New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis

Area of Science:

• Fuzzy Set Theory
• Information Theory
• Decision Sciences

Background:

• Intuitionistic fuzzy sets (IFS) have limitations in handling complex uncertain data.
• Pythagorean fuzzy sets (PFS) extend IFS, offering improved capabilities to address imperfections.
• Entropy measures quantify information content within fuzzy sets.

Purpose of the Study:

• To propose a new Pythagorean fuzzy entropy measure for Pythagorean fuzzy sets.
• To enhance the quantification of information within PFS.
• To provide a flexible tool for complex multi-criteria decision-making problems with uncertain data.

Main Methods:

• Development of a novel Pythagorean fuzzy entropy formula.
• Application of the entropy measure in a multi-criteria company selection case study.
• Comparative analysis with existing entropy measures for PFS and IFS.
• Integration of the entropy measure into the Complex Proportional Assessment (COPRAS) method for weight calculation.

Main Results:

• The proposed Pythagorean fuzzy entropy reliably quantifies the degree of fuzziness in both PFS and IFS.
• Numerical illustrations demonstrate the effectiveness and flexibility of the new entropy measure.
• The COPRAS method, utilizing weights derived from the proposed entropy, yields reliable decision-making outcomes.
• Comparative analysis confirms the similarity of results with existing state-of-the-art entropy methods.

Conclusions:

• The proposed Pythagorean fuzzy entropy is a valuable and flexible tool for complex decision-making under uncertainty.
• The new entropy measure offers a reliable method for assessing information content in PFS and IFS.
• The integration with COPRAS provides a robust approach for multi-criteria decision-making problems.