Max-Min Aggregation in Fuzzy Linguistic Systems and Machine Learning: A Narrative Review

Nguyen Van Han

doi:10.4108/eetcasa.9751

Authors

Nguyen Van Han Thuyloi University https://orcid.org/0000-0002-4054-565X

DOI:

https://doi.org/10.4108/eetcasa.9751

Keywords:

Linguistic Variables, Aggregation Operators, Explainable AI, Machine Learning, Max-Min Aggregation, Fuzzy logic, Fuzzy Linguistic Systems

Abstract

Max-min aggregation functions play a fundamental role in fuzzy linguistic systems and machine learning by providing interpretable and mathematically sound methods for combining imprecise and qualitative information. This narrative review synthesizes the key concepts, models, and applications of max-min aggregation, highlighting its significance in enabling human-centric reasoning and explainable AI. We discuss theoretical foundations, linguistic modeling frameworks, and diverse practical applications, including decision support systems and fuzzy rule-based classifiers. Challenges such as scalability, integration with deep learning, and semantic standardization are identified, along with promising future research directions. This review aims to provide a comprehensive understanding of max-min aggregation’s contributions to interpretable and flexible AI systems

References

[1] José Alcalá-Fdez, Luciano Sánchez, Salvador García, María J del Jesus, Sebastián Ventura, Cristóbal Romero, Jaume Bacardit, Vicente M Rivas, Alberto Fernández, and Francisco Herrera. Fuzzy association rules: General model and applications. IEEE Transactions on Fuzzy Systems, 19(5):845–865, 2011.

[2] Sergio Alonso and Enrique Herrera-Viedma. Handling qualitative ratings in multi-criteria decision making processes with linguistic labels. Information Sciences, 177(23):5404–5418, 2007.

[3] Gleb Beliakov, Ana Pradera, and Tomasa Calvo. Aggregation functions: A guide for practitioners. Springer Science & Business Media, 2007.

[4] Oscar Castillo and Patricia Melin. Integration of fuzzy logic in data mining and big data analytics: A review. Soft Computing, 11(8):665–679, 2007.

[5] Oscar Cordón, Francisco Herrera, Falk Hoffmann, and Luis Magdalena. Genetic fuzzy systems: Evolutionary tuning and learning of fuzzy knowledge bases. World Scientific, 2001.

[6] Jianguo Deng, Weiguo Jiang, and Jiashuai Hu. Developing interpretable fuzzy systems for medical decision support: A genetic fuzzy rule-based approach. Expert Systems with Applications, 127:115–126, 2019.

[7] Soumik Ghosh, Arnab Kumar Ghosh, and Swagatam Das. Fuzzy logic for explainable machine learning: A survey. IEEE Transactions on Fuzzy Systems, 2022. In press.

[8] Francisco Herrera and Luis Martínez. Linguistic decision analysis: Steps for solving decision problems under linguistic information. Fuzzy Sets and Systems, 115(1):67–82, 2000.

[9] Erich Peter Klement, Radko Mesiar, and Endre Pap. Triangular norms. Springer Science & Business Media, 2000.

[10] Jerry M Mendel. Uncertain rule-based fuzzy logic systems: Introduction and new directions. Prentice Hall, 2001.

[11] Ronald R Yager. On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Transactions on Systems, Man, and Cybernetics, 18(1):183–190, 1988.

[12] Lotfi A Zadeh. The concept of a linguistic variable and its application to approximate reasoning—i. Information sciences, 8(3):199 249, 1975.

[13] Lotfi A Zadeh. Fuzzy logic = computing with words. IEEE Transactions on Fuzzy Systems, 4(2):103–111, 1996.

[14] Hans-Jürgen Zimmermann. Fuzzy set theory—and its applications. Springer Science & Business Media, 1991.