Complex systems modeling is a rapidly developing research field which incorporates various scientific sectors from bio medicine and energy to economic and social sciences. However, as the systems’ complexity increases pure mathematical modeling techniques prove to be a rather laborious task which demands wasting many resources and in many occasions, could not lead to the desired system response. This realization led researchers turn their attention into the field of computational intelligence; Neural Networks and Fuzzy Logic etc. In this way scientists were able to provide a model of a system which is strongly characterized by fuzziness and uncertainties. Fuzzy Cognitive Maps (FCM) in another methodology which lies in the field of computational intelligence. FCM came as a combination of Neural Networks and Fuzzy Logic and were first introduced by B. Kosko in 1986. All these years they have been applied on a variety of systems such as social, psychological, medical, agricultural, marketing, business management, energy, advertising etc, both for systems modeling and decision-making support systems, with very promising results. Classical FCM approach uses the experts’ knowledge in order to create the initial knowledge base of each system. Based on the experts’ knowledge, the interrelations among the system variables are determined and the system response is defined. Through years, improvements have been made and learning algorithms were embodied in the initial approach. Learning algorithms used data information and history to update the weights (the interconnections) among concepts (variables), contributed to the optimization of FCMs and reached more efficient systems’ response. However, all these decades, researchers have mentioned some weak points as well. In the last years substantial research has been made in order to overcome some of the well-known limitations of the FCM methodology. This paper will apply a revised approach of the Fuzzy Cognitive Maps method on a techno-economic study of an autonomous hybrid system photovoltaic and geothermal energy Specifically, the FCM model of this system includes twenty-five concepts and three of them are considered as outputs, the total system efficiency, the total energy production and the total system cost. The aim of the study is to provide maximum performance with the minimum total cost. To this end results for both the classic and revised approach of the FCM method are provided and discussed. Computational Intelligence and especially Fuzzy Cognitive Maps are a very promising field in modeling complex systems. The latest approaches of the method show that FCM can open new paths towards higher efficiency, more accurate models and effective decision-making results.
State Feedback of Complex Systems Using Fuzzy Cognitive Maps
