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Volumn 200, Issue , 2012, Pages 99-115

The median of a random fuzzy number. the 1-norm distance approach

Author keywords

1 Norm distance; Fuzzy arithmetic; Fuzzy numbers; Median; Random fuzzy numbers; Statistical robustness

Indexed keywords

1-NORM DISTANCE; FUZZY ARITHMETICS; FUZZY NUMBERS; MEDIAN; STATISTICAL ROBUSTNESS;

EID: 84861102038     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2011.11.004     Document Type: Article
Times cited : (69)

References (38)
  • 1
    • 0042572669 scopus 로고    scopus 로고
    • Fuzzy numbers are the only fuzzy sets that keep invertible operations invertible
    • PII S0165011497001371
    • B. Bouchon-Meunier, O. Kosheleva, V. Kreinovich, and H.T. Nguyen Fuzzy numbers are the only fuzzy sets that keep invertible operations invertible Fuzzy Sets Syst. 91 1997 155 163 (Pubitemid 127683710)
    • (1997) Fuzzy Sets and Systems , vol.91 , Issue.2 , pp. 155-163
    • Bouchon-Meunier, B.1    Kosheleva, O.2    Kreinovich, V.3    Nguyen, H.T.4
  • 2
    • 0003211244 scopus 로고
    • Convex Analysis and Measurable Multifunctions
    • Springer-Verlag Berlin
    • C. Castaing, and M. Valadier Convex Analysis and Measurable Multifunctions Lecture Notes in Mathematics vol. 580 1977 Springer-Verlag Berlin
    • (1977) Lecture Notes in Mathematics , vol.580
    • Castaing, C.1    Valadier, M.2
  • 6
    • 77956535320 scopus 로고    scopus 로고
    • The behavioral meaning of the median
    • C. Borgelt, G. González-Rodríguez, W. Trutschnig, M.A. Gil, P. Grzegorzewski, O. Hryniewicz, Springer Heidelberg
    • I. Couso, and L. Sánchez The behavioral meaning of the median C. Borgelt, G. González-Rodríguez, W. Trutschnig, M.A. Gil, P. Grzegorzewski, O. Hryniewicz, Combining Soft Computing and Statistical Methods in Data Analysis 2010 Springer Heidelberg 115 123
    • (2010) Combining Soft Computing and Statistical Methods in Data Analysis , pp. 115-123
    • Couso, I.1    Sánchez, L.2
  • 7
    • 33750282724 scopus 로고    scopus 로고
    • On the use of the bootstrap for estimating functions with functional data
    • DOI 10.1016/j.csda.2005.10.012, PII S0167947305002793
    • A. Cuevas, M. Febrero, and R. Fraiman On the use of the bootstrap for estimating functions with functional data Comput. Stat. Data Anal. 51 2006 1063 1074 (Pubitemid 44635882)
    • (2006) Computational Statistics and Data Analysis , vol.51 , Issue.2 , pp. 1063-1074
    • Cuevas, A.1    Febrero, M.2    Fraiman, R.3
  • 8
    • 0001770861 scopus 로고    scopus 로고
    • Metric spaces of fuzzy sets
    • P. Diamond, and P. Kloeden Metric spaces of fuzzy sets Fuzzy Sets Syst. 100 1999 63 71 (Pubitemid 129682572)
    • (1999) Fuzzy Sets and Systems , vol.100 , Issue.SUPPL. 1 , pp. 63-71
    • Diamond, P.1    Kloeden, P.2
  • 9
    • 0002231562 scopus 로고
    • The notion of breakdown point
    • P.J. Bickel, K. Doksum, J.L. Hodges Jr. Wadsworth Belmont
    • D.L. Donoho, and P.J. Huber The notion of breakdown point P.J. Bickel, K. Doksum, J.L. Hodges Jr. A Festschrift for Erich L. Lehmann 1983 Wadsworth Belmont 157 184
    • (1983) A Festschrift for Erich L. Lehmann , pp. 157-184
    • Donoho, D.L.1    Huber, P.J.2
  • 10
    • 0002448681 scopus 로고
    • Systems of linear fuzzy constraints
    • D. Dubois, and H. Prade Systems of linear fuzzy constraints Fuzzy Sets Syst. 3 1980 37 48
    • (1980) Fuzzy Sets Syst. , vol.3 , pp. 37-48
    • Dubois, D.1    Prade, H.2
  • 11
    • 77955509665 scopus 로고    scopus 로고
    • An application of fuzzy random variables to control charts
    • A. Faraz, and A.F. Shapiro An application of fuzzy random variables to control charts Fuzzy Sets Syst. 161 2010 2684 2694
    • (2010) Fuzzy Sets Syst. , vol.161 , pp. 2684-2694
    • Faraz, A.1    Shapiro, A.F.2
  • 12
    • 0347141868 scopus 로고    scopus 로고
    • Trimmed means for functional data
    • R. Fraimann, and G. Muñiz Trimmed means for functional data Test 10 2001 419 440 (Pubitemid 33684642)
    • (2001) Test , vol.10 , Issue.2 , pp. 419-440
    • Fraiman, R.1    Muniz, G.2
  • 13
