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Volumn 30, Issue 1, 2014, Pages 5-29

Random fuzzy sets: Why, when, how

Author keywords

Functional data; Fuzzy statistics; Metric space; Random elements

Indexed keywords


EID: 84900793341     PISSN: 18893805     EISSN: 23871725     Source Type: Journal    
DOI: None     Document Type: Review
Times cited : (13)

References (65)
  • 1
    • 0040927550 scopus 로고    scopus 로고
    • A generalized real-valued measure of the inequality associated with a fuzzy random variable
    • Alonso, M.C., Brezmes, T., Lubiano, M.A. and Bertoluzza, C. (2001). A generalized real-valued measure of the inequality associated with a fuzzy random variable. Int. J. Approx. Reasoning, 26, 47-66.
    • (2001) Int. J. Approx. Reasoning , vol.26 , pp. 47-66
    • Alonso, M.C.1    Brezmes, T.2    Lubiano, M.A.3    Bertoluzza, C.4
  • 2
    • 50549204934 scopus 로고
    • Integrals of set-valued functions
    • Aumann, R.J. (1965). Integrals of set-valued functions. J. Math. Anal. Appl., 12, 1-12.
    • (1965) J. Math. Anal. Appl. , vol.12 , pp. 1-12
    • Aumann, R.J.1
  • 7
    • 0005819262 scopus 로고    scopus 로고
    • Traditional techniques to prove some limit theorems for fuzzy random variables
    • Bertoluzza, C., Gil, M. A. and Ralescu, D. A. (eds.), Physica, Heidelberg
    • Colubi, A. (2002). Traditional techniques to prove some limit theorems for fuzzy random variables. In: Bertoluzza, C., Gil, M. A. and Ralescu, D. A. (eds.), Statistical Modeling, Analysis and Management for Fuzzy Data, 64-71. Physica, Heidelberg.
    • (2002) Statistical Modeling, Analysis and Management for Fuzzy Data , pp. 64-71
    • Colubi, A.1
  • 8
    • 78751643502 scopus 로고    scopus 로고
    • Statistics with fuzzy random variables
    • Colubi, A., Coppi, R., D'Urso, P. and Gil, M.A. (2007). Statistics with fuzzy random variables. Metron, 65, 277-303.
    • (2007) Metron , vol.65 , pp. 277-303
    • Colubi, A.1    Coppi, R.2    D'Urso, P.3    Gil, M.A.4
  • 12
    • 84856101730 scopus 로고    scopus 로고
    • Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets
    • Dubois, D. and Prade, H. (2012). Gradualness, uncertainty and bipolarity: making sense of fuzzy sets. Fuzzy Sets and Systems, 192, 3-24.
    • (2012) Fuzzy Sets and Systems , vol.192 , pp. 3-24
    • Dubois, D.1    Prade, H.2
  • 13
    • 16344392532 scopus 로고
    • Ensembles aléatoires flous
    • Féron, R. (1976a). Ensembles aléatoires flous. C. R. Acad. Sc. Paris A, 282, 903-906.
    • (1976) C. R. Acad. Sc. Paris A , vol.282 , pp. 903-906
    • Féron, R.1
  • 14
    • 58149125488 scopus 로고
    • Ensembles flous attachés ̀a un ensemble aléatoire flou
    • Féron, R. (1976b). Ensembles flous attachés ̀a un ensemble aléatoire flou. Publ. Econometr., 9, 51-66.
    • (1976) Publ. Econometr. , vol.9 , pp. 51-66
    • Féron, R.1
  • 15
    • 58149109285 scopus 로고
    • Sur les notions de distance et d'ecart dans une structure floue et leurs applications aux ensembles aléatoires flous
    • Féron, R. (1979). Sur les notions de distance et d'ecart dans une structure floue et leurs applications aux ensembles aléatoires flous. C. R. Acad. Sc. Paris A, 289, 35-38.
    • (1979) C. R. Acad. Sc. Paris A , vol.289 , pp. 35-38
    • Féron, R.1
  • 16
    • 0000315591 scopus 로고
    • Les éléments aléatoires de nature quelconque dans un espace distancié
    • Fréchet, M. (1948). Les éléments aléatoires de nature quelconque dans un espace distancié. Ann. L'Inst. H. Poincaré, 10, 215-310.
    • (1948) Ann. L'inst. H. Poincaré , vol.10 , pp. 215-310
    • Fréchet, M.1
  • 17
    • 65749313022 scopus 로고
    • Conferencias sobre los elementos aleatorios de naturaleza cualquiera
    • Fréchet, M. (1950). Conferencias sobre los elementos aleatorios de naturaleza cualquiera. Trabajos de Estadística, 1, 157-181.
    • (1950) Trabajos de Estadística , vol.1 , pp. 157-181
    • Fréchet, M.1
  • 18
    • 0032188569 scopus 로고    scopus 로고
