Statistical reasoning with set-valued information: Ontic vs. epistemic views

International Journal of Approximate Reasoning - Tập 55 Số 7 - Trang 1502-1518 - 2014
Inés Couso1, Didier Dubois2,3
1Universidad de Oviedo [Oviedo] (Calle San Francisco, 1, 33003 Oviedo, Asturias - Spain)
2CNRS - Centre National de la Recherche Scientifique (France)
3IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (Institut de recherche en informatique de Toulouse - IRIT 118 Route de Narbonne 31062 Toulouse Cedex 9 - France)

Tóm tắt

Từ khóa


Tài liệu tham khảo

Baudrit, 2007, Joint propagation of probability and possibility in risk analysis: Towards a formal framework, Int. J. Approx. Reason., 45, 82, 10.1016/j.ijar.2006.07.001

Bertoluzza, 1995, On a new class of distances between fuzzy numbers, Mathw. Soft Comput., 2, 71

Blanco-Fernández, 2014, A distance-based statistical analysis of fuzzy number-valued data, Int. J. Approx. Reason., 55, 1487, 10.1016/j.ijar.2013.09.020

Boukezzoula, 2011, A midpoint-radius approach to regression with interval data, Int. J. Approx. Reason., 52, 1257, 10.1016/j.ijar.2011.07.002

2009

Chalco-Cano, 2013, Some remarks on fuzzy differential equations via differential inclusions, Fuzzy Sets Syst., 10.1016/j.fss.2013.04.017

Colubi, 2009, Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy- and real-valued data, Fuzzy Sets and Systems, 160, 344, 10.1016/j.fss.2007.12.019

Colubi, 2011, Nonparametric criteria for supervised classification of fuzzy data, Int. J. Approx. Reason., 52, 1272, 10.1016/j.ijar.2011.05.007

Cordón, 2011, A historical review of evolutionary learning methods for Mamdani-type fuzzy rule-based systems: Designing interpretable genetic fuzzy systems, Int. J. Approx. Reason., 52, 894, 10.1016/j.ijar.2011.03.004

Couso, 2009, On the variability of the concept of variance for fuzzy random variables, IEEE Trans. Fuzzy Syst., 17, 1070, 10.1109/TFUZZ.2009.2021617

Couso, 2010, Independence concepts in evidence theory, Int. J. Approx. Reason., 51, 748, 10.1016/j.ijar.2010.02.004

Couso, 2001, The necessity of the strong α-cuts, Int. J. Uncertain. Fuzziness Knowledge-Based Systems, 9, 249, 10.1142/S0218488501000788

Couso, 2000, A survey of concepts of independence for imprecise probabilities, Risk Decis. Policy, 5, 165, 10.1017/S1357530900000156

Couso, 2008, Higher order models for fuzzy random variables, Fuzzy Sets and Systems, 159, 237, 10.1016/j.fss.2007.09.004

Couso, 2011, Upper and lower probabilities induced by a fuzzy random variable, Fuzzy Sets and Systems, 165, 1, 10.1016/j.fss.2010.10.005

Couso, 2011, Mark-recapture techniques in statistical tests for imprecise data, Int. J. Approx. Reason., 52, 240, 10.1016/j.ijar.2010.07.009

De Campos, 1990, The concept of conditional fuzzy measure, Int. J. Intell. Syst., 5, 237, 10.1002/int.4550050302

De Cooman, 2002, An imprecise hierarchical model for behaviour under uncertainty, Theory and Decision, 52, 327, 10.1023/A:1020296514974

Dempster, 1967, Upper and lower probabilities induced by a multivalued mapping, Ann. Math. Stat., 38, 325, 10.1214/aoms/1177698950

Denoeux, 2011, Maximum likelihood estimation from fuzzy data using the EM algorithm, Fuzzy Sets and Systems, 183, 72, 10.1016/j.fss.2011.05.022

Denoeux, 2010, Representing uncertainty on set-valued variables using belief functions, Artificial Intelligence, 174, 479, 10.1016/j.artint.2010.02.002

Diamond, 1988, Fuzzy least squares, Inform. Sci., 46, 141, 10.1016/0020-0255(88)90047-3

Diamond, 1994

Dubois, 2006, Possibility theory and statistical reasoning, Comput. Statist. Data Anal., 51, 47, 10.1016/j.csda.2006.04.015

Dubois, 2011, The role of fuzzy sets in decision sciences: Old techniques and new directions, Fuzzy Sets and Systems, 184, 3, 10.1016/j.fss.2011.06.003

Dubois, 2012, Conditioning in Dempster–Shafer theory: Prediction vs. revision, vol. 164, 385

Dubois, 2004, Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities, Reliab. Comput., 10, 273, 10.1023/B:REOM.0000032115.22510.b5

Dubois, 1988

Dubois, 1988, Incomplete conjunctive information, Comput. Math. Appl., 15, 797, 10.1016/0898-1221(88)90117-4

Dubois, 1992, When upper probabilities are possibility measures, Fuzzy Sets and Systems, 49, 65, 10.1016/0165-0114(92)90110-P

Dubois, 1997, The three semantics of fuzzy sets, Fuzzy Sets and Systems, 90, 141, 10.1016/S0165-0114(97)00080-8

D. Dubois, H. Prade, Formal representations of uncertainty, in: [5], 2009, pp. 85–156, Chap. 3.

Dubois, 2012, Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets, Fuzzy Sets and Systems, 192, 3, 10.1016/j.fss.2010.11.007

