Aczel-Alsina-based aggregation operators for intuitionistic hesitant fuzzy set environment and their application to multiple attribute decision-making process

Wajid Ali; Tanzeela Shaheen; Iftikhar Ul Haq; Hamza Toor; Faraz Akram; Harish Garg; Md. Zia Uddin; Mohammad Mehedi Hassan; Wajid Ali; Tanzeela Shaheen; Iftikhar Ul Haq; Hamza Toor; Faraz Akram; Harish Garg; Md. Zia Uddin; Mohammad Mehedi Hassan

doi:10.3934/math.2023916

AIMS Mathematics

2023, Volume 8, Issue 8: 18021-18039. doi: 10.3934/math.2023916

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Aczel-Alsina-based aggregation operators for intuitionistic hesitant fuzzy set environment and their application to multiple attribute decision-making process

1.
Department of Mathematics, Air University, E-9, Islamabad, Pakistan
2.
Biomedical Engineering Department, Riphah International University, Islamabad, Pakistan
3.
School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala-147004, Punjab, India
4.
Department of Mathematics, Graphic Era Deemed to be University, Dehradun, 248002, Uttarakhand, India
5.
Software and Service Innovation, SINTEF Digital, Oslo-0373, Norway
6.
Information Systems Department, College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi Arabia

Received: 10 February 2023 Revised: 28 April 2023 Accepted: 09 May 2023 Published: 25 May 2023
MSC : 03E72, 08A72, 54A40

An intuitionistic hesitant fuzzy set is an extension of the fuzzy set which deals with uncertain information and vague environments. Multiple-attribute decision-making problems (MADM) are one of the emerging topics and an aggregation operator plays a vital role in the aggregate of different preferences to a single number. The Aczel-Alsina norm operations are significant terms that handle the impreciseness and undetermined data. In this paper, we build some novel aggregation operators for the different pairs of the intuitionistic hesitant fuzzy sets (IHFSs), namely as Aczel-Alsina average and geometric operators. Several characteristics of the proposed operators are also described in detail. Based on these operators, a multi-attribute decision-making algorithm is stated to solve the decision-making problems. A numerical example has been taken to display and validate the approach. A feasibility and comparative analysis with existing studies are performed to show its superiority.
- intuitionistic fuzzy sets,
- IHFSs,
- Aczel-Alsina aggregation operators,
- MADM
Citation: Wajid Ali, Tanzeela Shaheen, Iftikhar Ul Haq, Hamza Toor, Faraz Akram, Harish Garg, Md. Zia Uddin, Mohammad Mehedi Hassan. Aczel-Alsina-based aggregation operators for intuitionistic hesitant fuzzy set environment and their application to multiple attribute decision-making process[J]. AIMS Mathematics, 2023, 8(8): 18021-18039. doi: 10.3934/math.2023916

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Abstract

An intuitionistic hesitant fuzzy set is an extension of the fuzzy set which deals with uncertain information and vague environments. Multiple-attribute decision-making problems (MADM) are one of the emerging topics and an aggregation operator plays a vital role in the aggregate of different preferences to a single number. The Aczel-Alsina norm operations are significant terms that handle the impreciseness and undetermined data. In this paper, we build some novel aggregation operators for the different pairs of the intuitionistic hesitant fuzzy sets (IHFSs), namely as Aczel-Alsina average and geometric operators. Several characteristics of the proposed operators are also described in detail. Based on these operators, a multi-attribute decision-making algorithm is stated to solve the decision-making problems. A numerical example has been taken to display and validate the approach. A feasibility and comparative analysis with existing studies are performed to show its superiority.

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