메뉴 건너뛰기




Volumn 157, Issue 19, 2006, Pages 2569-2578

Strong laws of large numbers for independent fuzzy set-valued random variables

Author keywords

Fuzzy set valued random variables; The extended Hausdorff metric; The strong law of large numbers

Indexed keywords

METRIC SYSTEM; NUMBER THEORY; NUMERICAL METHODS; PROBABILITY; RANDOM PROCESSES;

EID: 33748164797     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2003.06.011     Document Type: Article
Times cited : (37)

References (37)
  • 1
    • 0000056568 scopus 로고
    • A strong law of large numbers for random compact sets
    • Artstein Z., and Vitale R.A. A strong law of large numbers for random compact sets. Ann. Probab. 3 (1975) 879-882
    • (1975) Ann. Probab. , vol.3 , pp. 879-882
    • Artstein, Z.1    Vitale, R.A.2
  • 2
    • 50549204934 scopus 로고
    • Integrals of set-valued functions
    • Aumann R. Integrals of set-valued functions. J. Math. Anal. Appl. 12 (1965) 1-12
    • (1965) J. Math. Anal. Appl. , vol.12 , pp. 1-12
    • Aumann, R.1
  • 5
    • 33748200614 scopus 로고    scopus 로고
    • A. Colubi, Traditional techniques to prove some limit theorems for fuzzy random variables, in: C. Bertoluzza, M.A. Gil, D.A. Ralescu, (Eds.), Statistical Modeling, Analysis and Management for Fuzzy Data, Physica, 2002, pp. 64-71.
  • 7
    • 33748167818 scopus 로고    scopus 로고
    • Y. Chen, Fuzzy Systems and Mathematics, Huazhong Institute Press of Science and Technology, 1984, in Chinese.
  • 8
    • 0001936197 scopus 로고
    • A strong limit theorem for random sets
    • Cressie N. A strong limit theorem for random sets. Suppl. Adv. in Appl. Probab. 10 (1978) 36-46
    • (1978) Suppl. Adv. in Appl. Probab. , vol.10 , pp. 36-46
    • Cressie, N.1
  • 10
    • 0000212640 scopus 로고
    • Integration of correspondences
    • Lecam L., Neyman J., and Scott E.L. (Eds), University of California Press, Berkeley
    • Debreu G. Integration of correspondences. In: Lecam L., Neyman J., and Scott E.L. (Eds). Proc. Fifth Berkeley Symposium Math. Stat. and Probability II, Part I (1966), University of California Press, Berkeley 351-372
    • (1966) Proc. Fifth Berkeley Symposium Math. Stat. and Probability II, Part I , pp. 351-372
    • Debreu, G.1
  • 13
    • 33748156098 scopus 로고    scopus 로고
    • E. Giné, G. Hahn, J. Zinn, Limit theorems for random sets: an application of probability in Banach space results, Lecture Notes in Mathematics vol. 990, 1983, pp. 112-135.
  • 14
    • 33748127911 scopus 로고    scopus 로고
    • F. Hiai, Strong laws of large numbers for multivalued random variables, in: G. Salinetti, (Ed.), Multifunctions and Integrands, Lecture Notes in Mathematics vol. 1091, Springer, Berlin, pp. 160-172.
  • 15
    • 0001577815 scopus 로고
    • Integrals, Conditional expectations and martingales of multivalued functions
    • Hiai F., and Umegaki H. Integrals, Conditional expectations and martingales of multivalued functions. J. Multivariate Anal. 7 (1977) 149-182
    • (1977) J. Multivariate Anal. , vol.7 , pp. 149-182
    • Hiai, F.1    Umegaki, H.2
  • 16
    • 0002514633 scopus 로고
    • A strong law of large numbers for fuzzy random sets
    • Inoue H. A strong law of large numbers for fuzzy random sets. Fuzzy Sets and Systems 41 (1991) 285-291
    • (1991) Fuzzy Sets and Systems , vol.41 , pp. 285-291
    • Inoue, H.1
  • 19
    • 0020231129 scopus 로고
    • The strong law of large numbers for fuzzy random variables
    • Kruse R. The strong law of large numbers for fuzzy random variables. Inform. Sci. 28 (1982) 233-241
    • (1982) Inform. Sci. , vol.28 , pp. 233-241
    • Kruse, R.1
  • 20
    • 6344232554 scopus 로고
    • Fuzzy random variables: definition and theorems
    • Kwakernaak H. Fuzzy random variables: definition and theorems. Inform. Sci. 15 (1978) 1-29
    • (1978) Inform. Sci. , vol.15 , pp. 1-29
    • Kwakernaak, H.1
  • 21
    • 26944480882 scopus 로고
