메뉴 건너뛰기




Volumn 65, Issue 3, 2007, Pages 277-303

Statistics with fuzzy random variables

Author keywords

ANOVA for fuzzy data; Distances between fuzzy data; Estimation; Fuzzy data; Hypothesis testing; Informational paradigm; Regression analysis

Indexed keywords


EID: 78751643502     PISSN: 00261424     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (23)

References (67)
  • 4
    • 38249038096 scopus 로고
    • Multidimensional least-squares fitting of fuzzy models
    • Celminš, A. (1987) Multidimensional least-squares fitting of fuzzy models, Math. Modeling, 9, 669-690.
    • (1987) Math. Modeling , vol.9 , pp. 669-690
    • Celminš, A.1
  • 7
    • 0037186685 scopus 로고    scopus 로고
    • A theoretical framework for data mining: The "informational Paradigm"
    • Coppi, R. (2002) A theoretical framework for data mining: the "Informational Paradigm", Comp. Stat. Data Anal., 38, 501-515.
    • (2002) Comp. Stat. Data Anal. , vol.38 , pp. 501-515
    • Coppi, R.1
  • 9
    • 84891838336 scopus 로고    scopus 로고
    • Management of uncertainty in statistical reasoning: The case of regression analysis
    • (in press)
    • Coppi, R. (2007) Management of uncertainty in statistical reasoning: the case of regression analysis, International Journal of Approximate Reasoning, (in press).
    • (2007) International Journal of Approximate Reasoning
    • Coppi, R.1
  • 10
    • 33748065155 scopus 로고    scopus 로고
    • Regression analysis with fuzzy informational paradigm: A leastsquares approach using membership function information
    • Coppi, R. and D'Urso, P. (2003) Regression analysis with fuzzy informational paradigm: a leastsquares approach using membership function information, Int. J. Pure Appl. Math., 8 (3), 279-306.
    • (2003) Int. J. Pure Appl. Math. , vol.8 , Issue.3 , pp. 279-306
    • Coppi, R.1    D'Urso, P.2
  • 11
    • 34247126587 scopus 로고    scopus 로고
    • Component models for fuzzy data
    • Coppi, R., D'Urso, P. and Giordani, P. (2006a) Component models for fuzzy data, Psychometrika, 71, 733-761.
    • (2006) Psychometrika , vol.71 , pp. 733-761
    • Coppi, R.1    D'Urso, P.2    Giordani, P.3
  • 12
    • 33750310787 scopus 로고    scopus 로고
    • Least squares estimation of a linear regression model with LR fuzzy response
    • Coppi, R., D'Urso, P., Giordani, P. and Santoro, A. (2006b) Least squares estimation of a linear regression model with LR fuzzy response, Comp. Stat. Data Anal., 51, 267-286.
    • (2006) Comp. Stat. Data Anal. , vol.51 , pp. 267-286
    • Coppi, R.1    D'Urso, P.2    Giordani, P.3    Santoro, A.4
  • 13
  • 16
    • 0000325717 scopus 로고
    • Fuzzy least squares
    • Diamond, P. (1988) Fuzzy least squares, Information Sciences, 46, 141-157.
    • (1988) Information Sciences , vol.46 , pp. 141-157
    • Diamond, P.1
  • 18
    • 0037454064 scopus 로고    scopus 로고
    • Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data
    • D'Urso, P. (2003) Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data, Comp. Stat. Data Anal., 42, 47-72.
    • (2003) Comp. Stat. Data Anal. , vol.42 , pp. 47-72
    • D'Urso, P.1
  • 19
    • 33750291939 scopus 로고    scopus 로고
    • Fuzzy clusterwise linear regression analysis with symmetrical fuzzy output variable
    • D'Urso, P. and Santoro, A. (2006) Fuzzy clusterwise linear regression analysis with symmetrical fuzzy output variable, Comp. Stat. Data Anal., 51, 287-313.