    • 50949086005 scopus 로고    scopus 로고
    • Robust functional estimation using the spatial median and spherical principal components
    • D. Gervini Robust functional estimation using the spatial median and spherical principal components Biometrika 95 2008 587 600
    • (2008) Biometrika , vol.95 , pp. 587-600
    • Gervini, D.1
  • 15
    • 33750359747 scopus 로고    scopus 로고
    • A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing
    • DOI 10.1016/j.csda.2006.04.006, PII S0167947306000922
    • G. González-Rodríguez, A. Colubi, and M.A. Gil A fuzzy representation of random variables: an operational tool in exploratory analysis and hypothesis testing Comput. Stat. Data Anal. 51 2006 163 176 (Pubitemid 44634796)
    • (2006) Computational Statistics and Data Analysis , vol.51 , Issue.1 , pp. 163-176
    • Gonzalez-Rodriguez, G.1    Colubi, A.2    Angeles Gil, M.3
  • 16
    • 84856734042 scopus 로고    scopus 로고
    • Fuzzy data treated as functional data. A one-way ANOVA test approach
    • in press (doi:)
    • G. González-Rodríguez, A. Colubi, M.A. Gil, Fuzzy data treated as functional data. A one-way ANOVA test approach, Comput. Stat. Data Anal., in press (doi: 10.1016/j.csda.2010.06.013).
    • Comput. Stat. Data Anal.
    • González-Rodríguez, G.1    Colubi, A.2    Gil, M.A.3
  • 17
    • 33748078152 scopus 로고    scopus 로고
    • Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data
    • DOI 10.1016/j.fss.2003.11.021, PII S0165011406002089, Fuzzy Sets and Probability/Statistics Theory
    • G. González-Rodríguez, M. Montenegro, A. Colubi, and M.A. Gil Bootstrap techniques and fuzzy random variables: synergy in hypothesis testing with fuzzy data Fuzzy Sets Syst. 157 2006 2608 2613 (Pubitemid 44301500)
    • (2006) Fuzzy Sets and Systems , vol.157 , Issue.19 , pp. 2608-2613
    • Gonzalez-Rodriguez, G.1    Montenegro, M.2    Colubi, A.3    Gil, M.A.4
  • 18
    • 77956629509 scopus 로고    scopus 로고
    • Service quality gaps analysis based on Fuzzy linguistic SERVQUAL with a case study in hospital out-patient services
    • H.-Y. Hu, Y.-C. Lee, and T.-M. Yen Service quality gaps analysis based on Fuzzy linguistic SERVQUAL with a case study in hospital out-patient services TQM J. 22 2010 499 515
    • (2010) TQM J. , vol.22 , pp. 499-515
    • Hu, H.-Y.1    Lee, Y.-C.2    Yen, T.-M.3
  • 19
    • 0012777173 scopus 로고
    • Intégration des applications measurables dont la valeur est un compact convexe
    • M. Hukuhara Intégration des applications measurables dont la valeur est un compact convexe Funkcial. Ekvac. 10 1967 205 223
    • (1967) Funkcial. Ekvac. , vol.10 , pp. 205-223
    • Hukuhara, M.1
  • 21
    • 0001378385 scopus 로고    scopus 로고
    • An asymptotic α-test for the expectation of random fuzzy variables
    • R. Körner An asymptotic α-test for the expectation of random fuzzy variables J. Stat. Plann. Inference 83 2000 331 346
    • (2000) J. Stat. Plann. Inference , vol.83 , pp. 331-346
    • Körner, R.1
  • 22
    • 0001913306 scopus 로고    scopus 로고
    • On the variance of random fuzzy variables
    • C. Bertoluzza, M.A. Gil, D.A. Ralescu, Physica-Verlag Heidelberg
    • R. Körner, and W. Näther On the variance of random fuzzy variables C. Bertoluzza, M.A. Gil, D.A. Ralescu, Statistical Modeling, Analysis and Management of Fuzzy Data 2002 Physica-Verlag Heidelberg 22 39
    • (2002) Statistical Modeling, Analysis and Management of Fuzzy Data , pp. 22-39
    • Körner, R.1    Näther, W.2
  • 23
    • 33748164797 scopus 로고    scopus 로고
    • Strong laws of large numbers for independent fuzzy set-valued random variables
    • DOI 10.1016/j.fss.2003.06.011, PII S0165011406002053, Fuzzy Sets and Probability/Statistics Theory
    • S. Li, and Y. Ogura Strong laws of large numbers for independent fuzzy set-valued random variables Fuzzy Sets Syst. 157 2006 2569 2578 (Pubitemid 44314002)
    • (2006) Fuzzy Sets and Systems , vol.157 , Issue.19 , pp. 2569-2578
    • Li, S.1    Ogura, Y.2
  • 25
    • 0001605105 scopus 로고    scopus 로고
    • On strong laws of large numbers for random upper semicontinuous functions
