Abstract
In real-world applications, mathematical models must often deal with values that are missing or undefined. The aim of this paper is to provide a survey on types and reasons for such non-availability. It motivates the need to handle different reasons for missingness in a different, but appropriate way. In particular, non-existence, ignorance, and inconsistency are studied. The paper also presents a novel way of how to compute with different types of missing values at the same time.
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References
Łukasiewicz, J.: O logice trojwartosciowej. Ruch Filozoficzny 5, 170–171 (1920)
Malinowski, G.: The Many Valued and Nonmonotonic Turn in Logic. North-Holand, Amsterdam (2007)
Bergmann, M.: An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems. Cambridge University Press, Cambridge/New York (2008)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)
Běhounek, L., Novák, V.: Towards fuzzy partial logic. In: In Proceedings of the IEEE 45th International Symposium on Multiple-Valued Logics (ISMVL 2015), pp. 139–144 (2015)
Běhounek, L., Daňková, M.: Towards fuzzy partial set theory. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016), pp. 482–494 (2016)
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)
Novák, V.: Towards fuzzy type theory with partial functions. In: Advances in Fuzzy Logic and Technology, pp. 25–37 (2017)
Burda, M., Murinová, P., Pavliska, V.: Undefined values in fuzzy logic. In: Advances in Fuzzy Logic and Technology, pp. 604–610 (2017)
Gelman, A., Hill, J.: Data Analysis Using Regression and Multilevel/Hierarchical Models. Analytical Methods for Social Research. Cambridge University Press, New York (2007)
Liu, Y., Gopalakrishnan, V.: An overview and evaluation of recent machine learning imputation methods using cardiac imaging data. Data 2(1), 8 (2017)
Hájek, P., Havránek, T.: Mechanizing Hypothesis Formation (Mathematical Foundations for a General Theory). Springer, Berlin (1978)
Burda, M., Murinová, P., Pavliska, V.: Fuzzy association rules on data with undefined values. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2018) (2018, page accepted)
Dubois, D., Hüllermeier, E., Prade, H.: A systematic approach to the assessment of fuzzy association rules. Data Min. Knowl. Disc. 13(2), 167–192 (2006)
Chen, Q., Kawase, S.: An approach towards consistency degrees of fuzzy theories. Fuzzy Sets Syst. 113, 237–251 (2000)
Cornelis, C., Deschrijver, G., Kerre, E.E.: Implication in intuitionistic fuzzy and interval-valued fuzzy set theroy: construction, classification, application. Int. J. Approx. Reason. 35, 55–95 (2004)
Dubois, D., Prade, H.: Interval-valued fuzzy sets, possibility theory and imprecise probability. In: EUSFLAT Conference (2005)
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)
Goguen, J.A.: L-fuzzy sets. J. Math. Anal. Appl. 18(1), 145–174 (1967)
Dubois, D.: On ignorance and contradiction considered as truth-values*. Logic J. IGPL 16(2), 195–216 (2008)
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Authors acknowledge support by project “LQ1602 IT4Innovations excellence in science” and by GAČR 16-19170S.
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Burda, M., Murinová, P., Pavliska, V. (2019). On Missing Membership Degrees: Modelling Non-existence, Ignorance and Inconsistency. In: Destercke, S., Denoeux, T., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Uncertainty Modelling in Data Science. SMPS 2018. Advances in Intelligent Systems and Computing, vol 832. Springer, Cham. https://doi.org/10.1007/978-3-319-97547-4_4
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DOI: https://doi.org/10.1007/978-3-319-97547-4_4
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