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AIMS Mathematics

2023, Volume 8, Issue 5: 11916-11942. doi: 10.3934/math.2023602
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Research article

Sine hyperbolic fractional orthotriple linear Diophantine fuzzy aggregation operator and its application in decision making

  • 1.
    Department of Mathematics Deanship of Applied Sciences Umm Al-Qura University, Makkah, Saudi Arabia
  • 2.
    Department of Mathematics, Riphah International University Faisalabad Campus, Pakistan
  • 3.
    Programme of Mathematics, Faculty of Ocean Engineering Technology and Informatics Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia
  • 4.
    Department of Mathematics, Abdul Wali khan University Mardan, KP, Pakistan
  • Received: 29 December 2022 Revised: 27 February 2023 Accepted: 02 March 2023 Published: 20 March 2023

  • MSC : 03E72, 47S40

  • The idea of sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs), which allows more uncertainty than fractional orthotriple fuzzy sets (FOFSs) is noteworthy. The regularity and symmetry of the origin are maintained by the widely recognized sine hyperbolic function, which satisfies the experts' expectations for the properties of the multi-time process. Compared to fractional orthotriple linear Diophantine fuzzy sets, sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs) provide a significant idea for enabling more uncertainty. The objective of this research is to provide some reliable sine hyperbolic operational laws for FOLDFSs in order to sustain these properties and the significance of sinh-FOLDFSs. Both the accuracy and score functions for the sinh-FOLDFSs are defined. We define a group of averaging and geometric aggregation operators on the basis of algebraic t-norm and t-conorm operations. The basic characteristics of the defined operators are studied. Using the specified aggregation operators, a group decision-making method for solving real-life decision-making problem is proposed. To verify the validity of the proposed method, we compare our method with other existing methods.

    Citation: Muhammad Naeem, Muhammad Qiyas, Lazim Abdullah, Neelam Khan. Sine hyperbolic fractional orthotriple linear Diophantine fuzzy aggregation operator and its application in decision making[J]. AIMS Mathematics, 2023, 8(5): 11916-11942. doi: 10.3934/math.2023602

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  • The idea of sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs), which allows more uncertainty than fractional orthotriple fuzzy sets (FOFSs) is noteworthy. The regularity and symmetry of the origin are maintained by the widely recognized sine hyperbolic function, which satisfies the experts' expectations for the properties of the multi-time process. Compared to fractional orthotriple linear Diophantine fuzzy sets, sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs) provide a significant idea for enabling more uncertainty. The objective of this research is to provide some reliable sine hyperbolic operational laws for FOLDFSs in order to sustain these properties and the significance of sinh-FOLDFSs. Both the accuracy and score functions for the sinh-FOLDFSs are defined. We define a group of averaging and geometric aggregation operators on the basis of algebraic t-norm and t-conorm operations. The basic characteristics of the defined operators are studied. Using the specified aggregation operators, a group decision-making method for solving real-life decision-making problem is proposed. To verify the validity of the proposed method, we compare our method with other existing methods.


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