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ON THE DEBREU INTEGRAL OF FUZZY MAPPINGS IN BANACH SPACES

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In this paper, we introduce Debreu integral of fuzzy mappings in Banach spaces in terms of the Debreu integral of set-valued mappings, investigate properties of Debreu integral of fuzzy mappings in Banach spaces and obtain the convergence theorem for Debreu integral of fuzzy mappings in Banach spaces.

Abstract

In this paper, we introduce Debreu integral of fuzzy mappings in Banach spaces in terms of the Debreu integral of set-valued mappings, investigate properties of Debreu integral of fuzzy mappings in Banach spaces and obtain the convergence theorem for Debreu integral of fuzzy mappings in Banach spaces.

참고문헌 (11)

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  4. G. Debreu, "Integration of correspondences" (1967), Univ. California Press
  5. J. Diestel, "Vector measures. Math. Surveys", Amer. Math. Soc.,Providence R.I, 15 (1977)
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  7. E. Klein, "Theory of Correspondences" (1984), John Wiley & Sons
  8. N. Papageorgiou, "On the theory of Banach space valued multifunctions", J. Multivariate Anal, 17, pp.185~206 (1985)
  9. O. Kaleva, "Fuzzy differential equations", Fuzzy Sets and Systems, 24, pp.301~317 (1987)
  10. X. Xue, "Random fuzzy number integrals in Banach spaces", Fuzzy Sets and Systems, 66, pp.97~111 (1994)
  11. X. Xue, "On the convergence and representation of random fuzzy number integrals", Fuzzy Sets and Systems, 103, pp.115~125 (1999)

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