International Journal of Man-Machine Studies
AIP Conference Proceedings 151 on Neural Networks for Computing
Fuzzy engineering
A Soft Computing Approach for Modelling the Supervisor of Manufacturing Systems
Journal of Intelligent and Robotic Systems
Adaptive Random Fuzzy Cognitive Maps
IBERAMIA 2002 Proceedings of the 8th Ibero-American Conference on AI: Advances in Artificial Intelligence
Proceedings of the first international conference on Neutrosophy, neutrosophic logic, neutrosophic set, neutrosophic probability and statistics
Fuzzy Cognitive Maps Learning Using Particle Swarm Optimization
Journal of Intelligent Information Systems
Fuzzy Cognitive Maps in modeling supervisory control systems
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Comparing the inference capabilities of binary, trivalent and sigmoid fuzzy cognitive maps
Information Sciences: an International Journal
Genetic learning of fuzzy cognitive maps
Fuzzy Sets and Systems
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
A fuzzy cognitive map approach to differential diagnosis of specific language impairment
Artificial Intelligence in Medicine
A contextual fuzzy cognitive map framework for geographic information systems
IEEE Transactions on Fuzzy Systems
Contextual fuzzy cognitive map for decision support in geographic information systems
IEEE Transactions on Fuzzy Systems
On causal inference in fuzzy cognitive maps
IEEE Transactions on Fuzzy Systems
Dynamical cognitive network - an extension of fuzzy cognitive map
IEEE Transactions on Fuzzy Systems
Quotient FCMs-a decomposition theory for fuzzy cognitive maps
IEEE Transactions on Fuzzy Systems
Dynamic domination in fuzzy causal networks
IEEE Transactions on Fuzzy Systems
Fuzzy causal networks: general model, inference, and convergence
IEEE Transactions on Fuzzy Systems
Numerical and Linguistic Prediction of Time Series With the Use of Fuzzy Cognitive Maps
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Knowledge-Based Systems
Fuzzy cognitive maps for artificial emotions forecasting
Applied Soft Computing
Bi-linear adaptive estimation of Fuzzy Cognitive Networks
Applied Soft Computing
Fuzzy Grey Cognitive Maps in reliability engineering
Applied Soft Computing
International Journal of Artificial Life Research
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Fuzzy cognitive maps (FCMs) have been introduced by Kosko to model complex behavioral systems in various scientific areas. One issue that has not been adequately studied so far is the conditions under which they reach a certain equilibrium point after an initial perturbation. This is equivalent to studying the existence and uniqueness of solutions for their concept values. In this paper, we study the existence of solutions of FCMs equipped with continuous differentiable sigmoid functions having contractive or, at least, nonexpansive properties. This is done by using an appropriately defined contraction mapping theorem and the nonexpansive mapping theorem. It is proved that when the weight interconnections fulfill certain conditions, the concept values will converge to a unique solution, regardless of the exact values of the initial concept values perturbations, or in some cases, a solution exists that may not necessarily be unique; otherwise, the existence or the uniqueness of equilibrium cannot be assured. Based on these results, an adaptive weight-estimation algorithm is proposed that employs appropriate weight projection criteria to assure that the uniqueness of FCM solution is not compromised. In view of these results, recently proposed extensions of FCM, which are the fuzzy cognitive networks (FCN), are invoked.