On the continuity of fuzzy integral in relation with measure convergence

Authors

  • Arturo Flores F. Universidad de Tarapacá.
  • Heriberto Román F. Universidad de Tarapacá.
  • Rodney C. Bassanezi Universidad de Campinas.

DOI:

https://doi.org/10.22199/S07160917.1993.0002.00004

Keywords:

Funciones, Integrales

Abstract

The aim of this paper is to analyze the continuity of the fuzzy integral in relation to the measure convergence. More precisely, we introduce the concept of autocontinuity of a fuzzy measure with respect to another fuzzy measure and we establish necessary and sufficient conditions such that measure convergence of functions, with respect to a fuzzy measure, implies the convergence of the fuzzy integral with respect to another fuzzy measure.

Author Biographies

Arturo Flores F., Universidad de Tarapacá.

Departamento de Matemática.
Facultad de Ciencia.

Heriberto Román F., Universidad de Tarapacá.

Departamento de Matemática.
Facultad de Ciencia.

Rodney C. Bassanezi, Universidad de Campinas.

IMECC.

References

[1] Greco. G., Bassanezi, R.C.: On the continuity of fuzzy integrals. Fuzzy Sets and Systems, 53 N° 1 (1993), 87-91.

[2] Greco, G.; Bassanezi, R.C.: Continuidade das fuzzy integrals. Ata. Sem. Bras. Anal. Rio de Janeiro. 1985.

[3] Ralescu, D.; Adams, G. The FUZZY INTEGRALS. J. Anal Math. Appl., 75 (1990), 562-570.

[4] Román-Flores, H.: Sobre entropías fuzzy. Ph.D.Dissertation, IMECC-UNICAMP, Campinas-SP, Brasil, 1989.

[5] Sugeno, M.: Fuzzy measures and fuzzy integrals: A survey, in: M.
Gupta et al., Eds. Fuzzy Automata and Decision Process. (North-Holland, Amsterdam, (1977), 89-102.

[6] Wang, Z.: The autocontinuity of set function and the fuzzy integral. J. Math. Anal. Appl., 99 (1984), 195-218.

Published

2018-04-03

How to Cite

[1]
A. Flores F., H. Román F., and R. C. Bassanezi, “On the continuity of fuzzy integral in relation with measure convergence”, Proyecciones (Antofagasta, On line), vol. 12, no. 2, pp. 137-147, Apr. 2018.

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