A distance-based statistical analysis of fuzzy number-valued data

International Journal of Approximate Reasoning

Volumn 55, Issue 7, 2014, Pages 1487-1501

  Blanco Fernandez, A ^a   Casals, M R ^a   Colubi, A ^a   Corral, N ^a   Garcia Barzana, M ^a   Gil, M A ^a   Gonzalez Rodriguez, G ^a   Lpez, M T ^a   Lubiano, M A ^a   Montenegro, M ^a   Ramos Guajardo, A B ^a   De La Rosa De Sáa, Sara ^a   Sinova, B ^a  

^a UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Distance between fuzzy data; Fuzzy data; Random experiments; Statistics

Indexed keywords

FUZZY RULES; FUZZY SETS; STATISTICAL METHODS;

CENTRAL LIMIT THEOREM; DISTANCE-BASED; FUZZY DATA; FUZZY NUMBERS; RANDOM ELEMENTS; RANDOM EXPERIMENTS; RANDOM FUZZY SET; REAL LIFE DATA;

STATISTICS;

EID: 84897139873     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2013.09.020     Document Type: Conference Paper

References (53)

1. C. Bertoluzza, N. Corral, and A. Salas On a new class of distances between fuzzy numbers Mathw. Soft Comput. 2 1995 71 84
2. A. Blanco-Fernández, M.R. Casals, A. Colubi, N. Corral, S. de la Rosa de Sáa, M. García-Bárzana, M.A. Gil, G. González-Rodríguez, M.T. López, M.A. Lubiano, M. Montenegro, A.B. Ramos-Guajardo, and B. Sinova Random fuzzy sets: a mathematical tool to develop statistical fuzzy data analysis Iranian J. Fuzzy Syst. 10 2 2013 1 28
3. A. Colubi, R. Coppi, P. D'Urso, and M.A. Gil Statistics with fuzzy random variables Metron LXV 3 2007 277 303
4. A. Colubi, G. González-Rodríguez, and M.A. Gil A new characterization of discrete random variables by means of fuzzy sets: graphical features Abst. 56th Ses. Int. Stat. Inst. ISI 2007, Lisbon, Portugal 2007 165
5. A. Colubi, G. González-Rodríguez, M.A. Gil, and M.R. Casals A characterizing functional representation of continuous distributions focussed on relevant parameters Abst. Kick-off Meeting ERCIM WG on Comput. & Stat. and Int. Work. Comput. & Fin. Econom. Geneva, Switzerland 2007 40
6. A. Colubi, G. González-Rodríguez, M.A. Gil, and W. Trutschnig Nonparametric criteria for supervised classification of fuzzy data Int. J. Approx. Reason. 52 2011 1272 1282
7. I. Couso, and L. Sánchez Mark-recapture techniques in statistical tests for imprecise data Int. J. Approx. Reason. 52 2 2011 240 260
8. T. Denœux Maximum likelihood estimation from fuzzy data using the EM algorithm Fuzzy Sets Syst. 183 2011 72 91
9. T. Denœux, M.H. Masson, and P.A. Hébert Nonparametric rank-based statistics and significance tests for fuzzy data Fuzzy Sets Syst. 153 2005 1 28
10. P. Diamond, and P. Kloeden Metric spaces of fuzzy sets Fuzzy Sets Syst. 100 1999 63 71 (Pubitemid 129682572)
11. N.R. Draper, and W.G. Hunter Transformations: some examples revisited Technometrics 11 1969 129 132
12. D. Dubois, and H. Prade Gradual elements in a fuzzy set Soft Comput. 12 2008 165 175 (Pubitemid 47412748)
13. D. Dubois, and H. Prade Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets Fuzzy Sets Syst. 192 2012 3 24
14. R. Féron Ensembles aléatoires flous C. R. Math. Acad. Sci. Paris A 282 1976 903 906
15. R. Féron Ensembles flous attachés à un ensemble aléatoire flou Publ. Econom. 9 1976 51 66
16. R. Féron Sur les notions de distance et d'ecart dans une structure floue et leurs applications aux ensembles aléatoires flous C. R. Math. Acad. Sci. Paris A 289 1979 35 38
17. M.B. Ferraro, R. Coppi, G. González-Rodríguez, and A. Colubi A linear regression model for imprecise response Int. J. Approx. Reason. 51 7 2010 759 770
18. M. Fréchet Les éléments aléatoires de nature quelconque dans un espace distancié Ann. Inst. Henri Poincaré 10 1948 215 310
19. M.A. Gil, A. Colubi, and P. Terán Random fuzzy sets: why, when, how BEIO 30 2014 in press
20. M.A. Gil, M.A. Lubiano, M. Montenegro, and M.T. López Least squares fitting of an affine function and strength of association for interval-valued data Metrika 56 2002 97 111
21. M.A. Gil, M. Montenegro, G. González-Rodríguez, A. Colubi, and M.R. Casals Bootstrap approach to the multi-sample test of means with imprecise data Comput. Stat. Data Anal. 51 2006 148 162 (Pubitemid 44634803)
22. E. Giné, and J. Zinn Bootstrapping general empirical measures Ann. Probab. 18 1990 851 869
23. G. González-Rodríguez, A. Blanco, A. Colubi, and M.A. Lubiano Estimation of a simple linear regression model for fuzzy random variables Fuzzy Sets Syst. 160 2009 357 370