    • (2006) Comp. Stat. Data Anal. , vol.51 , pp. 287-313
    • D'Urso, P.1    Santoro, A.2
  • 20
    • 0842264210 scopus 로고    scopus 로고
    • Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination
    • Ferraty, F. and Vieu, P. (2004) Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination, J. Nonparametr. Stat., 16, 111- 125.
    • (2004) J. Nonparametr. Stat. , vol.16 , pp. 111-125
    • Ferraty, F.1    Vieu, P.2
  • 21
    • 80955130369 scopus 로고    scopus 로고
    • Nonparametric regression with fuzzy random variables through the support function
    • Flórez, J. L., Colubi, A., González-Rodríguez, G. and Gil, M. A. (2006) Nonparametric regression with fuzzy random variables through the support function, Proc. IPMU 2006, 724-730.
    • (2006) Proc. IPMU 2006 , pp. 724-730
    • Flórez, J.L.1    Colubi, A.2    González-Rodríguez, G.3    Gil, M.A.4
  • 22
    • 0000315591 scopus 로고
    • Les éléments aléatoires de natures quelconque dans un éspace distancié
    • Fréchet, M. (1948) Les éléments aléatoires de natures quelconque dans un éspace distancié, Ann. Inst. H. Poincaré, 10, 215-310.
    • (1948) Ann. Inst. H. Poincaré , vol.10 , pp. 215-310
    • Fréchet, M.1
  • 24
    • 17444420921 scopus 로고
    • An operative extension of the likelihood ratio test from fuzzy data
    • Gil, M. A. and Casals, M. R. (1988a) An operative extension of the likelihood ratio test from fuzzy data, Stat. Papers, 29, 191-203.
    • (1988) Stat. Papers , vol.29 , pp. 191-203
    • Gil, M.A.1    Casals, M.R.2
  • 25
    • 38249032831 scopus 로고
    • The minimum inaccuracy estimates in χ2 tests for goodness of fit with fuzzy observations
    • Gil, M. A., Corral, N. and Gil, P. (1988b) The minimum inaccuracy estimates in χ2 tests for goodness of fit with fuzzy observations, J. Statist. Plan. Infer., 19, 95-115.
    • (1988) J. Statist. Plan. Infer. , vol.19 , pp. 95-115
    • Gil, M.A.1    Corral, N.2    Gil, P.3
  • 26
    • 0024704395 scopus 로고
    • The likelihood ratio test for goodness of fit with fuzzy experimental observations
    • Gil, M. A., Corral, N. and Casals, M. R. (1989) The likelihood ratio test for goodness of fit with fuzzy experimental observations, IEEE Trans. Syst., Man, Cyber., 19, 771-779.
    • (1989) IEEE Trans. Syst., Man, Cyber. , vol.19 , pp. 771-779
    • Gil, M.A.1    Corral, N.2    Casals, M.R.3
  • 29
    • 0036400795 scopus 로고    scopus 로고
    • Least squares fitting of an affine function and strength of association for interval-valued data
    • Gil, M. A., Lubiano, M. A., Montenegro, M. and López, M. T. (2002) Least squares fitting of an affine function and strength of association for interval-valued data, Metrika, 56, 97-111.
    • (2002) Metrika , vol.56 , pp. 97-111
    • Gil, M.A.1    Lubiano, M.A.2    Montenegro, M.3    López, M.T.4
  • 31
    • 33750359747 scopus 로고    scopus 로고
    • A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing
    • González-Rodríguez, G., Colubi, A. and Gil, M. A. (2006a) A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing, Comp. Stat. Data Anal., 51, 163-176.
    • (2006) Comp. Stat. Data Anal. , vol.51 , pp. 163-176
    • González-Rodríguez, G.1    Colubi, A.2    Gil, M.A.3
  • 32
    • 33748078152 scopus 로고    scopus 로고
    • Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data
    • González-Rodríguez, G., Montenegro, M., Colubi, A. and Gil, M. A. (2006b) Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data, Fuzzy Sets and Systems, 157, 2608-2613.
