attribute Group Decision Making with q-Rung Interval-Valued Orthopair Fuzzy Information and Their Applications to the Selection of Green Suppliers |
title_sort |
methods for multiple-attribute group decision making with q-rung interval-valued orthopair fuzzy information and their applications to the selection of green suppliers |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2019-01-01 |
description |
In the practical world, there commonly exist different types of multiple-attribute group decision making (MAGDM) problems with uncertain information. Symmetry among some attributes’ information that is already known and unknown, and symmetry between the pure attribute sets and fuzzy attribute membership sets, can be an effective way to solve this type of MAGDM problem. In this paper, we investigate four forms of information aggregation operators, including the Hamy mean (HM) operator, weighted HM (WHM) operator, dual HM (DHM) operator, and the dual-weighted HM (WDHM) operator with the q-rung interval-valued orthopair fuzzy numbers (q-RIVOFNs). Then, some extended aggregation operators, such as the q-rung interval-valued orthopair fuzzy Hamy mean (q-RIVOFHM) operator; q-rung interval-valued orthopairfuzzy weighted Hamy mean (q-RIVOFWHM) operator; q-rung interval-valued orthopair fuzzy dual Hamy mean (q-RIVOFDHM) operator; and q-rung interval-valued orthopair fuzzy weighted dual Hamy mean (q-RIVOFWDHM) operator are presented, and some of their precious properties are studied in detail. Finally, a real example for green supplier selection in green supply chain management is provided, to demonstrate the proposed approach and to verify its rationality and scientific nature. |
topic |
multiple attribute group decision making (MAGDM) Pythagorean fuzzy set (PFSs) q-rung orthopair fuzzy sets (q-RIVOFSs) q-RIVOFWHM operator q-RIVOFWDHM operator green suppliers selection |
url |
http://www.mdpi.com/2073-8994/11/1/56 |
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