q-Spherical fuzzy rough sets and their usage in multi-attribute decision-making problems

Ahmad Bin Azim; Ahmad ALoqaily; Asad Ali; Sumbal Ali; Nabil Mlaiki; Fawad Hussain; Ahmad Bin Azim; Ahmad ALoqaily; Asad Ali; Sumbal Ali; Nabil Mlaiki; Fawad Hussain

doi:10.3934/math.2023415

AIMS Mathematics

2023, Volume 8, Issue 4: 8210-8248. doi: 10.3934/math.2023415

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q-Spherical fuzzy rough sets and their usage in multi-attribute decision-making problems

1.
Department of Mathematics & Statistics, Hazara University, Mansehra, 21120 Pakistan
2.
Department of Mathematics and Sciences, Prince Sultan University. Riyadh, 11586 Saudi Arabia
3.
School of computer, Data, and Mathematical Sciences, Western Sydney University, Australia-Sydney-2150
4.
Department of Mathematics, Abbottabad University of Science and Technology, Pakistan

Received: 15 October 2020 Revised: 07 January 2023 Accepted: 16 January 2023 Published: 01 February 2023
MSC : 60L70, 68N17

This article's purpose is to investigate and generalize the concepts of rough set, in addition to the q-spherical fuzzy set, and to introduce a novel concept that is called q-spherical fuzzy rough set (q-SFRS). This novel approach avoids the complications of more recent ideas like the intuitionistic fuzzy rough set, Pythagorean fuzzy rough set, and q-rung orthopair fuzzy rough set. Since mathematical operations known as "aggregation operators" are used to bring together sets of data. Popular aggregation operations include the arithmetic mean and the weighted mean. The key distinction between the weighted mean and the arithmetic mean is that the latter allows us to weight the various values based on their importance. Various aggregation operators make different assumptions about the input (data kinds) and the kind of information that may be included in the model. Because of this, some new q-spherical fuzzy rough weighted arithmetic mean operator and q-spherical fuzzy rough weighted geometric mean operator have been introduced. The developed operators are more general. Because the picture fuzzy rough weighted arithmetic mean (PFRWAM) operator, picture fuzzy rough weighted geometric mean (PFRWGM) operator, spherical fuzzy rough weighted arithmetic mean (SFRWAM) operator and spherical fuzzy rough weighted geometric mean (SFRWGM) operator are all the special cases of the q-SFRWAM and q-SFRWGM operators. When parameter q = 1, the q-SFRWAM operator reduces the PFRWAM operator, and the q-SFRWGM operator reduces the PFRWGM operator. When parameter q = 2, the q-SFRWAM operator reduces the SFRWAM operator, and the q-SFRWGM operator reduces the SFRWGM operator. Besides, our approach is more flexible, and decision-makers can choose different values of parameter q according to the different risk attitudes. In addition, the basic properties of these newly presented operators have been analyzed in great depth and expounded upon. Additionally, a technique called multi-criteria decision-making (MCDM) has been established, and a detailed example has been supplied to back up the recently introduced work. An evaluation of the offered methodology is established at the article's conclusion. The results of this research show that, compared to the q-spherical fuzzy set, our method is better and more effective.
- q-spherical fuzzy relation,
- q-spherical fuzzy approximation,
- q-spherical fuzzy rough set,
- aggregation operators,
- decision-making problems
Citation: Ahmad Bin Azim, Ahmad ALoqaily, Asad Ali, Sumbal Ali, Nabil Mlaiki, Fawad Hussain. q-Spherical fuzzy rough sets and their usage in multi-attribute decision-making problems[J]. AIMS Mathematics, 2023, 8(4): 8210-8248. doi: 10.3934/math.2023415

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Abstract

This article's purpose is to investigate and generalize the concepts of rough set, in addition to the q-spherical fuzzy set, and to introduce a novel concept that is called q-spherical fuzzy rough set (q-SFRS). This novel approach avoids the complications of more recent ideas like the intuitionistic fuzzy rough set, Pythagorean fuzzy rough set, and q-rung orthopair fuzzy rough set. Since mathematical operations known as "aggregation operators" are used to bring together sets of data. Popular aggregation operations include the arithmetic mean and the weighted mean. The key distinction between the weighted mean and the arithmetic mean is that the latter allows us to weight the various values based on their importance. Various aggregation operators make different assumptions about the input (data kinds) and the kind of information that may be included in the model. Because of this, some new q-spherical fuzzy rough weighted arithmetic mean operator and q-spherical fuzzy rough weighted geometric mean operator have been introduced. The developed operators are more general. Because the picture fuzzy rough weighted arithmetic mean (PFRWAM) operator, picture fuzzy rough weighted geometric mean (PFRWGM) operator, spherical fuzzy rough weighted arithmetic mean (SFRWAM) operator and spherical fuzzy rough weighted geometric mean (SFRWGM) operator are all the special cases of the q-SFRWAM and q-SFRWGM operators. When parameter q = 1, the q-SFRWAM operator reduces the PFRWAM operator, and the q-SFRWGM operator reduces the PFRWGM operator. When parameter q = 2, the q-SFRWAM operator reduces the SFRWAM operator, and the q-SFRWGM operator reduces the SFRWGM operator. Besides, our approach is more flexible, and decision-makers can choose different values of parameter q according to the different risk attitudes. In addition, the basic properties of these newly presented operators have been analyzed in great depth and expounded upon. Additionally, a technique called multi-criteria decision-making (MCDM) has been established, and a detailed example has been supplied to back up the recently introduced work. An evaluation of the offered methodology is established at the article's conclusion. The results of this research show that, compared to the q-spherical fuzzy set, our method is better and more effective.

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