On the continuity of fuzzy integral in relation with measure convergence

• Flores F., Arturo ^[1] ; Román F., Heriberto ^[1] ; Bassanezi, Rodney C. ^[2]
  1. [1] Universidad de Tarapacá

     Universidad de Tarapacá

     Arica, Chile

     
  2. [2] Universidad de Campinas.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 12, Nº. 2, 1993, págs. 137-147
• Idioma: inglés
• DOI: 10.22199/S07160917.1993.0002.00004
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• Resumen

  • 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.

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