Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting
In this study, we developed an approach to investigate multiple attribute group decision-making (MAGDM) problems, in which the attribute values take the form of Pythagorean fuzzy numbers whose information about attribute weights is incompletely known. First, the Pythagorean fuzzy Choquet integral ge...
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doaj-08b2cdd4c33b471cbb22bb86510038ab2021-09-06T19:40:38ZengDe GruyterJournal of Intelligent Systems0334-18602191-026X2018-09-0129185887610.1515/jisys-2018-0099Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy SettingKhan Muhammad Sajjad Ali0Abdullah Saleem1Lui Peide2Department of Mathematics, Hazara University, Mansehra, KPK, PakistanDepartment of Mathematics, Abdul Wali Khan University, Mardan, KPK, PakistanSchool of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, ChinaIn this study, we developed an approach to investigate multiple attribute group decision-making (MAGDM) problems, in which the attribute values take the form of Pythagorean fuzzy numbers whose information about attribute weights is incompletely known. First, the Pythagorean fuzzy Choquet integral geometric operator is utilized to aggregate the given decision information to obtain the overall preference value of each alternative by experts. In order to obtain the weight vector of the criteria, an optimization model based on the basic ideal of the traditional gray relational analysis method is established, and the calculation steps for solving Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of gray relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of gray relation to both the positive-ideal solution and negative-ideal solution simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.https://doi.org/10.1515/jisys-2018-0099multiple attribute decision makinggray relational analysis (gra)pythagorean fuzzy numbersincomplete weight information |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Khan Muhammad Sajjad Ali Abdullah Saleem Lui Peide |
spellingShingle |
Khan Muhammad Sajjad Ali Abdullah Saleem Lui Peide Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting Journal of Intelligent Systems multiple attribute decision making gray relational analysis (gra) pythagorean fuzzy numbers incomplete weight information |
author_facet |
Khan Muhammad Sajjad Ali Abdullah Saleem Lui Peide |
author_sort |
Khan Muhammad Sajjad Ali |
title |
Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting |
title_short |
Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting |
title_full |
Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting |
title_fullStr |
Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting |
title_full_unstemmed |
Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting |
title_sort |
gray method for multiple attribute decision making with incomplete weight information under the pythagorean fuzzy setting |
publisher |
De Gruyter |
series |
Journal of Intelligent Systems |
issn |
0334-1860 2191-026X |
publishDate |
2018-09-01 |
description |
In this study, we developed an approach to investigate multiple attribute group decision-making (MAGDM) problems, in which the attribute values take the form of Pythagorean fuzzy numbers whose information about attribute weights is incompletely known. First, the Pythagorean fuzzy Choquet integral geometric operator is utilized to aggregate the given decision information to obtain the overall preference value of each alternative by experts. In order to obtain the weight vector of the criteria, an optimization model based on the basic ideal of the traditional gray relational analysis method is established, and the calculation steps for solving Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of gray relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of gray relation to both the positive-ideal solution and negative-ideal solution simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. |
topic |
multiple attribute decision making gray relational analysis (gra) pythagorean fuzzy numbers incomplete weight information |
url |
https://doi.org/10.1515/jisys-2018-0099 |
work_keys_str_mv |
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