    • (2006) Fuzzy Sets and Systems , vol.157 , pp. 2608-2613
    • González-Rodríguez, G.1    Montenegro, M.2    Colubi, A.3    Gil, M.A.4
  • 34
    • 33750339169 scopus 로고    scopus 로고
    • The coefficient of concordance for vague data
    • Grzegorzewski, P. (2006) The coefficient of concordance for vague data, Comp. Stat. Data Anal., 51, 314-322.
    • (2006) Comp. Stat. Data Anal. , vol.51 , pp. 314-322
    • Grzegorzewski, P.1
  • 35
    • 33750310790 scopus 로고    scopus 로고
    • Goodman-Kruskal measure of dependence for fuzzy ordered categorical data
    • Hryniewicz, O. (2006) Goodman-Kruskal measure of dependence for fuzzy ordered categorical data, Comp. Stat. Data Anal., 51, 323-334.
    • (2006) Comp. Stat. Data Anal. , vol.51 , pp. 323-334
    • Hryniewicz, O.1
  • 37
    • 33750332020 scopus 로고    scopus 로고
    • Least squares estimation in linear regression models with vague concepts
    • (López-Díaz, M, Gil, M. A. Grzegorzewski, P., Hryniewicz, O., Lawry, J., Eds.), Springer, Heidelberg
    • Krätschmer, V. (2004) Least squares estimation in linear regression models with vague concepts, In: Soft Methodology and Random Information Systems, (López-Díaz, M, Gil, M. A. Grzegorzewski, P., Hryniewicz, O., Lawry, J., Eds.), Springer, Heidelberg, 407-414.
    • (2004) Soft Methodology and Random Information Systems , pp. 407-414
    • Krätschmer, V.1
  • 38
    • 0001378385 scopus 로고    scopus 로고
    • An asymptotic α-test for the expectation of random fuzzy variables
    • Körner, R. (2000) An asymptotic α-test for the expectation of random fuzzy variables, J. Stat. Plan. Infer., 83, 331-345.
    • (2000) J. Stat. Plan. Infer. , vol.83 , pp. 331-345
    • Körner, R.1
  • 39
    • 0001913306 scopus 로고    scopus 로고
    • On the variance of random fuzzy variables
    • (Bertoluzza, C., Gil, M. A., Ralescu, D. A., Eds.), Physica-Verlag, Heidelberg
    • Körner, R. and Näther, W. (2002) On the variance of random fuzzy variables, In: Statistical Modeling, Analysis and Management of Fuzzy Data, (Bertoluzza, C., Gil, M. A., Ralescu, D. A., Eds.), Physica-Verlag, Heidelberg, 22-39.
    • (2002) Statistical Modeling, Analysis and Management of Fuzzy Data , pp. 22-39
    • Körner, R.1    Näther, W.2
  • 41
    • 6344232554 scopus 로고
    • Fuzzy random variables I: Definitions and theorems
    • Kwakernaak, H. (1978) Fuzzy random variables I: Definitions and theorems, Inform. Sci., 15, 1-29.
    • (1978) Inform. Sci. , vol.15 , pp. 1-29
    • Kwakernaak, H.1
  • 42
    • 26944480882 scopus 로고
    • Fuzzy random variables II: Algorithms and examples for the discrete case
    • Kwakernaak, H. (1979) Fuzzy random variables II: Algorithms and examples for the discrete case, Inform. Sci., 17, 253-278.
    • (1979) Inform. Sci. , vol.17 , pp. 253-278
    • Kwakernaak, H.1
  • 43
    • 75549085558 scopus 로고    scopus 로고
    • Statistical inferences on the S-mean squared dispersion of a fuzzy random variable
    • Lubiano, M. A., Alonso, M. C. and Gil, M. A. (1999a) Statistical inferences on the S-mean squared dispersion of a fuzzy random variable, Proc. EUROFUSE-SIC'99, 532-537.
    • (1999) Proc. EUROFUSE-SIC'99 , pp. 532-537
    • Lubiano, M.A.1    Alonso, M.C.2    Gil, M.A.3
  • 44
    • 0345920697 scopus 로고    scopus 로고
    • Estimating the expected value of fuzzy random variables in random samplings from finite populations
    • Lubiano, M. A. and Gil, M. A. (1999) Estimating the expected value of fuzzy random variables in random samplings from finite populations, Stat. Papers, 40, 277-295.
