A Study on Subjectivities of Type 1 and 2 in Parameters of Differential Equations

Rosana Motta Jafelice, Ana Maria Bertone, Rodney Carlos Bassanezi


This study presents the Verhulst's model for the analysis of population growth with the rate of reproductivity depending on the fertility rate and the country economic development. These linguistic variables are defined through Fuzzy Rule-Based Systems (FRBS). The analysis is made for FRBS types 1 and 2 where in the first case, the inference method used is Mamdani's and the defuzzification is the center of gravity. For type 2 FRBS is used the inference method by Karnik Mendel (KM) where the output is defuzzificated by the Type Reducer method. A comparative study of the solutions of the Verhulst's model for both techniques is performed. I has been noticed that the region determined by the solutions corresponding to the minimum and maximum rate resulting from FRBS type 2 is contained in the region built similarly from type 1, showing a higher accuracy in the response.

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DOI: https://doi.org/10.5540/tema.2015.016.01.0051

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Trends in Computational and Applied Mathematics

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