Algorithm for Multiple Attribute Decision-Making with Interactive Archimedean Norm Operations Under Pythagorean Fuzzy Uncertainty
Recently, a great attention is paid toward developing aggregation operators for Pythagorean fuzzy set (PFS). However, few of them have adopted the rules of Archimedean t-conorm and t-norm (ATT) to aggregate the numbers. Motivated by this, the keep interest of the present work is to define some Pytha...
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doaj-42c102e746bb48959ad3bacb2dbca7822021-02-01T15:03:47ZengAtlantis PressInternational Journal of Computational Intelligence Systems 1875-68832020-12-0114110.2991/ijcis.d.201215.002Algorithm for Multiple Attribute Decision-Making with Interactive Archimedean Norm Operations Under Pythagorean Fuzzy UncertaintyLei WangHarish GargRecently, a great attention is paid toward developing aggregation operators for Pythagorean fuzzy set (PFS). However, few of them have adopted the rules of Archimedean t-conorm and t-norm (ATT) to aggregate the numbers. Motivated by this, the keep interest of the present work is to define some Pythagorean fuzzy interaction aggregation operators with the aid of ATT. To do this, the objective of the work is divided into three folds. In the first fold, we define some interactive operations law for PFSs and propose their corresponding new interaction Pythagorean operators, namely Archimedean based Pythagorean fuzzy interactive weighted averaging (A-PFIWA) operator and Archimedean based Pythagorean fuzzy interactive weighted geometric (A-PFIWG) operator. In the second fold, we investigate their desirable properties and study the several special cases of the proposed ones with respect the existing ones. Lastly, we design an algorithm to solve the multiple attribute decision-making issues with Pythagorean fuzzy uncertainties and explain their utilization with a numerical example. Further, several examples are discussed to demonstrate the validity and superiority of the proposed method. The novelties of proposed operators are that they not only can offer a more flexible method via selecting diverse forms of ATT, but also can reflect the interactive influence among membership degree and nonmembership degree for PFSs.https://www.atlantis-press.com/article/125949973/viewMultiple attribute decision-makingArchimedean normPythagorean fuzzy setsAggregation operatorsOperation laws |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lei Wang Harish Garg |
spellingShingle |
Lei Wang Harish Garg Algorithm for Multiple Attribute Decision-Making with Interactive Archimedean Norm Operations Under Pythagorean Fuzzy Uncertainty International Journal of Computational Intelligence Systems Multiple attribute decision-making Archimedean norm Pythagorean fuzzy sets Aggregation operators Operation laws |
author_facet |
Lei Wang Harish Garg |
author_sort |
Lei Wang |
title |
Algorithm for Multiple Attribute Decision-Making with Interactive Archimedean Norm Operations Under Pythagorean Fuzzy Uncertainty |
title_short |
Algorithm for Multiple Attribute Decision-Making with Interactive Archimedean Norm Operations Under Pythagorean Fuzzy Uncertainty |
title_full |
Algorithm for Multiple Attribute Decision-Making with Interactive Archimedean Norm Operations Under Pythagorean Fuzzy Uncertainty |
title_fullStr |
Algorithm for Multiple Attribute Decision-Making with Interactive Archimedean Norm Operations Under Pythagorean Fuzzy Uncertainty |
title_full_unstemmed |
Algorithm for Multiple Attribute Decision-Making with Interactive Archimedean Norm Operations Under Pythagorean Fuzzy Uncertainty |
title_sort |
algorithm for multiple attribute decision-making with interactive archimedean norm operations under pythagorean fuzzy uncertainty |
publisher |
Atlantis Press |
series |
International Journal of Computational Intelligence Systems |
issn |
1875-6883 |
publishDate |
2020-12-01 |
description |
Recently, a great attention is paid toward developing aggregation operators for Pythagorean fuzzy set (PFS). However, few of them have adopted the rules of Archimedean t-conorm and t-norm (ATT) to aggregate the numbers. Motivated by this, the keep interest of the present work is to define some Pythagorean fuzzy interaction aggregation operators with the aid of ATT. To do this, the objective of the work is divided into three folds. In the first fold, we define some interactive operations law for PFSs and propose their corresponding new interaction Pythagorean operators, namely Archimedean based Pythagorean fuzzy interactive weighted averaging (A-PFIWA) operator and Archimedean based Pythagorean fuzzy interactive weighted geometric (A-PFIWG) operator. In the second fold, we investigate their desirable properties and study the several special cases of the proposed ones with respect the existing ones. Lastly, we design an algorithm to solve the multiple attribute decision-making issues with Pythagorean fuzzy uncertainties and explain their utilization with a numerical example. Further, several examples are discussed to demonstrate the validity and superiority of the proposed method. The novelties of proposed operators are that they not only can offer a more flexible method via selecting diverse forms of ATT, but also can reflect the interactive influence among membership degree and nonmembership degree for PFSs. |
topic |
Multiple attribute decision-making Archimedean norm Pythagorean fuzzy sets Aggregation operators Operation laws |
url |
https://www.atlantis-press.com/article/125949973/view |
work_keys_str_mv |
AT leiwang algorithmformultipleattributedecisionmakingwithinteractivearchimedeannormoperationsunderpythagoreanfuzzyuncertainty AT harishgarg algorithmformultipleattributedecisionmakingwithinteractivearchimedeannormoperationsunderpythagoreanfuzzyuncertainty |
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1724315312603529216 |