    • (1999) Stat. Papers , vol.40 , pp. 277-295
    • Lubiano, M.A.1    Gil, M.A.2
  • 45
    • 84883256462 scopus 로고    scopus 로고
    • F-Inequality indices for fuzzy random variables
    • (Bertoluzza, C., Gil, M.A., Ralescu, D.A., Eds.), Physica-Verlag, Heidelberg
    • Lubiano, M. A. and Gil, M. A. (2002) f -Inequality indices for fuzzy random variables, In: Statistical Modeling, Analysis and Management of Fuzzy Data (Bertoluzza, C., Gil, M.A., Ralescu, D.A., Eds.), Physica-Verlag, Heidelberg, 43-63.
    • (2002) Statistical Modeling, Analysis and Management of Fuzzy Data , pp. 43-63
    • Lubiano, M.A.1    Gil, M.A.2
  • 46
    • 0033474919 scopus 로고    scopus 로고
    • On the Rao-Blackwell theorem for fuzzy random variables
    • Lubiano, M. A., Gil, M. A. and López-Díaz, M. (1999b) On the Rao-Blackwell theorem for fuzzy random variables, Kybernetika, 35, 167-175.
    • (1999) Kybernetika , vol.35 , pp. 167-175
    • Lubiano, M.A.1    Gil, M.A.2    López-Díaz, M.3
  • 48
    • 0035271558 scopus 로고    scopus 로고
    • Two-sample hypothesis tests of means of a fuzzy random variable
    • Montenegro, M., Casals, M. R., Lubiano, M. A. and Gil, M. A. (2001) Two-sample hypothesis tests of means of a fuzzy random variable, Inform. Sci, 133, 89-100.
    • (2001) Inform. Sci , vol.133 , pp. 89-100
    • Montenegro, M.1    Casals, M.R.2    Lubiano, M.A.3    Gil, M.A.4
  • 49
    • 33748062166 scopus 로고    scopus 로고
    • Introduction to ANOVA with fuzzy random variables
    • (López-Díaz, M., Gil, M. A. Grzegorzewski, P., Hryniewicz, O., Lawry, J., Eds.), Springer, Heidelberg
    • Montenegro, M., González-Rodríguez, G., Gil, M. A., Colubi, A. and Casals, M. R. (2004a) Introduction to ANOVA with fuzzy random variables, In: Soft Methodology and Random Information Systems, (López-Díaz, M., Gil, M. A. Grzegorzewski, P., Hryniewicz, O., Lawry, J., Eds.), Springer, Heidelberg, 487-494.
    • (2004) Soft Methodology and Random Information Systems , pp. 487-494
    • Montenegro, M.1    González-Rodríguez, G.2    Gil, M.A.3    Colubi, A.4    Casals, M.R.5
  • 50
    • 17444382280 scopus 로고    scopus 로고
    • Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable
    • Montenegro, M., Colubi, A., Casals, M. R. and Gil, M. A. (2004b) Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable, Metrika, 59, 31-49.
    • (2004) Metrika , vol.59 , pp. 31-49
    • Montenegro, M.1    Colubi, A.2    Casals, M.R.3    Gil, M.A.4
  • 51
    • 0034360621 scopus 로고    scopus 로고
    • On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data
    • Näther, W. (2000) On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data, Metrika, 51, 201-221.
    • (2000) Metrika , vol.51 , pp. 201-221
    • Näther, W.1
  • 52
    • 0035271525 scopus 로고    scopus 로고
    • Random fuzzy variables of second order and applications to statistical inference
    • Näther, W. (2001) Random fuzzy variables of second order and applications to statistical inference, Inform. Sci., 133, 69-88.
    • (2001) Inform. Sci. , vol.133 , pp. 69-88
    • Näther, W.1
  • 53
    • 33750306206 scopus 로고    scopus 로고
    • Regression with fuzzy random data
    • Näther, W. (2006) Regression with fuzzy random data, Comp. Stat. Data Anal., 51, 235-252.
