A novel approach towards Heronian mean operators in multiple attribute decision making under the environment of bipolar complex fuzzy information

Tahir Mahmood; Ubaid Ur Rehman; Muhammad Naeem; Tahir Mahmood; Ubaid Ur Rehman; Muhammad Naeem

doi:10.3934/math.2023095

AIMS Mathematics

2023, Volume 8, Issue 1: 1848-1870. doi: 10.3934/math.2023095

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A novel approach towards Heronian mean operators in multiple attribute decision making under the environment of bipolar complex fuzzy information

1.
Department of Mathematics and Statistics, International Islamic University Islamabad, Pakistan
2.
Deanship of Joint First Year Umm Al-Qura University Makkah, Saudi Arabia

Received: 01 September 2022 Revised: 01 October 2022 Accepted: 10 October 2022 Published: 26 October 2022
MSC : 03E72, 90B50, 90C31

One of the most effective and impressive approaches to tackle uncertainty is the theory of bipolar complex fuzzy set (BCFS). The theory of BCFS modified the theory of fuzzy set (FS), bipolar FS (BFS), and complex FS. Further, the Heronian mean (HM) and generalized HM (GHM) give the aggregation operators (AOs), which have the benefits of taking into account the interrelatedness among the parameters. Up till now, in the prevailing literature, these operators are not introduced in the setting of BCFS. Thus, in this article, our goal is to introduce HM and GHM operators under a bipolar complex fuzzy setting. Firstly, we initiate the bipolar complex fuzzy generalized Heronian mean (BCFGHM) operator. Then, a few of its particular cases by changing the values of the parameter to show its supremacy. We also initiate the bipolar complex fuzzy weighted generalized Heronian mean (BCFWGHM) operator. Secondly, we interpret a method called the "multiple attribute decision making" (MADM) procedure by employing the initiated operators. Next, we provide a descriptive example (selection of the finest renewable energy generation project) to portray the applicability and usefulness of the initiated MADM procedure. Finally, to demonstrate the usefulness of the propounded operators and MADM procedure we compare our initiated work with several present operators and MADM techniques.
- bipolar complex fuzzy sets,
- generalized Heronian mean operators,
- decision-making procedure
Citation: Tahir Mahmood, Ubaid Ur Rehman, Muhammad Naeem. A novel approach towards Heronian mean operators in multiple attribute decision making under the environment of bipolar complex fuzzy information[J]. AIMS Mathematics, 2023, 8(1): 1848-1870. doi: 10.3934/math.2023095

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Abstract

One of the most effective and impressive approaches to tackle uncertainty is the theory of bipolar complex fuzzy set (BCFS). The theory of BCFS modified the theory of fuzzy set (FS), bipolar FS (BFS), and complex FS. Further, the Heronian mean (HM) and generalized HM (GHM) give the aggregation operators (AOs), which have the benefits of taking into account the interrelatedness among the parameters. Up till now, in the prevailing literature, these operators are not introduced in the setting of BCFS. Thus, in this article, our goal is to introduce HM and GHM operators under a bipolar complex fuzzy setting. Firstly, we initiate the bipolar complex fuzzy generalized Heronian mean (BCFGHM) operator. Then, a few of its particular cases by changing the values of the parameter to show its supremacy. We also initiate the bipolar complex fuzzy weighted generalized Heronian mean (BCFWGHM) operator. Secondly, we interpret a method called the "multiple attribute decision making" (MADM) procedure by employing the initiated operators. Next, we provide a descriptive example (selection of the finest renewable energy generation project) to portray the applicability and usefulness of the initiated MADM procedure. Finally, to demonstrate the usefulness of the propounded operators and MADM procedure we compare our initiated work with several present operators and MADM techniques.

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