Extension of TOPSIS method under intuitionistic fuzzy hypersoft environment based on correlation coefficient and aggregation operators to solve decision making problem

Rana Muhammad Zulqarnain; Xiao Long Xin; Muhammad Saeed; Rana Muhammad Zulqarnain; Xiao Long Xin; Muhammad Saeed

doi:10.3934/math.2021167

AIMS Mathematics

2021, Volume 6, Issue 3: 2732-2755. doi: 10.3934/math.2021167

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Research article

Extension of TOPSIS method under intuitionistic fuzzy hypersoft environment based on correlation coefficient and aggregation operators to solve decision making problem

1.
School of Mathematics, Northwest University Xi'an, China
2.
School of Science, Xi'an Polytechnic University, Xi'an 710048, China
3.
Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan

Received: 30 October 2020 Accepted: 20 December 2020 Published: 05 January 2021
MSC : 03E72, 62A86, 68T35, 90B50

Intuitionistic fuzzy hypersoft set is an extension of the intuitionistic fuzzy soft set used to express insufficient evaluation, uncertainty, and anxiety in decision-making. It is a new technique to realize computational intelligence and decision-making under uncertain conditions. The intuitionistic fuzzy hypersoft set can deal with uncertain and fuzzy information more effectively. The concepts and properties of the correlation coefficient and the weighted correlation coefficient of the intuitionistic fuzzy hypersoft sets are proposed in the following research. A prioritization technique for order preference by similarity to ideal solution (TOPSIS) based on correlation coefficients and weighted correlation coefficients is introduced under the intuitionistic fuzzy hypersoft sets. We also introduced aggregation operators, such as intuitionistic fuzzy hypersoft weighted average and intuitionistic fuzzy hypersoft weighted geometric operators. Based on the established TOPSIS method and aggregation operators, the decision-making algorithm is proposed under an intuitionistic fuzzy hypersoft environment to resolve uncertain and confusing information. A case study on decision-making difficulties proves the application of the proposed algorithm. Finally, a comparative analysis with the advantages, effectiveness, flexibility, and numerous existing studies demonstrates this method's effectiveness.
- hypersoft set,
- intuitionistic fuzzy soft set,
- intuitionistic fuzzy hypersoft set,
- correlation coefficient,
- weighted correlation coefficient,
- TOPSIS
Citation: Rana Muhammad Zulqarnain, Xiao Long Xin, Muhammad Saeed. Extension of TOPSIS method under intuitionistic fuzzy hypersoft environment based on correlation coefficient and aggregation operators to solve decision making problem[J]. AIMS Mathematics, 2021, 6(3): 2732-2755. doi: 10.3934/math.2021167

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Abstract

Intuitionistic fuzzy hypersoft set is an extension of the intuitionistic fuzzy soft set used to express insufficient evaluation, uncertainty, and anxiety in decision-making. It is a new technique to realize computational intelligence and decision-making under uncertain conditions. The intuitionistic fuzzy hypersoft set can deal with uncertain and fuzzy information more effectively. The concepts and properties of the correlation coefficient and the weighted correlation coefficient of the intuitionistic fuzzy hypersoft sets are proposed in the following research. A prioritization technique for order preference by similarity to ideal solution (TOPSIS) based on correlation coefficients and weighted correlation coefficients is introduced under the intuitionistic fuzzy hypersoft sets. We also introduced aggregation operators, such as intuitionistic fuzzy hypersoft weighted average and intuitionistic fuzzy hypersoft weighted geometric operators. Based on the established TOPSIS method and aggregation operators, the decision-making algorithm is proposed under an intuitionistic fuzzy hypersoft environment to resolve uncertain and confusing information. A case study on decision-making difficulties proves the application of the proposed algorithm. Finally, a comparative analysis with the advantages, effectiveness, flexibility, and numerous existing studies demonstrates this method's effectiveness.

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