Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making

Area of Science:

• Fuzzy Set Theory
• Information Theory
• Decision Sciences

Background:

• Existing knowledge/uncertainty measures for Atanassov's intuitionistic fuzzy sets (AIFS) often rely on intuitionistic fuzzy entropy, which may not accurately reflect knowledge content.
• Approaches based on the distinction between an AIFS and its complement can lead to information loss during decision-making processes.

Purpose of the Study:

• To develop a more applicable and accurate knowledge measure for AIFS.
• To quantify the knowledge amount of an AIFS by measuring its distance to the AIFS with maximum uncertainty.
• To extend axiomatic properties for knowledge measures to a more general level.

Main Methods:

• Quantified knowledge amount of an AIFS using the distance to the AIFS with maximum uncertainty.
• Developed a new knowledge measure based on an intuitionistic fuzzy distance measure.
• Investigated properties of the proposed measure through mathematical analysis and numerical examples.

Main Results:

• A novel distance-based knowledge measure for AIFS was developed and its properties analyzed.
• The proposed measure overcomes limitations of existing entropy-based and complementary set-based approaches.
• The measure was successfully applied to multi-attribute group decision-making (MAGDM) problems.

Conclusions:

• The proposed knowledge measure provides a more effective way to quantify knowledge in AIFS.
• The developed MAGDM method, utilizing the new knowledge measure, is effective for evaluating threats, such as malicious code.
• The study demonstrates the practical utility and validity of the proposed approach in real-world applications.