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This study introduces new correlation measures for hesitant 2-tuple fuzzy linguistic sets (H2FLS) to analyze subjective data. The findings show these new methods are more effective for decision-making than existing techniques.

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Area of Science:

  • Statistics
  • Decision Science
  • Fuzzy Set Theory

Background:

  • Correlation analysis is crucial for statistical data interpretation, measuring linear relationships between variables.
  • Hesitant 2-tuple fuzzy linguistic sets (H2FLS) are effective for handling subjective and reluctant data.
  • Existing correlation measures may not adequately address the complexities of fuzzy linguistic data.

Purpose of the Study:

  • To develop and apply novel correlation measures for hesitant 2-tuple fuzzy linguistic sets (H2FLS).
  • To introduce concepts of mean and variance for hesitant 2-tuple fuzzy linguistic elements (H2FLEs).
  • To extend correlation analysis to include weighted and ordered weighted coefficients for H2FLSs.

Main Methods:

  • Introduction of mean and variance for hesitant 2-tuple fuzzy linguistic elements (H2FLEs).
  • Development of a new correlation coefficient for H2FLSs.
  • Investigation of weighted and ordered weighted correlation coefficients.
  • Application of the Best-Worst Method (BWM) for determining criteria weights in unknown scenarios.

Main Results:

  • A new correlation coefficient for H2FLSs was established, demonstrating superior performance.
  • Weighted and ordered weighted correlation coefficients were developed and applied.
  • The proposed methods were validated through a practical decision-making example.
  • Comparative analysis confirmed the enhanced applicability of the new correlation measures.

Conclusions:

  • The proposed correlation coefficient for H2FLSs offers a more satisfactory approach compared to existing methods.
  • The developed techniques are applicable and effective for decision-making processes, even with unknown criteria weights.
  • This research enhances the utility of H2FLS in statistical analysis and decision support systems.