    • I. Molchanov On strong laws of large numbers for random upper semicontinuous functions J. Math. Anal. Appl. 235 1999 349 355
    • (1999) J. Math. Anal. Appl. , vol.235 , pp. 349-355
    • Molchanov, I.1
  • 26
    • 0035271558 scopus 로고    scopus 로고
    • Two-sample hypothesis tests of means of a fuzzy random variable
    • DOI 10.1016/S0020-0255(01)00078-0, PII S0020025501000780
    • M. Montenegro, M.R. Casals, M.A. Lubiano, and M.A. Gil Two-sample hypothesis tests of means of a fuzzy random variable Inf. Sci 133 2001 89 100 (Pubitemid 32380833)
    • (2001) Information Sciences , vol.133 , Issue.1-2 , pp. 89-100
    • Montenegro, M.1    Casals, M.R.2    Lubiano, M.A.3    Gil, M.A.4
  • 27
    • 17444382280 scopus 로고    scopus 로고
    • Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable
    • DOI 10.1007/s001840300270
    • M. Montenegro, A. Colubi, M.R. Casals, and M.A. Gil Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable Metrika 59 2004 31 49 (Pubitemid 40549717)
    • (2004) Metrika , vol.59 , Issue.1 , pp. 31-49
    • Montenegro, M.1    Colubi, A.2    Casals, M.R.3    Gil, M.A.4
  • 29
    • 0041351880 scopus 로고    scopus 로고
    • A strong law of large numbers for generalized random sets from the viewpoint of empirical processes
    • DOI 10.1090/S0002-9939-03-06842-4
    • F.N. Proske, and M.L. Puri A strong law of large numbers for generalized random sets from the viewpoint of empirical processes Proc. Am. Math. Soc. 131 2003 2937 2944 (Pubitemid 37056542)
    • (2003) Proceedings of the American Mathematical Society , vol.131 , Issue.9 , pp. 2937-2944
    • Proske, F.N.1    Puri, M.L.2
  • 30
    • 0000565701 scopus 로고
    • The concept of normality for fuzzy random variables
    • M.L. Puri, and D.A. Ralescu The concept of normality for fuzzy random variables Ann. Probab. 11 1985 1373 1379
    • (1985) Ann. Probab. , vol.11 , pp. 1373-1379
    • Puri, M.L.1    Ralescu, D.A.2
  • 32
    • 0022093460 scopus 로고
    • Inequality relation between fuzzy numbers and its use in fuzzy optimization
    • J. Ramík, and J. Římánek Inequality relation between fuzzy numbers and its use in fuzzy optimization Fuzzy Sets Syst. 16 1985 123 138 (Pubitemid 15528219)
    • (1985) Fuzzy Sets and Systems , vol.16 , Issue.2 , pp. 123-138
    • Ramik, J.1    Rimanek, J.2
  • 33
    • 0011595661 scopus 로고
    • Applications of fuzzy set concepts to behavioral sciences
    • (Inf. Sci. 179, 3964-3972)
    • M. Smithson, Applications of fuzzy set concepts to behavioral sciences, Math. Soc. Sci. 2 (1982) 257-274 (Inf. Sci. 179, 3964-3972).
    • (1982) Math. Soc. Sci. , vol.2 , pp. 257-274
    • Smithson, M.1
  • 34
    • 70349097188 scopus 로고    scopus 로고
    • A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread
    • W. Trutschnig, G. González-Rodríguez, A. Colubi, and M.A. Gil A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread Inf. Sci. 179 2009 3964 3972
    • (2009) Inf. Sci. , vol.179 , pp. 3964-3972
    • Trutschnig, W.1    González-Rodríguez, G.2    Colubi, A.3    Gil, M.A.4
  • 36
    • 67349132220 scopus 로고    scopus 로고
    • A new linear ordering of fuzzy numbers on subsets of F (R)
    • E. Valvis A new linear ordering of fuzzy numbers on subsets of F (R) Fuzzy Optim. Decis. Making 8 2009 141 163
    • (2009) Fuzzy Optim. Decis. Making , vol.8 , pp. 141-163
    • Valvis, E.1
  • 37
    • 0019585325 scopus 로고
    • A procedure for ordering fuzzy subsets of the unit interval
    • R.R. Yager A procedure for ordering fuzzy subsets of the unit interval Inf. Sci. 24 1981 143 161
    • (1981) Inf. Sci. , vol.24 , pp. 143-161
    • Yager, R.R.1
  • 38
    • 0016458950 scopus 로고
    • The concept of a linguistic variable and its application to approximate reasoning. Part 1
    • Part 2, Inf. Sci. 8, 301-353; Part 3, Inf. Sci. 9, 43-80
    • L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning. Part 1, Inf. Sci. 8 (1975) 199-249; Part 2, Inf. Sci. 8, 301-353; Part 3, Inf. Sci. 9, 43-80.
    • (1975) Inf. Sci. , vol.8 , pp. 199-249
    • Zadeh, L.A.1


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