A novel picture fuzzy Aczel-Alsina geometric aggregation information: Application to determining the factors affecting mango crops

Muhammad Naeem; Younas Khan; Shahzaib Ashraf; Wajaree Weera; Bushra Batool; Muhammad Naeem; Younas Khan; Shahzaib Ashraf; Wajaree Weera; Bushra Batool

doi:10.3934/math.2022681

AIMS Mathematics

2022, Volume 7, Issue 7: 12264-12288. doi: 10.3934/math.2022681

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Research article

A novel picture fuzzy Aczel-Alsina geometric aggregation information: Application to determining the factors affecting mango crops

1.
Deanship of Combined First Year, Umm Al-Qura University, Makkah, Saudi Arabia
2.
Department of Rural Sociology, The University of Agriculture, Peshawar, Pakistan
3.
Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan
4.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
5.
Department of Mathematics, University of Sargodha, Sargodha, Pakistan

Received: 28 December 2021 Revised: 31 March 2022 Accepted: 19 April 2022 Published: 24 April 2022
MSC : 03B52, 03E72

Picture fuzzy (PF) sets are extremely reasonable to represent the uncertain, imprecise, and inconsistent information that exists in scientific and engineering fields. To meet decision makers' preference selection, the operational flexibility of aggregation operators shows its importance in dealing with the flexible decision-making problems in the PF environment. With assistance from Aczel-Alsina operations, we introduce the aggregation strategies of PFNs. We initially broaden the Aczel-Alsina norms to PF situations and present a few new operations of PFNs in view of which we build up a few new PF aggregation operators, for instance, the PF Aczel-Alsina weighted geometric, order weighted geometric, and hybrid weighted geometric operators. Furthermore, a decision support approach has been developed using the proposed aggregation operators under the PF environment. In this method, the aggregated results of each evaluated alternative are determined, and their score values are obtained. Then, all alternatives were ranked in decreasing order, and the best one was determined based on the highest score value. An illustrative example related to mango production is presented to investigate the most influential factor that resulted in mango production minimization. Finally, a comparison study was conducted on the proposed decision support method and the existing relative techniques. The result shows that the proposed method can overcome the insufficiency of lacking decision flexibility in the existing MAGDM method by the PF weighted geometric aggregation operators.
- Aczel-Alsina norms,
- picture fuzzy numbers,
- geometric operators,
- decision making
Citation: Muhammad Naeem, Younas Khan, Shahzaib Ashraf, Wajaree Weera, Bushra Batool. A novel picture fuzzy Aczel-Alsina geometric aggregation information: Application to determining the factors affecting mango crops[J]. AIMS Mathematics, 2022, 7(7): 12264-12288. doi: 10.3934/math.2022681

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Abstract

Picture fuzzy (PF) sets are extremely reasonable to represent the uncertain, imprecise, and inconsistent information that exists in scientific and engineering fields. To meet decision makers' preference selection, the operational flexibility of aggregation operators shows its importance in dealing with the flexible decision-making problems in the PF environment. With assistance from Aczel-Alsina operations, we introduce the aggregation strategies of PFNs. We initially broaden the Aczel-Alsina norms to PF situations and present a few new operations of PFNs in view of which we build up a few new PF aggregation operators, for instance, the PF Aczel-Alsina weighted geometric, order weighted geometric, and hybrid weighted geometric operators. Furthermore, a decision support approach has been developed using the proposed aggregation operators under the PF environment. In this method, the aggregated results of each evaluated alternative are determined, and their score values are obtained. Then, all alternatives were ranked in decreasing order, and the best one was determined based on the highest score value. An illustrative example related to mango production is presented to investigate the most influential factor that resulted in mango production minimization. Finally, a comparison study was conducted on the proposed decision support method and the existing relative techniques. The result shows that the proposed method can overcome the insufficiency of lacking decision flexibility in the existing MAGDM method by the PF weighted geometric aggregation operators.

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