Fagin, 1991, A new approach to updating beliefs, 347

Ferraro, 2010, A linear regression model for imprecise response, Int. J. Approx. Reason., 51, 759, 10.1016/j.ijar.2010.04.003

Ferson, 2002, Computing variance for interval data is NP-hard, SIGACT News, 33, 108, 10.1145/564585.564604

Gebhardt, 1998, Fuzzy set-theoretic methods in statistics, 311

González-Rodríguez, 2009, Estimation of a simple linear regression model for fuzzy random variables, Fuzzy Sets and Systems, 160, 357, 10.1016/j.fss.2008.07.007

González-Rodríguez, 2012, Fuzzy data treated as functional data. A one-way ANOVA test approach, Comput. Stat. Data Anal., 56, 943, 10.1016/j.csda.2010.06.013

Jaffray, 1992, Bayesian updating and belief functions, IEEE Trans. Syst. Man Cybern., 22, 1144, 10.1109/21.179852

Körner, 1997, On the variance of fuzzy random variables, Fuzzy Sets and Systems, 92, 83, 10.1016/S0165-0114(96)00169-8

Halpern, 2003

Herzig, 2003, Action representation and partially observable planning using epistemic logic, 1067

Huellermeier, 1997, An approach to modelling and simulation of uncertain dynamical systems, Int. J. Uncertain. Fuzziness Knowl.-Based Syst., 5, 117, 10.1142/S0218488597000117

Kendall, 1974, Foundations of a theory of random sets, 322

Kreinovich, 2006, Computing mean and variance under Dempster–Shafer uncertainty: Towards faster algorithms, Int. J. Approx. Reason., 42, 212, 10.1016/j.ijar.2005.12.001

Kruse, 1987

Kwakernaak, 1978, Fuzzy random variables – I. Definitions and theorems, Inform. Sci., 15, 1, 10.1016/0020-0255(78)90019-1

Kwakernaak, 1979, Fuzzy random variables – II. Algorithms and examples for the discrete case, Inform. Sci., 17, 253, 10.1016/0020-0255(79)90020-3

Lindley, 1982, Scoring rules and the inevitability of probability, Int. Stat. Rev., 50, 1, 10.2307/1402448

Loquin, 2010, Kriging and epistemic uncertainty: a critical discussion, 269

Loquin, 2010, Kriging with ill-known variogram and data, vol. 6379, 219

Matheron, 1975

Moore, 1979, Methods and Applications of Interval Analysis, 10.1137/1.9781611970906

Nguyen, 1978, On random sets and belief functions, J. Math. Anal. Appl., 65, 531, 10.1016/0022-247X(78)90161-0

Paris, 1994

Pichon, 2012, Relevance and truthfulness in information correction and fusion, Int. J. Approx. Reason., 53, 159, 10.1016/j.ijar.2011.02.006

Prade, 2011, Maximum-likelihood principle for possibility distributions viewed as families of probabilities, 2987

Puri, 1986, Fuzzy random variables, J. Math. Anal. Appl., 114, 409, 10.1016/0022-247X(86)90093-4

Ramos-Guajardo, 2012, K-sample tests for equality of variances of random fuzzy sets, Comput. Statist. Data Anal., 56, 956, 10.1016/j.csda.2010.11.025

Shackle, 1961

Shafer, 1976

Shafer, 1985, Languages and designs for probability, Cogn. Sci., 9, 309, 10.1207/s15516709cog0903_2

Spadoni, 2011, Computing the variance of interval and fuzzy data, Fuzzy Sets and Systems, 165, 24, 10.1016/j.fss.2010.09.003

Sánchez, 2009, Genetic learning of fuzzy rules based on low quality data, Fuzzy Sets and Systems, 160, 2524, 10.1016/j.fss.2009.03.004

Sánchez, 2007, Advocating the use of imprecisely observed data in genetic fuzzy systems, IEEE Trans. Fuzzy Syst., 15, 551, 10.1109/TFUZZ.2007.895942

Sánchez, 1998, Learning from imprecise examples with GA-P algorithms, Mathw. Soft Comput., 2–3, 305

Sánchez, 2009, Obtaining linguistic fuzzy rule-based regression models from imprecise data with multiobjective genetic algorithms, Soft Comput., 13, 307

Smets, 1997, The normative representation of quantified beliefs by belief functions, Artificial Intelligence, 92, 229, 10.1016/S0004-3702(96)00054-9

Tanaka, 1999

Trutschnig, 2009, A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread, Inform. Sci., 179, 3964, 10.1016/j.ins.2009.06.023

Trutschnig, 2013, SAFD – An R package for statistical analysis of fuzzy data in towards advanced data analysis by combining soft computing and statistics, 107, 10.1007/978-3-642-30278-7_10

Walley, 1991

Yager, 1987, Set-based representations of conjunctive and disjunctive knowledge, Inform. Sci., 41, 1, 10.1016/0020-0255(87)90002-8

Yen, 1990, Generalizing the Dempster–Shafer theory to fuzzy sets, IEEE Trans. Syst. Man Cybern., 20, 559, 10.1109/21.57269

Zadeh, 1975, The concept of a linguistic variable and its application to approximate reasoning, Part I, Inform. Sci., 8, 199, 10.1016/0020-0255(75)90036-5

Zadeh, 1978, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 1, 10.1016/0165-0114(78)90029-5

Zadeh, 1978, PRUF — a meaning representation language for natural languages, Int. J. Man-Mach. Stud., 10, 395, 10.1016/S0020-7373(78)80003-0