Modeling uncertainties associated with multi-attribute decision-making based evaluation of cooling system using interval-valued complex intuitionistic fuzzy hypersoft settings

Muhammad Arshad; Muhammad Saeed; Atiqe Ur Rahman; Sanaa A. Bajri; Haifa Alqahtani; Hamiden Abd El-Wahed Khalifa; Muhammad Arshad; Muhammad Saeed; Atiqe Ur Rahman; Sanaa A. Bajri; Haifa Alqahtani; Hamiden Abd El-Wahed Khalifa

doi:10.3934/math.2024559

AIMS Mathematics

2024, Volume 9, Issue 5: 11396-11422. doi: 10.3934/math.2024559

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Research article

Modeling uncertainties associated with multi-attribute decision-making based evaluation of cooling system using interval-valued complex intuitionistic fuzzy hypersoft settings

1.
Department of Mathematics, University of Management and Technology, Lahore 54000, Pakistan
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
3.
Department of Statistics and Business Analytics, United Arab Emirates University, UAE
4.
Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia
5.
Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt

Received: 30 January 2024 Revised: 06 March 2024 Accepted: 15 March 2024 Published: 25 March 2024
MSC : 03E72, 68T35, 90B50

Academics encounter a challenge regulating data-driven unpredictability in numerous complicated decision scenarios. Regulating the cyclical nature of appraisal attributes, determining lower and higher limitations, granting multi-parametric values as a means of assessing argumentation, and modeling uncertainty are a few examples of these problems. It requires the incorporation of complex plane settings, interval-valued intuitionistic fuzzy settings, and hypersoft settings. Inspired by these kinds of scenarios, the goal of this research was to articulate a new theoretical framework, the interval-valued complex intuitionistic fuzzy hypersoft set ($ \Gamma $-set), which can handle these kinds of problems as a whole under the umbrella of a single framework. First, the concepts of $ \Gamma $-set, as well as its set operations and aggregations, such as decision matrix, cardinal matrix, aggregate matrix, and cardinality set, were examined. The second phase offers an appealing algorithm that consists of nine steps that go from taking into account necessary set construction to making the best choice. A prototype case study analyzing eighteen evaluation qualities and thirty-four sub-attributes for determining an optimal cooling system ($ \mathbb{CSYS}) $ for a factory validates the provided algorithm. Informative comparison analysis and preferred study features were provided as essential components of research to assist academics in making significant advances regarding their field and gradually, but thoroughly, advancing their specialization.
- complex fuzzy set,
- interval-valued fuzzy set,
- complex fuzzy soft set,
- hypersoft set,
- decision making,
- optimization
Citation: Muhammad Arshad, Muhammad Saeed, Atiqe Ur Rahman, Sanaa A. Bajri, Haifa Alqahtani, Hamiden Abd El-Wahed Khalifa. Modeling uncertainties associated with multi-attribute decision-making based evaluation of cooling system using interval-valued complex intuitionistic fuzzy hypersoft settings[J]. AIMS Mathematics, 2024, 9(5): 11396-11422. doi: 10.3934/math.2024559

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Abstract

Academics encounter a challenge regulating data-driven unpredictability in numerous complicated decision scenarios. Regulating the cyclical nature of appraisal attributes, determining lower and higher limitations, granting multi-parametric values as a means of assessing argumentation, and modeling uncertainty are a few examples of these problems. It requires the incorporation of complex plane settings, interval-valued intuitionistic fuzzy settings, and hypersoft settings. Inspired by these kinds of scenarios, the goal of this research was to articulate a new theoretical framework, the interval-valued complex intuitionistic fuzzy hypersoft set ($ \Gamma $-set), which can handle these kinds of problems as a whole under the umbrella of a single framework. First, the concepts of $ \Gamma $-set, as well as its set operations and aggregations, such as decision matrix, cardinal matrix, aggregate matrix, and cardinality set, were examined. The second phase offers an appealing algorithm that consists of nine steps that go from taking into account necessary set construction to making the best choice. A prototype case study analyzing eighteen evaluation qualities and thirty-four sub-attributes for determining an optimal cooling system ($ \mathbb{CSYS}) $ for a factory validates the provided algorithm. Informative comparison analysis and preferred study features were provided as essential components of research to assist academics in making significant advances regarding their field and gradually, but thoroughly, advancing their specialization.

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