Affiliations: [a] School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, Shandong, China
| [b] Department of Pure and Applied Mathematics the University of Haripur, Pakistan
| [c] Department of Mathematics and Statistics International Islamic University Islamabad, Pakistan
| [d] Department of Mathematics University of Malakand KPK, Pakistan
Abstract: Pythagorean fuzzy set (PyFS) is an extension of various fuzzy concepts, such as fuzzy set (FS), intuitionistic FS, and it is enhanced mathematical gizmo to pact with uncertain and vague information. In this article, some drawbacks in the Dombi operational rules for Pythagorean fuzzy numbers (PyFNs) are examined and some improved Dombi operational laws for PyFNs are developed. We also find out that the value aggregated using the existing Dombi aggregation operators (DAOs) is not a PyFN. Furthermore, we developed two new aggregations, improved existing aggregation operators (AOs) for aggregating Pythagorean fuzzy information (PyFI) and are applied to multiple-attribute decision making (MADM). To acquire full advantage of power average (PA) operators proposed by Yager, the Pythagorean fuzzy Dombi power average (PyFDPA) operator, the Pythagorean fuzzy Dombi weighted power average (PyFDWPA) operator, Pythagorean fuzzy Dombi power geometric (PyFDPG) operator, Pythagorean fuzzy Dombi weighted geometric (PyFDPWG) operator, improved the existing AOs and their desirable properties are discussed. The foremost qualities of these developed Dombi power aggregation operators is that they purge the cause of discomfited data and are more supple due to general parameter. Additionally, based on these Dombi power AOs, a novel MADM approach is instituted. Finally, a numerical example is given to show the realism and efficacy of the proposed approach and judgment with the existing approaches is also specified.
Keywords: Pythagorean fuzzy set, PA operator, Dombi t-norm and Dombi t-conorm, MADM
