Complex, Hypercomplex and Fuzzy-Valued Neural Networks

Agnieszka Niemczynowicz, PhD, is an Associate Professor at Cracow University of Technology. Her work focuses on mathematical modeling, data analysis, and machine learning, applied across science and engineering. She has published ~50 articles, led international grants, and received the 2022 Doak Award for a top paper in the Journal of Sound and Vibration.racow University of Technology, PolandIrina Perfilieva, Ph.D., Dr.h.c., is an author and co-author of seven books on mathematical principles of fuzzy sets and fuzzy logic, and more than 270 papers in the area of fuzzy logic, fuzzy approximation and fuzzy relation equations. She has received several awards, including an IFSA fellow and an honorary member of EUSFLAT. Her recent interests are in the area of data analysis and the mathematical foundation of neural networks.Dr. Luis M. Garcia Raffi is a full professor in Applied Mathematics at Universitat Politècnica de València, with PhDs in Physics and Mathematics. His research spans Physics (Nuclear Physics, Phononics), Mathematics (Analysis, Topology, Machine Learning), and Didactics. He has authored several articles, collaborated internationally, and teaches AI-related topics.Radosław Antoni Kycia holds PhDs in Physics (Jagiellonian University) and Geometry, Topology and Geometric Analysis (Masaryk University). He is an Associate Professor at Cracow University of Technology. His research focuses on quantum systems, topology, and machine learning. He has published over 40 articles and participated in national and EU-funded scientific projects.

• 1. Preface 2. Introduction 3. Part I. Real-valued neural networks a. Applications in LLM models and RAG method b. Applications in image processing c. Application in time series analysis References 4. Part II. Complex- and Quaternionic-valued neural networks and their applications a. Applications in image processing b. Applications in time series analysis References 5. Part III. Theoretical Foundation of Computation with Neural Networks, from classic to fuzzy References 6. Conclusions References