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Complex pythagorean fuzzy aggregation operators based on confidence levels and their applications.

Tahir Mahmood1, Zeeshan Ali1, Kifayat Ullah2

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Summary

This study introduces new operational laws for complex Pythagorean fuzzy (CPF) settings and novel confidence operators (CCPFWA, CCPFOWA, CCPFWG, CCPFOWG) to analyze decision-making alternatives. These methods enhance multi-attribute decision-making (MADM) with detailed analysis and graphical representation.

Keywords:
aggregation operatorscomplex pythagorean fuzzy setsconfidence levelsdecision making

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Area of Science:

  • Decision Sciences
  • Fuzzy Logic Systems
  • Operations Research

Background:

  • Complex Pythagorean fuzzy (CPF) sets offer advanced modeling capabilities for uncertainty.
  • Existing methods for multi-attribute decision-making (MADM) may lack precision in complex scenarios.

Purpose of the Study:

  • To develop novel operational laws and confidence operators for CPF settings.
  • To introduce new confidence CPF weighted averaging (CCPFWA), ordered weighted averaging (CCPFOWA), weighted geometric (CCPFWG), and ordered weighted geometric (CCPFOWG) operators.
  • To apply these operators in a MADM framework for evaluating alternatives.

Main Methods:

  • Development of new operational laws for complex Pythagorean fuzzy numbers.
  • Introduction of four novel confidence-based CPF aggregation operators.
  • Application of these operators within a multi-attribute decision-making (MADM) model.
  • Comparative analysis, sensitivity analysis, and graphical illustrations.

Main Results:

  • The proposed operational laws and confidence operators effectively handle complex Pythagorean fuzzy data.
  • The developed MADM approach demonstrates superiority and capability in selecting optimal alternatives.
  • Sensitivity analysis confirms the robustness and practicality of the proposed methods.

Conclusions:

  • The new CPF operational laws and confidence operators provide a powerful tool for decision-making.
  • The introduced MADM framework offers a reliable method for complex decision problems.
  • The study highlights the effectiveness and advantages of the proposed techniques through practical examples.