    • Fuzzy random variables: algorithms and examples for the discrete case
    • Kwakernaak H. Fuzzy random variables: algorithms and examples for the discrete case. Inform. Sci. 17 (1979) 253-278
    • (1979) Inform. Sci. , vol.17 , pp. 253-278
    • Kwakernaak, H.1
  • 22
    • 0001139291 scopus 로고    scopus 로고
    • Fuzzy random variables, conditional expectations and fuzzy martingales
    • Li S., and Ogura Y. Fuzzy random variables, conditional expectations and fuzzy martingales. J. Fuzzy Math. 4 (1996) 905-927
    • (1996) J. Fuzzy Math. , vol.4 , pp. 905-927
    • Li, S.1    Ogura, Y.2
  • 23
    • 0032384177 scopus 로고    scopus 로고
    • Convergence of set valued sub- and super-martingales in the Kuratowski-Mosco sense
    • Li S., and Ogura Y. Convergence of set valued sub- and super-martingales in the Kuratowski-Mosco sense. Ann. Probab. 26 (1998) 1384-1402
    • (1998) Ann. Probab. , vol.26 , pp. 1384-1402
    • Li, S.1    Ogura, Y.2
  • 24
    • 0000074041 scopus 로고    scopus 로고
    • Convergence of set valued and fuzzy valued martingales
    • Li S., and Ogura Y. Convergence of set valued and fuzzy valued martingales. Fuzzy Sets and Systems 101 (1999) 453-461
    • (1999) Fuzzy Sets and Systems , vol.101 , pp. 453-461
    • Li, S.1    Ogura, Y.2
  • 25
    • 0012653644 scopus 로고    scopus 로고
    • Convergence in graph for fuzzy valued martingales and smartingales
    • Bertoluzza C., Gil M.A., and Ralescu D.A. (Eds), Physica-Verlag, Wurzburg
    • Li S., and Ogura Y. Convergence in graph for fuzzy valued martingales and smartingales. In: Bertoluzza C., Gil M.A., and Ralescu D.A. (Eds). Statistical Modeling, Analysis and Management for Fuzzy Data (2002), Physica-Verlag, Wurzburg 72-89
    • (2002) Statistical Modeling, Analysis and Management for Fuzzy Data , pp. 72-89
    • Li, S.1    Ogura, Y.2
  • 28
    • 0141850347 scopus 로고    scopus 로고
    • Central limit theorems for generalized set-valued random variables
    • Li S., Ogura Y., Proske F.N., and Puri M.L. Central limit theorems for generalized set-valued random variables. J. Math. Anal. Appl. 285 (2002) 250-263
    • (2002) J. Math. Anal. Appl. , vol.285 , pp. 250-263
    • Li, S.1    Ogura, Y.2    Proske, F.N.3    Puri, M.L.4
  • 30
    • 0001605105 scopus 로고    scopus 로고
    • On strong laws of large numbers for random upper semicontinuous functions
    • Molchanov I.S. On strong laws of large numbers for random upper semicontinuous functions. J. Math. Anal. Appl. 235 (1999) 249-355
    • (1999) J. Math. Anal. Appl. , vol.235 , pp. 249-355
    • Molchanov, I.S.1
  • 31
    • 0000184942 scopus 로고
    • Strong law of large numbers for Banach space valued random sets
    • Puri M.L., and Ralescu D.A. Strong law of large numbers for Banach space valued random sets. Ann. Probab. 11 (1983) 222-224
    • (1983) Ann. Probab. , vol.11 , pp. 222-224
    • Puri, M.L.1    Ralescu, D.A.2
  • 33
    • 0004487245 scopus 로고
    • A strong law of large numbers for random sets in Banach spaces
    • Taylor R.L., and Inoue H. A strong law of large numbers for random sets in Banach spaces. Bull. Inst. Math. Acad. Sinica 13 (1985) 403-409
    • (1985) Bull. Inst. Math. Acad. Sinica , vol.13 , pp. 403-409
    • Taylor, R.L.1    Inoue, H.2
  • 34
    • 0000268852 scopus 로고
    • Convergence of weighted sums of random sets
    • Taylor R.L., and Inoue H. Convergence of weighted sums of random sets. Stochastic Anal. Appl. 3 (1985) 379-396
    • (1985) Stochastic Anal. Appl. , vol.3 , pp. 379-396
    • Taylor, R.L.1    Inoue, H.2
  • 35
    • 33748169178 scopus 로고    scopus 로고
    • R.L. Taylor, H. Inoue, Laws of large numbers for random sets, Random Sets, Minneapolis, MN, IMA Volumes in Mathematics and its Applications 97, Springer, New York, 1997, pp. 347-360.
  • 36
    • 33748139314 scopus 로고    scopus 로고
    • P. Terán, An embedding theorem for convex fuzzy sets, 2004, preprint


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.