DOI QR코드

DOI QR Code

퍼지수치 확률변수의 쇼케이 기댓값과 그 응용

Choquet expected values of fuzzy number-valued random variables and their applications

  • 발행 : 2005.02.01

초록

본 논문에서는 구간수치 확률변수와 퍼지수치 확률변수를 생각하고 이들의 쇼케이 적분을 조사한다. 이러한 성질들을 이용하여 퍼지수치 확률변수의 르베그적분의 일반화인 퍼지수치 확률변수의 쇼케이 기대값을 정의한다. 특히 이들의 응용에 관한 예제들을 다룬다.

In this paper, we consider interval number-valued random variables and fuzzy number-valued random variables and discuss Choquet integrals of them. Using these properties, we define the Choquet expected value of fuzzy number-valued random variables which is a natural generalization of the Lebesgue expected value of fuzzy random variables. Furthermore, we discuss some application of them.

키워드

참고문헌

  1. J. Aubin, Set-valued analysis, 1990, Birkauser Boston
  2. R. J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965)1-12 https://doi.org/10.1016/0022-247X(65)90049-1
  3. F. Hiai and H. Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, J Multi. Analysis 7(1977) 149-182 https://doi.org/10.1016/0047-259X(77)90037-9
  4. L. C. Jang, B. M. Kil, Y. K. Kim and J. S. Kwon, Some properties of Choquet integrals of set-valued functions, Fuzzy Sets and Systems 91 (1997) 95-98 https://doi.org/10.1016/S0165-0114(96)00124-8
  5. L. C. Jang and J. S. Kwon, On the representation of Choquet integrals of set-valued functions and null sets, Fuzzy Sets and Systems 112(2000) 233-239 https://doi.org/10.1016/S0165-0114(98)00184-5
  6. L. C. Jang and T. Kim, On set-valued Choquet intgerals and convergence theorems, Advan. Stud. Contemp. Math. 6(1) (2003), 63-76
  7. L.C. Jang, T. Kim and J.D. Jeon, On set-valued Choquet integrals and convergence theorems (II), Bull. Korean Math. Soc. 40(1) (2003), 139-147 https://doi.org/10.4134/BKMS.2003.40.1.139
  8. L.C. Jang, T. Kim and J.D. Jeon, Oncomonotonically additive interval-valued functionals and interval-valued Choquet integrals (II), J of Fuzzy Logic and Intelligent Systems 14(1) (2004), 33-38 https://doi.org/10.5391/JKIIS.2004.14.1.033
  9. L.C. Jang, T. Kim and J.D. Jeon, On Choquet integrals of measurable fuzzy number-valued functions, Bull. Korean Math. Soc. 41(1) (2004), 95-107
  10. V. Kratschmer, Limit theorems for fuzzy random variables, Fuzzy Sets and Systems 126(2002), 253-263 https://doi.org/10.1016/S0165-0114(00)00100-7
  11. H. Kwakernaak, Fuzzy random variables- Definition and Theorems, Inf. Science 15(1978), 1-29 https://doi.org/10.1016/0020-0255(78)90019-1
  12. T. Murofushi and M. Sugeno, A theory of Fuzzy measures: representations, the Choquet integral, and null sets, J. Math. Anal. and Appl. 159 (1991) 532-549 https://doi.org/10.1016/0022-247X(91)90213-J
  13. M.L. Puri and D.A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114(1986), 409-422 https://doi.org/10.1016/0022-247X(86)90093-4
  14. Richard Alo, Andre de Korvin and Francois Modave, Decision Making for Robust Resilient systems, Proceedings of the 36th Hawaii international conference on System Science-2003
  15. D. Schmeidler, Integral representation without additivity, Proc. Amer. Math. Soc. 97(1986), 253-261
  16. B. Zhang, On measurability of fuzzy number-valued functions, Fuzzy Sets and Systems 120(2001), 505-509 https://doi.org/10.1016/S0165-0114(99)00061-5
  17. D. Zhang, C.Guo and Dayou Liu, Restudy on set-valued Choquet integrals, To appear in Fuzzy Sets and Systems