    • The fuzzy hyperbolic inequality index associated with fuzzy random variables
    • Gil, M.A., López-Díaz, M. and López-García, H. (1998). The fuzzy hyperbolic inequality index associated with fuzzy random variables. Eur. J. Oper. Res., 110, 377-391.
    • (1998) Eur. J. Oper. Res. , vol.110 , pp. 377-391
    • Gil, M.A.1    López-Díaz, M.2    López-García, H.3
  • 19
    • 33748062355 scopus 로고    scopus 로고
    • Overview on the development of fuzzy random variables
    • Gil, M.A., López-Díaz, M. and Ralescu, D.A. (2006). Overview on the development of fuzzy random variables. Fuzzy Sets and Systems, 157, 2546-2557.
    • (2006) Fuzzy Sets and Systems , vol.157 , pp. 2546-2557
    • Gil, M.A.1    López-Díaz, M.2    Ralescu, D.A.3
  • 20
    • 0001678364 scopus 로고
    • Bootstrapping general empirical measures
    • Giné, E. and Zinn, J. (1990). Bootstrapping general empirical measures. Ann. Probab., 18, 851-869.
    • (1990) Ann. Probab. , vol.18 , pp. 851-869
    • Giné, E.1    Zinn, J.2
  • 22
    • 84856734042 scopus 로고    scopus 로고
    • Fuzzy data treated as functional data. A one-way ANOVA test approach
    • González-Rodríguez, G., Colubi, A. and Gil, M.A. (2012). Fuzzy data treated as functional data. A one-way ANOVA test approach. Comp. Stat. Data Anal., 56, 943-955.
    • (2012) Comp. Stat. Data Anal. , vol.56 , pp. 943-955
    • González-Rodríguez, G.1    Colubi, A.2    Gil, M.A.3
  • 23
    • 80051795458 scopus 로고    scopus 로고
    • A future-oriented retirement transition adjustment framework
    • Hesketh, B., Griffin, B. and Loh, V. (2011). A future-oriented retirement transition adjustment framework. J. Vocat. Behav., 79, 303-314.
    • (2011) J. Vocat. Behav. , vol.79 , pp. 303-314
    • Hesketh, B.1    Griffin, B.2    Loh, V.3
  • 24
    • 38249011025 scopus 로고
    • Work adjustment theory: An empirical test using a fuzzy rating scale
    • Hesketh, B., McLachlan, K. and Gardner, D. (1992). Work adjustment theory: An empirical test using a fuzzy rating scale. J. Vocat. Behav., 40, 318-337.
    • (1992) J. Vocat. Behav. , vol.40 , pp. 318-337
    • Hesketh, B.1    McLachlan, K.2    Gardner, D.3
  • 25
    • 0009301926 scopus 로고
    • Use of fuzzy variables in developing new scales from the strong interest inventory
    • Hesketh, B., Hesketh, T., Hansen, J.-I. and Goranson, D. (1995). Use of fuzzy variables in developing new scales from the strong interest inventory. J. Couns. Psychol., 42, 85-99.
    • (1995) J. Couns. Psychol. , vol.42 , pp. 85-99
    • Hesketh, B.1    Hesketh, T.2    Hansen, J.-I.3    Goranson, D.4
  • 26
    • 0010899823 scopus 로고
    • Computerized fuzzy ratings: The concept of a fuzzy class
    • Hesketh, T. and Hesketh, B. (1994). Computerized fuzzy ratings: the concept of a fuzzy class. Behav. Res. Meth., Instr., & Comp., 26, 272-277.
    • (1994) Behav. Res. Meth., Instr., & Comp. , vol.26 , pp. 272-277
    • Hesketh, T.1    Hesketh, B.2
  • 27
    • 0024037874 scopus 로고
    • An application of a computerized fuzzy graphic rating scale to the psychological measurement of individual differences
    • Hesketh, T., Pryor, R. and Hesketh, B. (1988). An application of a computerized fuzzy graphic rating scale to the psychological measurement of individual differences. Int. J. Man-Machine Studies, 29, 21-35.
    • (1988) Int. J. Man-Machine Studies , vol.29 , pp. 21-35
    • Hesketh, T.1    Pryor, R.2    Hesketh, B.3
  • 28
    • 0001577815 scopus 로고
    • Integrals, conditional expectations, and martingales of multivalued junctions
    • Hiai, F. and Umegaki, H. (1977). Integrals, conditional expectations, and martingales of multivalued junctions. J. Multiv. Anal., 7, 149-182.
    • (1977) J. Multiv. Anal. , vol.7 , pp. 149-182
    • Hiai, F.1    Umegaki, H.2
  • 29
    • 0036642945 scopus 로고    scopus 로고
    • Measurability for fuzzy valued functions
    • Kim, Y.-K. (2002). Measurability for fuzzy valued functions. Fuzzy Sets and Systems, 129, 105-109.
    • (2002) Fuzzy Sets and Systems , vol.129 , pp. 105-109
