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“A Fuzzy Cognitive Maps Modeling, Learning and Simulation Framework for Studying Complex Systems”

“A Fuzzy Cognitive Maps Modeling, Learning and Simulation Framework for Studying Complex Systems” Maikel León 1, 2, ∗ , Gonzalo Nápoles 1 , Ciro Rodriguez 1 , María M. García 1 , Rafael Bello 1 , and Koen Vanhoof 2

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“A Fuzzy Cognitive Maps Modeling, Learning and Simulation Framework for Studying Complex Systems”

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  1. “A Fuzzy Cognitive Maps Modeling, Learning and Simulation Framework for Studying Complex Systems” Maikel León1,2, ∗, Gonzalo Nápoles1, Ciro Rodriguez1, María M. García1, Rafael Bello1, and Koen Vanhoof 2 1Central University of Las Villas, Cuba. ∗ mle@uclv.edu.cu 2Hasselt University, Belgium. • Fuzzy Cognitive Maps (FCM) are presented as an approach in modeling complex systems; they combine aspects of fuzzy logic, neural networks, semantic networks, expert systems, and nonlinear dynamical systems. An inspired on Particle Swarm Optimization (PSO) learning method for this technique is proposed and implemented. • A real problem was studied, showing a possible Travel Behavior modeling through FCM, with improvement on the knowledge structures originally modeled by using the learning method based on PSO. The case study shows social and politic repercussion offering policymakers a framework and real data to play with, in order to study and simulate individuals behavior and produce new knowledge to use in the development of city infrastructure and demographic planning. • If the values are not adequate, known by the execution of the heuristic function, then it is necessary a readjust process. • Results give new values for the weight matrix. “Application of PSO metaheuristic as a FCM learning method” • PSO is applied straight forwardly using an objective function defined by the user. • Each particle of the swarm is a weight matrix, encoded as a vector. Generate initial population using Wij as initial approximation Calculate initial evaluation Cross over good particles Mutation of random particles Initialize the vector Xpbest with best solutions found by each particle Initialize Xgbest as the best global found Initialize Wmax= 1.4, Wmin= 0.4, c1 =2.5, c2 =2.5, k = 0.381966011 For t=0 to Ngenerations wk= (Wmax - Wmin) * ((Ncmax - t) / (Ncmax + Wmin)) For each Xi Calculate Vi(t+1) and limit to [-Vmax, +Vmax] using wk Calculate Xi(t+1)= Xi(t) + k*Vi(t+1) and normalize Analyze the vector Swarm with Xi(t+1) and Speed with Vi(t+1) Evaluate the particle Xi(t+1) Analyze the vector Xpbest with the best solutions Update Xgbest with the best global particle endFor endFor M O D E L I N G T R A V E L B E H A V I O R C A S E S T U D Y IWINAC 2011 “4thINTERNATIONAL WORK-CONFERENCE on the INTERPLAY between NATURAL and ARTIFICIAL COMPUTATION” La Palma, Canary Islands, Spain. May 30 - June 3, 2011.

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