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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S. Coupland e R. I. John, Geometric type-1 and type-2 fuzzy logic systems, IEEE Trans. on Fuzzy Systems, 15 (1), (2007), 3 - 15.

H. Hagras, Type-2 FLCs: A new generation of fuzzy controllers, IEEE Computational Intelligence Magazine, 2 (1), (2007), 30 - 43.

E.H. Mamdani, S. Assilian, An experiment in linguistic synthesis with fuzzy logic controller, Intern. J. of Man-machine Studies 7(1) (1975) 1-13.

E.H. Mamdani, Advances in the linguistic synthesis of fuzzy controllers, Intern. J. of Man-Machine Studies, 8 (6) (1976) 669-678.

N. N. Karnik, J. M. Mendel and Q. Liang, Type-2 fuzzy logic systems, IEEE Trans. on Fuzzy Systems, 7, (1999), 643 - 658.

N. N. Karnik, J. M. Mendel, Centroid of a type-2 fuzzy set, Information Sciences, 132, (2001), 195 - 220.

J.M. Mendel, ``Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions'', Prentice-Hall, Upper - Saddle River, NJ, 2001.

D. Wu e M. Nie, Comparison and practical implementation of type-reduction algorithms for type-2 fuzzy sets and systems, Proc. IEEE Intl Conf. on Fuzzy Systems, Taipei, Taiwan, 2011.

D. Wu and W. W. Tan, A simplified architecture for type-2 FLSs and its application to nonlinear control, Proc. IEEE Conf. on

Cybernetics and Intelligent Systems, Singapore, (2004), 485 - 490.

D. Wu and W. W. Tan, A simplified type-2 fuzzy controller for real-time control, ISA Transactions, 15, (4), (2006), 503 - 516.

L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-1, Inform. Sci., 8, (1975) 199-249.

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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