Novel complex fuzzy distance measures with hesitance values and their applications in complex decision-making...

Area of Science:

• Fuzzy mathematics
• Information theory
• Decision science

Background:

• Complex fuzzy distance measures (CFDMs) are crucial for high-dimensional data but often neglect data hesitancy.
• Existing CFDMs struggle to represent the degree of uncertainty or imprecision inherent in complex datasets.
• Handling uncertainty and imprecision is vital across various scientific and engineering domains.

Purpose of the Study:

• To introduce novel complex fuzzy distance measures, specifically the complex fuzzy hesitance distance measure and complex fuzzy Euclidean Hesitance distance measure.
• To generalize existing complex fuzzy normalized Hamming and Euclidean distance measures.
• To develop a robust decision-making algorithm integrating these new measures for complex real-world problems.

Main Methods:

• Development of new distance measures based on complex fuzzy sets, incorporating a hesitancy degree.
• Introduction of new complex fuzzy operations and primary results within the proposed CFDMs framework.
• Formulation of a novel decision-making algorithm utilizing the proposed CFDMs.

Main Results:

• The proposed complex fuzzy hesitance distance measures effectively quantify data hesitancy, a limitation of prior CFDMs.
• New complex fuzzy operations and results are established, expanding the theoretical foundation.
• The developed decision-making algorithm demonstrates robust application in handling complex problems.

Conclusions:

• The novel complex fuzzy hesitance distance measures offer a significant advancement in analyzing complex and uncertain data.
• The proposed measures and decision-making algorithm provide a more comprehensive approach to real-world decision problems.
• Comparative analysis confirms the superiority of the proposed CFDMs over existing methods in specific contexts.