Cyber security control selection based decision support algorithm under single valued neutrosophic hesitant fuzzy Einstein aggregation information

Muhammad Kamran; Shahzaib Ashraf; Nadeem Salamat; Muhammad Naeem; Thongchai Botmart; Muhammad Kamran; Shahzaib Ashraf; Nadeem Salamat; Muhammad Naeem; Thongchai Botmart

doi:10.3934/math.2023280

AIMS Mathematics

2023, Volume 8, Issue 3: 5551-5573. doi: 10.3934/math.2023280

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Research article

Cyber security control selection based decision support algorithm under single valued neutrosophic hesitant fuzzy Einstein aggregation information

1.
Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan
2.
Department of Mathematics, Deanship of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia
3.
Department of Mathematics, Faculty of Sciences, Khon Kaen University, Khon Kaen 4002, Thailand
Correction on: AIMS Mathematics 8: 13795-13796.

Received: 18 September 2022 Revised: 03 December 2022 Accepted: 12 December 2022 Published: 19 December 2022
MSC : 03B52, 03E72

The single-valued neutrosophic hesitant fuzzy set (SV-NHFS) is a hybrid structure of the single-valued neutrosophic set and the hesitant fuzzy set that is designed for some incomplete, uncertain, and inconsistent situations in which each element has a few different values designed by the truth membership hesitant function, indeterminacy membership hesitant function, and falsity membership hesitant function. A strategic decision-making technique can help the decision-maker accomplish and analyze the information in an efficient manner. However, in our real lives, uncertainty will play a dominant role during the information collection phase. To handle such uncertainties in the data, we present a decision-making algorithm in the SV-NHFS environment. In this paper, we first presented the basic operational laws for SV-NHF information under Einstein's t-norm and t-conorm. Furthermore, important properties of Einstein operators, including the Einstein sum, product, and scalar multiplication, are done under SV-NHFSs. Then, we proposed a list of novel aggregation operators' names: Single-valued neutrosophic hesitant fuzzy Einstein weighted averaging, weighted geometric, order weighted averaging, and order weighted geometric aggregation operators. Finally, we discuss a multi-attribute decision-making (MADM) algorithm based on the proposed operators to address the problems in the SV-NHF environment. A numerical example is given to illustrate the work and compare the results with the results of the existing studies. Also, the sensitivity analysis and advantages of the stated algorithm are given in the work to verify and strengthen the study.
- neutrosophic information,
- aggregation operators,
- decision making
Citation: Muhammad Kamran, Shahzaib Ashraf, Nadeem Salamat, Muhammad Naeem, Thongchai Botmart. Cyber security control selection based decision support algorithm under single valued neutrosophic hesitant fuzzy Einstein aggregation information[J]. AIMS Mathematics, 2023, 8(3): 5551-5573. doi: 10.3934/math.2023280

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Abstract

The single-valued neutrosophic hesitant fuzzy set (SV-NHFS) is a hybrid structure of the single-valued neutrosophic set and the hesitant fuzzy set that is designed for some incomplete, uncertain, and inconsistent situations in which each element has a few different values designed by the truth membership hesitant function, indeterminacy membership hesitant function, and falsity membership hesitant function. A strategic decision-making technique can help the decision-maker accomplish and analyze the information in an efficient manner. However, in our real lives, uncertainty will play a dominant role during the information collection phase. To handle such uncertainties in the data, we present a decision-making algorithm in the SV-NHFS environment. In this paper, we first presented the basic operational laws for SV-NHF information under Einstein's t-norm and t-conorm. Furthermore, important properties of Einstein operators, including the Einstein sum, product, and scalar multiplication, are done under SV-NHFSs. Then, we proposed a list of novel aggregation operators' names: Single-valued neutrosophic hesitant fuzzy Einstein weighted averaging, weighted geometric, order weighted averaging, and order weighted geometric aggregation operators. Finally, we discuss a multi-attribute decision-making (MADM) algorithm based on the proposed operators to address the problems in the SV-NHF environment. A numerical example is given to illustrate the work and compare the results with the results of the existing studies. Also, the sensitivity analysis and advantages of the stated algorithm are given in the work to verify and strengthen the study.

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