Some average aggregation operators based on spherical fuzzy soft sets and their applications in multi-criteria decision making

Jabbar Ahmmad; Tahir Mahmood; Ronnason Chinram; Aiyared Iampan; Jabbar Ahmmad; Tahir Mahmood; Ronnason Chinram; Aiyared Iampan

doi:10.3934/math.2021454

AIMS Mathematics

2021, Volume 6, Issue 7: 7798-7832. doi: 10.3934/math.2021454

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Research article

Some average aggregation operators based on spherical fuzzy soft sets and their applications in multi-criteria decision making

1.
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
2.
Algebra and Applications Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand
3.
Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand

Received: 16 February 2021 Accepted: 11 May 2021 Published: 17 May 2021
MSC : 03E72, 62C86

Spherical fuzzy soft sets $\left(SF{{S}_{ft}}Ss \right)$ have its importance in a situation where human opinion is not only restricted to yes or no but some kind of abstinence or refusal aspects are also involved. Moreover, the notion of $SF{{S}_{ft}}S$ is free from all that complexities which suffers the contemporary theories because parameterization toll is a more important character of $SF{{S}_{ft}}S$. Also, note that aggregation operators are very effective apparatus to convert the overall information into a single value which further helps in decision-making problems. Due to these reasons, based on a spherical fuzzy soft set $\left(SF{{S}_{ft}}S \right)$, we have first introduced basic operational laws and then based on these introduced operational laws, some new notions like spherical fuzzy soft weighted average $\left(SF{{S}_{ft}}WA \right)$ aggregation operator, spherical fuzzy soft ordered weighted average $\left(SF{{S}_{ft}}OWA \right)$ aggregation operator and spherical fuzzy soft hybrid average $\left(SF{{S}_{ft}}HA \right)$ aggregation operators are introduced. Furthermore, the properties of these aggregation operators are discussed in detail. An algorithm is established in the environment of $SF{{S}_{ft}}S$ and a numerical example are given to show the authenticity of the introduced work. Moreover, a comparative study is established with other existing methods to show the validity and superiority of the established work.
- spherical fuzzy set,
- spherical fuzzy soft set,
- aggregation operators,
- multicriteria decision making
Citation: Jabbar Ahmmad, Tahir Mahmood, Ronnason Chinram, Aiyared Iampan. Some average aggregation operators based on spherical fuzzy soft sets and their applications in multi-criteria decision making[J]. AIMS Mathematics, 2021, 6(7): 7798-7832. doi: 10.3934/math.2021454

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Abstract

Spherical fuzzy soft sets $\left(SF{{S}_{ft}}Ss \right)$ have its importance in a situation where human opinion is not only restricted to yes or no but some kind of abstinence or refusal aspects are also involved. Moreover, the notion of $SF{{S}_{ft}}S$ is free from all that complexities which suffers the contemporary theories because parameterization toll is a more important character of $SF{{S}_{ft}}S$. Also, note that aggregation operators are very effective apparatus to convert the overall information into a single value which further helps in decision-making problems. Due to these reasons, based on a spherical fuzzy soft set $\left(SF{{S}_{ft}}S \right)$, we have first introduced basic operational laws and then based on these introduced operational laws, some new notions like spherical fuzzy soft weighted average $\left(SF{{S}_{ft}}WA \right)$ aggregation operator, spherical fuzzy soft ordered weighted average $\left(SF{{S}_{ft}}OWA \right)$ aggregation operator and spherical fuzzy soft hybrid average $\left(SF{{S}_{ft}}HA \right)$ aggregation operators are introduced. Furthermore, the properties of these aggregation operators are discussed in detail. An algorithm is established in the environment of $SF{{S}_{ft}}S$ and a numerical example are given to show the authenticity of the introduced work. Moreover, a comparative study is established with other existing methods to show the validity and superiority of the established work.

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