    • Kim, Y.-K.1
  • 31
    • 0002109629 scopus 로고    scopus 로고
    • On the variance of fuzzy random variables
    • Körner, R. (1997). On the variance of fuzzy random variables. Fuzzy Sets and Systems, 92, 83-93.
    • (1997) Fuzzy Sets and Systems , vol.92 , pp. 83-93
    • Körner, R.1
  • 32
    • 0001913306 scopus 로고    scopus 로고
    • On the variance of random fuzzy variables
    • (Bertoluzza, C., Gil, M.A. and 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. and Ralescu, D.A., eds.), 22-39. Physica-Verlag, Heidelberg.
    • (2002) Statistical Modeling, Analysis and Management of Fuzzy Data , pp. 22-39
    • Körner, R.1    Näther, W.2
  • 34
    • 0035480420 scopus 로고    scopus 로고
    • A unified approach to fuzzy random variables
    • Krätschmer, V. (2001). A unified approach to fuzzy random variables. Fuzzy Sets and Systems, 123, 1-9.
    • (2001) Fuzzy Sets and Systems , vol.123 , pp. 1-9
    • Krätschmer, V.1
  • 35
    • 10044295232 scopus 로고    scopus 로고
    • Probability theory in fuzzy sample spaces
    • Krätschmer, V. (2004). Probability theory in fuzzy sample spaces. Metrika, 60, 167-189.
    • (2004) Metrika , vol.60 , pp. 167-189
    • Krätschmer, V.1
  • 37
    • 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
  • 38
    • 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
  • 39
    • 0000074041 scopus 로고    scopus 로고
    • Convergence of set-valued and fuzzy-valued martingales
    • Li, S. and Ogura, Y. (1999). Convergence of set-valued and fuzzy-valued martingales. Fuzzy Sets and Systems, 101, 453-461.
    • (1999) Fuzzy Sets and Systems , vol.101 , pp. 453-461
    • Li, S.1    Ogura, Y.2
  • 40
    • 33748164797 scopus 로고    scopus 로고
    • Strong laws of large numbers for independent fuzzy set-valued random variables
    • Li, S. and Ogura, Y. (2006). Strong laws of large numbers for independent fuzzy set-valued random variables. Fuzzy Sets and Systems, 157, 2569-2578.
    • (2006) Fuzzy Sets and Systems , vol.157 , pp. 2569-2578
    • Li, S.1    Ogura, Y.2
  • 42
    • 0141850347 scopus 로고    scopus 로고
    • Central limit theorems for generalized set-valued random variables
    • Li, S., Ogura, Y., Proske, F. and Puri, M. L. (2003). Central limit theorems for generalized set-valued random variables. J. Math. Anal. Appl., 285, 250-263.
    • (2003) J. Math. Anal. Appl. , vol.285 , pp. 250-263
    • Li, S.1    Ogura, Y.2    Proske, F.3    Puri, M.L.4
  • 43
    • 33750329419 scopus 로고    scopus 로고
    • Tools for fuzzy random variables: Embeddings and measurabilities
    • López-Díaz, M. and Ralescu, D.A. (2006). Tools for fuzzy random variables: Embeddings and measurabilities. Comp. Stat. Data Anal., 51, 109-114.
    • (2006) Comp. Stat. Data Anal. , vol.51 , pp. 109-114
    • López-Díaz, M.1    Ralescu, D.A.2
  • 47
    • 0001605105 scopus 로고    scopus 로고
    • On strong laws of large numbers for random upper semicontinuous functions
    • Molchanov, I.S. (1999). On Strong Laws of Large Numbers for random upper semicontinuous functions. J. Math. Anal. Appl., 235, 349-355.
    • (1999) J. Math. Anal. Appl. , vol.235 , pp. 349-355
    • Molchanov, I.S.1
  • 49
    • 49349119632 scopus 로고
    • A note on the extension principle for fuzzy sets
    • Nguyen, H.T. (1978). A note on the extension principle for fuzzy sets. J. Math. Anal. Appl., 64, 369-380.
    • (1978) J. Math. Anal. Appl. , vol.64 , pp. 369-380
    • Nguyen, H.T.1
  • 51
    • 0035480416 scopus 로고    scopus 로고
    • Separability for graph convergence of sequences of fuzzy-valued random variables
    • Ogura, Y. and Li, S. (2001). Separability for graph convergence of sequences of fuzzy-valued random variables. Fuzzy Sets and Systems, 123, 19-27.
    • (2001) Fuzzy Sets and Systems , vol.123 , pp. 19-27
    • Ogura, Y.1    Li, S.2
  • 52
    • 33644501330 scopus 로고    scopus 로고
    • On limit theorems for random fuzzy sets including large deviation principles