24. G. González-Rodríguez, A. Colubi, P. D'Urso, and P. Giordani An asymptotic test about the asymmetry of random variables based on fuzzy tools J. Lawry, E. Miranda, A. Bugarin, S. Li, M.A. Gil, P. Grzegorzewski, O. Hryniewicz, Soft Methods for Integrated Uncertainty Modelling 2006 Springer Berlin/Heidelberg 87 94
25. G. González-Rodríguez, A. Colubi, P. D'Urso, and M. Montenegro Multi-sample test-based clustering for fuzzy random variables Int. J. Approx. Reason. 50 2009 721 731
26. G. González-Rodríguez, A. Colubi, and M.A. Gil Fuzzy data treated as functional data. A one-way ANOVA test approach Comput. Stat. Data Anal. 56 2012 943 955
27. 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)
28. G. González-Rodríguez, A. Colubi, M.A. Gil, and P. D'Urso An asymptotic two dependent samples test of equality of means of fuzzy random variables Proc. COMPSTAT'2006 2006 http://www.stat.unipg.it/iasc/Proceedings/ 2006/COMPSTAT/CD/145.pdf
29. G. González-Rodríguez, A. Colubi, M.A. Gil, and M.A. Lubiano A new way of quantifying the symmetry of a random variable: estimation and hypothesis testing J. Stat. Plan. Inference 142 2012 3061 3072
30. 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)
31. F. Herrera, E. Herrera-Viedma, and L. Martínez A fuzzy linguistic methodology to deal with unbalanced linguistic term sets IEEE Trans. Fuzzy Syst. 16 2008 354 370 (Pubitemid 351586037)
32. W. Hoeffding A class of statistics with asymptotically normal distribution Ann. Math. Stat. 19 1948 293 325
33. E.P. Klement, M.L. Puri, and D.A. Ralescu Limit theorems for fuzzy random variables Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 407 1986 171 182
34. R. Körner Linear models with random fuzzy variables PhD thesis 1997 Technische Universität Bergakademie Freiberg http://www.mathe.tu-freiberg. de/inst/stoch/Koerner/dissa.ps
35. R. Körner An asymptotic α-test for the expectation of random fuzzy variables J. Stat. Plan. Inference 83 2000 331 346
36. 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
37. R. Kruse, and K.D. Meyer Statistics with Vague Data 1987 D. Reidel Publishing Company Dordrecht
38. H. Levene Robust tests for equality of variances I. Olkin, Contributions to Probability and Statistics 1960 Stanford University Press Palo Alto 278 292
39. M.A. Lubiano, M.C. Alonso, and M.A. Gil Statistical inferences on the S-mean squared dispersion of a fuzzy random variable Proc. Joint EUROFUSE-SIC'99 1999 532 537
40. M.A. Lubiano, M.A. Gil, M. López-Díaz, and M.T. López The λ → -mean squared dispersion associated with a fuzzy random variable Fuzzy Sets Syst. 111 2000 307 317
41. M. Montenegro, M.R. Casals, M.A. Lubiano, and M.A. Gil Two-sample hypothesis tests of means of a fuzzy random variable Inform. Sci. 133 2001 89 100 (Pubitemid 32380833)
42. 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)
43. W. Näther Random fuzzy variables of second order and applications to statistical inference Inform. Sci. 133 2001 69 88 (Pubitemid 32380832)
44. H.T. Nguyen A note on the extension principle for fuzzy sets J. Math. Anal. Appl. 64 1978 369 380
45. M.L. Puri, and D.A. Ralescu The concept of normality for fuzzy random variables Ann. Probab. 11 1985 1373 1379
46. M.L. Puri, and D.A. Ralescu Random fuzzy sets J. Math. Anal. Appl. 114 1986 409 422
47. A.B. Ramos-Guajardo, A. Colubi, G. González-Rodríguez, and M.A. Gil One-sample tests for a generalized Fréchet variance of a fuzzy random variable Metrika 71 2010 185 202
48. A.B. Ramos-Guajardo, G. González-Rodríguez, M. Montenegro, and M.T. López Power analysis of the homoscedasticity test for random fuzzy sets C. Borgelt, G. González-Rodríguez, W. Trutschnig, M.A. Lubiano, M.A. Gil, P. Grzegorzewski, O. Hryniewicz, Combining Soft Computing and Statistical Methods in Data Analysis 2010 Springer-Verlag Heidelberg 537 544
49. A.B. Ramos-Guajardo, and M.A. Lubiano K-sample tests for equality of variances of random fuzzy sets Comput. Stat. Data Anal. 56 2012 956 966
50. 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 Inform. Sci. 179 2009 3964 3972
51. L.A. Zadeh The concept of a linguistic variable and its application to approximate reasoning, Part 1 Inform. Sci. 8 1975 199 249
52. L.A. Zadeh The concept of a linguistic variable and its application to approximate reasoning, Part 2 Inform. Sci. 8 1975 301 353
53. L.A. Zadeh The concept of a linguistic variable and its application to approximate reasoning, Part 3 Inform. Sci. 9 1975 43 80