    • (2006) Comp. Stat. Data Anal. , vol.51 , pp. 235-252
    • Näther, W.1
  • 55
    • 33750345703 scopus 로고    scopus 로고
    • Random and fuzzy sets in coarse data analysis
    • Nguyen, H.T. and Wu, B. (2006) Random and fuzzy sets in coarse data analysis, Comp. Stat. Data Anal., 51, 70-85.
    • (2006) Comp. Stat. Data Anal. , vol.51 , pp. 70-85
    • Nguyen, H.T.1    Wu, B.2
  • 56
    • 0242490050 scopus 로고    scopus 로고
    • Nonparametric regression analysis of uncertain and imprecise data using belief functions
    • Petit-Renaud, S. and Denoeux, T. (2004) Nonparametric regression analysis of uncertain and imprecise data using belief functions, Int. J. Approx. Reas., 35, 1-28.
    • (2004) Int. J. Approx. Reas. , vol.35 , pp. 1-28
    • Petit-Renaud, S.1    Denoeux, T.2
  • 58
    • 0001344926 scopus 로고
    • Fuzzy information and decision in statistical model
    • (Gupta, M. M., Rage, R. K., Yager, R. R., Eds.), North-Holland
    • Tanaka, H., Okuda, T. and Asai, K. (1979) Fuzzy information and decision in statistical model, In: Advances in Fuzzy Sets Theory and Applications (Gupta, M. M., Rage, R. K., Yager, R. R., Eds.), North-Holland, 303-320.
    • (1979) Advances in Fuzzy Sets Theory and Applications , pp. 303-320
    • Tanaka, H.1    Okuda, T.2    Asai, K.3
  • 61
    • 33750300042 scopus 로고    scopus 로고
    • Univariate statistical analysis with fuzzy data
    • Viertl, R. (2006) Univariate statistical analysis with fuzzy data, Comp. Stat. Data Anal., 51, 133-147.
    • (2006) Comp. Stat. Data Anal. , vol.51 , pp. 133-147
    • Viertl, R.1
  • 62
    • 0037119182 scopus 로고    scopus 로고
    • Least-squares fuzzy regression with fuzzy random variables
    • Wünsche, A. and Näther, W. (2002) Least-squares fuzzy regression with fuzzy random variables, Fuzzy Sets and Systems, 130, 43-50.
    • (2002) Fuzzy Sets and Systems , vol.130 , pp. 43-50
    • Wünsche, A.1    Näther, W.2
  • 63
    • 34248666540 scopus 로고
    • Fuzzy sets
    • Zadeh, L. A. (1965) Fuzzy Sets, Inform. Contr., 8, 338-353.
    • (1965) Inform. Contr. , vol.8 , pp. 338-353
    • Zadeh, L.A.1
  • 64
    • 0016458950 scopus 로고
    • The concept of a linguistic variable and its application to approximate reasoning
    • Zadeh, L. A. (1975) The concept of a linguistic variable and its application to approximate reasoning, Part 1, Inform. Sci., 8, 199-249;
    • (1975) Part 1, Inform. Sci. , vol.8 , pp. 199-249
    • Zadeh, L.A.1
  • 65
    • 0016459349 scopus 로고
    • The concept of a linguistic variable and its application to approximate reasoning
    • Part 2. Inform. Sci. 8, 301-353;
    • (1975) Part 2. Inform. Sci. , vol.8 , pp. 301-353
    • Zadeh, L.A.1
  • 66
    • 0016631726 scopus 로고
    • The concept of a linguistic variable and its application to approximate reasoning
    • Part 3. Inform. Sci. 9, 43-80.
    • (1975) Part 3. Inform. Sci. , vol.9 , pp. 43-80
    • Zadeh, L.A.1
  • 67
    • 84942928572 scopus 로고
    • Discussion: Probability Theory and Fuzzy Logic are complementary rather than competitive
    • Zadeh, L. A. (1995) Discussion: Probability Theory and Fuzzy Logic are complementary rather than competitive, Technometrics, 37, 271-276.
    • (1995) Technometrics , vol.37 , pp. 271-276
    • Zadeh, L.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.