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Area of Science:

  • Fuzzy mathematics and set theory.
  • Decision-making under uncertainty.
  • Computational intelligence.

Background:

  • Existing soft set structures are inadequate for real-world scenarios requiring classification of overlapping parameters.
  • Hypersoft sets provide a novel framework for handling such complex data structures.
  • Integrating fuzzy set theory with hypersoft sets addresses limitations in representing uncertainty.

Purpose of the Study:

  • To introduce novel fuzzy parameterized intuitionistic fuzzy hypersoft sets (fpifhs-set) and fuzzy parameterized neutrosophic hypersoft sets (fpnhs-set).
  • To develop and apply these new structures for decision-making problems, specifically addressing the COVID-19 pandemic.
  • To analyze the theoretical properties and operational characteristics of the proposed set structures.

Main Methods:

  • Development of fpifhs-set and fpnhs-set using algebraic and theoretical techniques.
  • Characterization of fundamental properties and set-theoretic operations for the novel structures.
  • Design of two novel algorithms for decision-making applications, validated against real-world data (COVID-19).

Main Results:

  • Successful development and theoretical validation of fpifhs-set and fpnhs-set.
  • Demonstrated efficacy of the proposed algorithms in solving a COVID-19 decision-making problem.
  • Comparative analysis showing advantageous aspects of the proposed models over existing methods.

Conclusions:

  • The proposed fuzzy parameterized hypersoft set structures effectively handle uncertainty and overlapping parameters in complex decision-making.
  • The developed algorithms provide a robust and advantageous approach for real-world applications like pandemic response.
  • The study establishes a foundation for further research into hypersoft set theory and its applications.