    • López-Díaz, M., Gil, M.A., Grzegorzewski, P., Hyrniewicz, O. and Lawry, J. (eds.), Springer, Berlin
    • Ogura, Y. and Li, S. (2004). On limit theorems for random fuzzy sets including large deviation principles. In: López-Díaz, M., Gil, M.A., Grzegorzewski, P., Hyrniewicz, O. and Lawry, J. (eds.), Soft Methodology and Random Information Systems. Springer, Berlin.
    • (2004) Soft Methodology and Random Information Systems
    • Ogura, Y.1    Li, S.2
  • 53
    • 68849090513 scopus 로고    scopus 로고
    • Large deviations for random upper semicontinuous functions
    • Ogura, Y. and Setokuchi, T. (2009). Large deviations for random upper semicontinuous functions. Tohoku Math. J., 61, 213-223.
    • (2009) Tohoku Math. J. , vol.61 , pp. 213-223
    • Ogura, Y.1    Setokuchi, T.2
  • 55
    • 0041351880 scopus 로고    scopus 로고
    • A strong law of large numbers for generalized random sets from the viewpoint of empirical processes
    • Proske, F.N. and Puri, M.L. (2003). A strong law of large numbers for generalized random sets from the viewpoint of empirical processes. Proc. Amer. Math. Soc., 131, 2937-2944.
    • (2003) Proc. Amer. Math. Soc. , vol.131 , pp. 2937-2944
    • Proske, F.N.1    Puri, M.L.2
  • 56
    • 0000565701 scopus 로고
    • The concept of normality for fuzzy random variables
    • Puri, M.L. and Ralescu, D.A. (1985). The concept of normality for fuzzy random variables. Ann. Probab., 11, 1373-1379.
    • (1985) Ann. Probab. , vol.11 , pp. 1373-1379
    • Puri, M.L.1    Ralescu, D.A.2
  • 58
    • 0000810441 scopus 로고
    • Convergence theorem for fuzzy martingales
    • Puri, M.L. and Ralescu, D.A. (1991). Convergence theorem for fuzzy martingales J. Math. Anal. Appl., 160, 107-122.
    • (1991) J. Math. Anal. Appl. , vol.160 , pp. 107-122
    • Puri, M.L.1    Ralescu, D.A.2
  • 59
    • 33947156711 scopus 로고    scopus 로고
    • Probabilistic foundations for measurement modelling with fuzzy random variables
    • Terán, P. (2007). Probabilistic foundations for measurement modelling with fuzzy random variables. Fuzzy Sets and Systems, 158, 973-986.
    • (2007) Fuzzy Sets and Systems , vol.158 , pp. 973-986
    • Terán, P.1
  • 60
    • 84876973264 scopus 로고    scopus 로고
    • Algebraic, metric and probabilistic properties of convex combinations based on the t-normed extension principle
    • Terán, P. (2013). Algebraic, metric and probabilistic properties of convex combinations based on the t-normed extension principle. Fuzzy Sets and Systems, 223, Pages 1-25.
    • (2013) Fuzzy Sets and Systems , vol.223 , pp. 1-25
    • Terán, P.1
  • 61
    • 33748063993 scopus 로고    scopus 로고
    • On borel measurability and large deviations for fuzzy random variables
    • Terán Agraz, P. (2006). On Borel measurability and large deviations for fuzzy random variables. Fuzzy Sets and Systems, 157, 2558-2568.
    • (2006) Fuzzy Sets and Systems , vol.157 , pp. 2558-2568
    • Terán Agraz, P.1
  • 63
    • 70349097188 scopus 로고    scopus 로고
    • A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread
    • Trutschnig, W., González-Rodríguez, G., Colubi, A. and Gil, M.A. (2009). A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread. Inform. Sci. 179, 3964-3972.
    • (2009) Inform. Sci. , vol.179 , pp. 3964-3972
    • Trutschnig, W.1    González-Rodríguez, G.2    Colubi, A.3    Gil, M.A.4
  • 64
    • 34248666540 scopus 로고
    • Fuzzy sets
    • Zadeh, L.A. (1965). Fuzzy sets. Inform. Control, 8, 338-353.
    • (1965) Inform. Control , vol.8 , pp. 338-353
    • Zadeh, L.A.1
  • 65
    • 0016458950 scopus 로고
    • The concept of a linguistic variable and its application to approximate reasoning. Part 1
    • Part 2: Inform. Sci., 8, 301-353; Part 3: Inform. Sci., 9, 43-80
    • Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Part 1: Inform. Sci., 8, 199-249; Part 2: Inform. Sci., 8, 301-353; Part 3: Inform. Sci., 9, 43-80.
    • (1975) Inform. Sci. , vol.8 , pp. 199-249
    • Zadeh, L.A.1


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