Mediative Fuzzy Logic for Controlling Population Size in Evolutionary Algorithms

ABSTRACT

In this paper we are presenting an intelligent method for controlling population size in evolutionary algorithms. The method uses Mediative Fuzzy Logic for modeling knowledge from experts about what should be the behavior of population size through generations based on the fitness variance and the number of generations that the algorithm is being stuck. Since, it is common that this kind of knowledge expertise can be susceptible to disagreement in a minor or a major part. We selected Mediative Fuzzy Logic (MFL) as a fuzzy method to achieve the inference. MFL is a novelty fuzzy inference method that can handle imperfect knowledge in a broader way than traditional fuzzy logic does.

In this paper we are presenting an intelligent method for controlling population size in evolutionary algorithms. The method uses Mediative Fuzzy Logic for modeling knowledge from experts about what should be the behavior of population size through generations based on the fitness variance and the number of generations that the algorithm is being stuck. Since, it is common that this kind of knowledge expertise can be susceptible to disagreement in a minor or a major part. We selected Mediative Fuzzy Logic (MFL) as a fuzzy method to achieve the inference. MFL is a novelty fuzzy inference method that can handle imperfect knowledge in a broader way than traditional fuzzy logic does.

Cite this paper

nullO. MONTIEL, O. CASTILLO, P. MELIN and R. SEPULVEDA, "Mediative Fuzzy Logic for Controlling Population Size in Evolutionary Algorithms,"*Intelligent Information Management*, Vol. 1 No. 2, 2009, pp. 108-119. doi: 10.4236/iim.2009.12016.

nullO. MONTIEL, O. CASTILLO, P. MELIN and R. SEPULVEDA, "Mediative Fuzzy Logic for Controlling Population Size in Evolutionary Algorithms,"

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[26] O. Nelles, “Nonlinear system identification from classical approaches to neural networks and fuzzy models,” Springer-Verlag, Germany, 2001.

[1] G. J. Klir, B. Yuan, “Fuzzy sets and fuzzy logic theory and applications,” Edition, Prentice Hall USA, 1995.

[2] L. A. Zadeh, “Fuzzy sets,” Information and Control, Vol. 8, pp. 338–353, 1965.

[3] J. M. Mendel, “Uncertain rule-based fuzzy logic systems introduction and new directions,” Edition, Prentice Hall, USA, 2000.

[4] O. Montiel, O. Castillo, P. Melin, A. Rodríguez Días, and R. Sepúlveda, ICAI, 2005.

[5] D. A. Bal, and W. H. McCulloch, Jr., “International business introduction and essentials,” Fifth Edition, pp. 138–140, 225, USA, 1993.

[6] R. I. Horwitz, “Complexity and contradiction in clinical trial research,” American Journal of Medicine, Vol. 8, pp. 498–510, 1987.

[7] J. S. Armstrong, “Principles of forecasting, A handbook for researchers and practitioners,” Edited by J. Scott Armstrong, University of University of Pennsylvania, Wharton School, Philadelphia, PA., USA, 2001.

[8] Aristotle, “The basic works of Aristotle,” Modern Library Classics, Richard McKeon Edition, 2001.

[9] R. Smith, “Aristotle’s logic, Stanford encyclopedia of philosophy,” 2004. http://plato.stanford.edu/entries/aristotle-logic/.

[10] D. Baltzly, “Stanford encyclopedia of philosophy,” 2004. http://plato.stanford.edu/entries/stoicism/.

[11] J. J. O’Connor E. F. Robertson, and A. DeMorgan, “MacTutor history of mathematics: Indexes of biographies (University of St. Andrews),” 2004, http://www-groups. dcs.st-andrews.ac.uk/~history/Mathematicians/De_Morgan.htm.

[12] G. Boole, “The calculus of logic,” Cambridge and Dublin Mathematical Journal, Vol. 3, pp. 183–98, 1848.

[13] J. J. O’Connor, E. F. Robertson, G. Boole, and MacTutor history of mathematics: Indexes of biographies,” University of St. Andrews, 2004. http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Boole.html.

[14] J. J. O’Connor, E. F. Robertson, F. L. G. Frege, and Mac Tutor history of mathematics: Indexes of Biographies University of St. Andrews, http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Frege.html.

[15] J. J. O’Connor and E. F. Robertson , L. E. J. Brouwer, MacTutor history of mathematics: Indexes of biographies,” University of St. Andrews, http://www-groups.dcs. st-adrews.ac.uk/~history/Mathematicians/Brouwer.html.

[16] J. J. O’Connor, E. F. Robertson, and A. Heyting, “MacTutor history of mathematics: Indexes of biographies,” University of St. Andrews, 2004. http://www-history. mcs.st-adrews.ac.uk/Mathematicians/Heyting.html.

[17] J. J. O’Connor, E. F. Robertson, and G. Gentzen, “MacTutor history of mathematics: Indexes of biographies,” University of St. Andrews, 2004. http://www-history. mcs.st-andrews.ac.uk/Mathematicians/Gentzen.html.

[18] J. J. O’Connor, E. F. Robertson, and J. Lukasiewicz, “MacTutor history of mathematics: Indexes of biographies,” University of St. Andrews, 2004. http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Lukasiewicz.html.

[19] Wikipedia the free encyclopedia, http://en.wikipedia.org/ wiki/Jan_Lukasiewicz.

[20] Wikipedia the free encyclopedia, http://en.wikipedia.org/ wiki/Newton_da_Costa.

[21] W. A. Carnielli, “How to build your own paraconsistent logic: An introduction to the logics of formal (in) consistency,” In: J. Marcos, D. Batens, and W. A. Carnielli, organizers, Proceedings of the Workshop on Paraconsistent Logic (WoPaLo), held in Trento, Italy, as part of the 14th European Summer School on Logic, Language and Information (ESSLLI’02), pp. 58–72, 5–9 August 2002.

[22] J. M. Mendel and R. B. John, “Type-2 fuzzy sets made simple,” IEEE Transactions on Fuzzy Systems, Vol. 10, No. 2, April 2002.

[23] K. Atanassov, “Intuitionistic guzzy dets: Theory and spplications,” Springer-Verlag, Heidelberg, Germany, 1999.

[24] M. Nikilova, N. Nikolov, C. Cornelis, and G. Deschrijver, “Survey of the research on intuitionistic fuzzy sets,” In: Advanced Studies in Contemporary Mathematics, Vol. 4, No. 2, , pp. 127–157, 2002.

[25] C. P. Melin, “A new method for fuzzy inference in intuitionistic fuzzy systems, proceedings of the international conference,” NAFIPS’03, IEEE Press, Chicago, Illinois, USA, Julio, pp. 20–25, 2003.

[26] O. Nelles, “Nonlinear system identification from classical approaches to neural networks and fuzzy models,” Springer-Verlag, Germany, 2001.