Explainable Uncertain Rule-Based Fuzzy Systems

Jerry M. Mendel received the Ph.D. degree in Electrical Engineering from the Polytechnic Institute of Brooklyn, Brooklyn, NY. Currently, he is Emeritus Professor of Electrical Engineering at the University of Southern California in Los Angeles, where he worked for 44 years. He has published close to 600 technical papers and is author and/or co-author of 12 books, including Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Directions (Prentice-Hall, 2001), Perceptual Computing: Aiding People in Making Subjective Judgments (Wiley & IEEE Press, 2010), Introduction to Type-2 Fuzzy Logic Control: Theory and Application (Wiley & IEEE Press, 2014) and Uncertain Rule-based Fuzzy Systems: Introduction and New Directions, 2nd ed. (Springer, 2017). He is a Life Fellow of the IEEE, a Distinguished Member of the IEEE Control Systems Society, and a Fellow of the International Fuzzy Systems Association and the Asia-Pacific AI Association. He was President of the IEEE Control Systems Society in 1986, a member of the Administrative Committee of the IEEE Computational Intelligence Society for nine years, and Chairman of its Fuzzy Systems Technical Committee and the Computing With Words Task Force of that TC. Among his awards are the 1983 Best Transactions Paper Award of the IEEE Geoscience and Remote Sensing Society, the 1992 Signal Processing Society Paper Award, the 2002 and 2014 Transactions on Fuzzy Systems Outstanding Paper Awards, a 1984 IEEE Centennial Medal, an IEEE Third Millenium Medal, a Fuzzy Systems Pioneer Award (2008) from the IEEE Computational Intelligence Society for fundamental theoretical contributions and seminal results in fuzzy systems, and the 2021 IEEE Lotfi A. Zadeh Pioneer Award for developing and promoting type-2 fuzzy logic. As of March 27, 2023, his publications have been cited (Google Scholar) more than 63,000 times, with an h-index of 100 and an i10-index of 320.

“Explainable uncertain rule-based fuzzy systems is a significant contribution to the field of computational intelligence. It provides valuable insights into the integration of uncertainty and interpretability in fuzzy logic systems, making it an essential resource for researchers and practitioners seeking to advance their understanding of explainable AI(XAI).” (Wael Badawy, Computing Reviews, June 27, 2025)

• Introduction.- Part 1: Type-1 Fuzzy Sets and Systems.- Short Primers on Type-1 Fuzzy Sets and Fuzzy Logic.- Type-1 Fuzzy Logic Systems.- Part 2: Type-2 Fuzzy Sets.- Sources of Uncertainty.- Type-2 Fuzzy Sets.- Operations on and Properties OF Type-2 Fuzzy Sets.- Type-2 Relations and Compositions.- Centroid of a Type-2 Fuzzy Set: Type-Reduction.- Part 3: Type-2 Fuzzy Logic Systems.- Mamdani Interval Type-2 Fuzzy Logic Systems (IT2 FLSS).- TSK Interval Type-2 Fuzzy Logic Systems.- General Type-2 Fuzzy Logic Systems (GT2 FLSS).- Conclusion.