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GENERALIZED FUZZY NUMBER VALUED BARTLE INTEGRALS

  • Park, Chun-Kee (Department of Mathematics, Kangwon National University)
  • Published : 2010.01.31

Abstract

In this paper we introduce the integration of scalar valued functions with respect to a generalized fuzzy number measure which we call the generalized fuzzy number valued Bartle integral. We first establish some properties of the generalized fuzzy number measures and then study the generalized fuzzy number valued Bartle integrals.

Keywords

set valued measure;generalized fuzzy number measure;set valued Bartle integral;generalized fuzzy number valued Bartle integral

References

  1. R. G. Bartle, A general bilinear vector integral, Studia Math. 15 (1956), 337–352. https://doi.org/10.4064/sm-15-3-337-352
  2. J. Diestel and J. J. Uhl Jr., Vector Measures, Math. Surveys, Vol. 15, Amer. Math. Soc., Providence R.I., 1977.
  3. C. V. Negoita and D. A. Ralescu, Application of Fuzzy Sets to Systems Analysis, Wiley, New York, 1975.
  4. N. S. Papageorgiou, On the theory of Banach space valued multifunctions. 1. Integration and conditional expectation. 2. Set valued martingales and set valued measures, J. Multivariate Anal. 17 (1985), 185–227. https://doi.org/10.1016/0047-259X(85)90078-8
  5. J. Wu and C. Wu, The w-derivatives of fuzzy mappings in Banach spaces, Fuzzy Sets and Systems 119 (2001), 375–381. https://doi.org/10.1016/S0165-0114(98)00468-0
  6. W. Z. Wu, W. X. Zhang, and R. M. Wang, Set valued Bartle integrals, J. Math. Anal. Appl. 255 (2001), 1–20. https://doi.org/10.1006/jmaa.2000.6976
  7. X. Xue, M. Ha, and M. Ma, Random fuzzy number integrals in Banach spaces, Fuzzy Sets and Systems 66 (1994), 97–111. https://doi.org/10.1016/0165-0114(94)90303-4
  8. X. Xue, M. Ha, and C. Wu, On the extension of the fuzzy number measures in Banach spaces: Part I. Representation of the fuzzy number measures, Fuzzy Sets and Systems 78 (1996), 347–354. https://doi.org/10.1016/0165-0114(96)84616-1

Cited by

  1. Lebesgue Decomposition Theorem and Weak Radon-Nikodým Theorem for Generalized Fuzzy Number Measures vol.2015, 2015, https://doi.org/10.1155/2015/576134
  2. A new integral with respect to a generalized fuzzy number measure vol.29, pp.5, 2015, https://doi.org/10.3233/IFS-151650