Fuzzy Cognitive Maps: A Comprehensive Survey and Comparative Analysis

Abstract

: Fuzzy cognitive maps (FCMs) are a soft computing paradigm that combines fuzzy logic, neural networks, and graph theory to represent causality and reasoning in complex systems. Since their introduction in the 1980s as a generalization of cognitive maps, they have matured into a versatile framework that spans many variants, learning algorithms, and application areas. This survey consolidates that body of work into a single structured reference. The underlying literature search was conducted and is reported with reference to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 statement, with a full flow diagram and a reproducible per-database search protocol. It traces the development of FCMs from graph-based encodings of expert knowledge to modern modeling and decision-support tools, and it presents the underlying mathematics, including concept activation dynamics, weight update rules, activation and membership functions, defuzzification, and error functions for supervised learning. The survey positions itself against recent reviews, distinguishes the main reasoning-rule families (classical, memory-based, quasi-nonlinear, and long-term cognitive networks), and organizes Hebbian, gradient-based, evolutionary, swarm intelligence, reinforcement, and hybrid learning algorithms into a unified taxonomy, with a qualitative and critical comparison of their supervision requirements, computational complexity, scalability, and the assumptions under which each has been validated. The survey catalogs variants developed to handle uncertainty and richer dynamics, organized into uncertainty-oriented, temporal, and machine-learning-integrated groups, including gray, interval, neutrosophic, rough, high-order, random, dynamic, deep, quantum-inspired, and chaotic FCMs. It reviews stability and convergence criteria and open theoretical questions. Further sections cover evaluation metrics and datasets; interpretability across static, dynamic, causal-effect, and actionable (counterfactual) levels, together with explanation evaluation, fairness considerations, and expert-bias mitigation; a comparison with Bayesian networks, neural networks, system dynamics, and agent-based models, together with an explicit account of failure cases and boundary conditions under which those alternatives are preferable; practical guidelines for concept selection and membership-function tuning; applications across engineering, energy, health care, economics, and other domains; and available software tools. The survey closes by identifying the challenges and research directions that connect FCMs with modern machine learning and explainable artificial intelligence (XAI), and it is intended to serve as both a rigorous entry point for newcomers and a working reference for practitioners.