Abstract
Cognitive modeling has been crucial in understanding and simulating complex systems, especially for decision-making processes. From Tolman’s cognitive maps of rats to Kosko’s fuzzy cognitive maps and modern quantum cognitive models, researchers have sought representations that combine human expertise with computational rigor. This survey offers a comprehensive, historical, and mathematical treatment of concept maps, cognitive maps, and a rich family of fuzzy and hybrid cognitive map models. We discuss rule-based, crisp, gray, rough, neutrosophic, and quantum cognitive maps, and we review machine learning algorithms used to train them, including Hebbian and differential Hebbian learning, genetic and evolutionary algorithms, particle swarm optimization, reinforcement learning, and other hybrid techniques. The aim is to present a unified theoretical framework that traces the development of cognitive mapping from its origins to the latest advances, providing clear pathways for future research.