A λ-c- genetic Algorithm for Integrals with Fuzzy Measure

Gholam Hassan Shirdel

Abstract


In this paper, beginning we define a fuzzy Parametric measure, with having values of a weight function on n points. Afterwards, we obtain one equation by use from properties of fuzzy measure that with solving equation, we define parameters of fuzzy measure. For solving equation, we design a  genetic algorithm and hereby we provide the facility of solving integrals.


Keywords


fuzzy measure; fuzzy integral; genetic algorithm

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References


A. Basile, Fuzzy Sets and Systems 21, 243-247 (1987).

M. T. Chu, Z. Shyu, J. and G. H. Tzeng, IEEE Transactions on Engineering Management 54 (2), 237-339 (2007).

C. M. Feng, P. G. Wu and K. C. Chia, European Journal Operational Research 192, 451-464 (2009).

D. E. Goldberg, Addison-Wesley, Reading, MA, 1989.

L. Galand, P. Perny, O. Spanjaard, European Journal of Operational Research 204 (2), 303-315 (2010)

M. Grabisch, European Journal of Operational Research 89 (3), 445-456 (1996).

M. Grabisch, Fuzzy measures and integrals, Springer Verlag (2000).

M. Grabisch, T. Murofushi and M. Sugeno, Fuzzy Sets and Systems 92, 167-189 (1997).

M. Grabisch, Fuzzy Sets and Systems 69, 279-298 (1995).

Y. C. Hu, Neurocomputing 72, 331-340 (2008).

K. Leszczynski, P. Penczek and W. Grochuliski, Fuzzy Sets and Systems 15, 147-158 (1985).

D. Liginlal and T. T. Ow, Fuzzy Sets and Systems 157, 3040-3054 (2006).

T. Murofushi and M. Sugeno, Fuzzy Sets and systems 29, 201-227 (1989).

Y. Narukawa and V. Torra, Information Sciences 177, 4686-4695 (2007).

Y. Narukawa, T. Murofushi and M. Sugeno, Fuzzy Sets and systems 112, 177-186 (2000).

T. Onisawa, M. Sugeno, M. Y. Nishiwaki, H. Kawai and Y. Harima, Fuzzy Sets and Systems 20, 259-289 (1986).

M. Sugeno, Theory of fuzzy integrals and applications, Ph.D. Dissertation, Tokyo Institute of Technology, 1974.

G. H. Tzeng, Y. P. Q. Yang, C. T. lin and C. B. Chen, Information Sciences 169, 409-426 (2005).

Z. Wang and G. J. Klir, Fuzzy measure theory, Plenum Press, New York, 1992.

S. T. Wierzchon, Fuzzy Sets and Systems 9, 69-78(1983)




DOI: http://dx.doi.org/10.24294/ijmss.v1i3.546

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