Abstract
Starting with a descriptive characterization of probability on the intuitionistic fuzzy sets, different formulations of continuity are presented. The main instrument is a Cignoli representation theorem on IF probabilities by classical Kolmogorovian probabilities.
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References
Atanassov, K.T.: Intuitionistic Fuzzy Sets: Theory and Applications. STUDFUZZ. Physica Verlag, Heidelberg (1999)
Atanassov, K.T.: On Intuitionistic Fuzzy Sets. Springer, Berlin (2012)
Cignoli, L., D’Ottaviano, M., Mundici, D.: Algebraic Foundations of Many-valued Reasoning. Kluwer, Dordrecht (2000)
Ciungu, L., Riečan, B.: General form of probabilities on IF-sets. In: Fuzzy Logic and Applications. Proc. WILF Palermo, pp. 101–107 (2009)
Ciungu, L., Riečan, B.: Representation theorem for probabilities on IFS-events. Information Sciences 180, 793–798 (2010)
Ciungu, L., Kelemenová, J., Riečan, B.: A new point of view to the inclusion exclusion principle. In: 6th Int. Conf. on Intelligent Systems, IS 2012, Varna, Bulgaria, pp. 142–144 (2012)
Chovanec, F.: Difference Posets and their Graphical Representation. Liptovsk y Mikuláš (2014) (in Slovak)
Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer, Dordrecht (2000)
Dvurečenskij, A., Rachunek: Riečan and Bosbach states for bounded non-commutative RI-monoids. Math. Slovaca 56, 487–500 (2006)
Foulis, D., Bennett, M.: Efect algebras and unsharp quantum logics. Found. Phys. 24, 1325–1346 (1994)
Grzegorzewski, P., Mrowka, E.: Probability of intuistionistic fuzzy events. In: Grzegorzewski, P., et al. (eds.) Soft Metods in Probability, Statistics and Data Analysis, pp. 105–115 (2002)
Kopka, F., Chovanec, F.: D-posets. Math. Slovaca 44, 21–34 (1994)
Lendelová, K.: A note on invariant observables. International Journal of Theoretical Physics 45, 915–923 (2006)
Michalíková, A.: Absolute value and limit of the function defined on IF sets. Notes on Intuitionistic Fuzzy Sets 18, 8–15 (2012)
Montagna, F.: An algebraic approach to propositional fuzzy logic. J. Logic Lang. Inf (D. Mundici et al. eds.), Special issue on Logics of Uncertainty 9, 91–124 (2000)
Riečan, B.: A descriptive definition of the probability on intuitionistic fuzzy sets. In: Wagenecht, M., Hampet, R. (eds.) EUSFLAT 2003, pp. 263–266 (2003)
Riečan, B.: Representation of probabilities on IFS events. In: Lopez-Diaz, et al. (eds.) Soft Methodology and Random Information Systems, pp. 243–248 (2004)
Riečan, B.: On a problem of Radko Mesiar: general form of IF-probabilities. Fuzzy Sets and Systems 152, 1485–1490 (2006)
Riečan, B.: Probability theory on intuitionistic fuzzy events. In: Aguzzoli, S., et al. (eds.) Algebraic and Proof theoretic Aspects of Non-Classical Logic, Papers in Honour of Daniele Mundici’s 60th Birthday. LNCS, pp. 290–308. Springer, Heidelberg (2007)
Riečan, B.: Analysis of Fuzzy Logic Models. In: Koleshko, V.M. (ed.) Intelligent Systems, pp. 219–244. INTECH (2012)
Riečan, B., Mundici, D.: Probability in MV-algebras. In: Pap, E. (ed.) Handbook of Measure Theory II, pp. 869–910. Elsevier, Heidelberg (2002)
Riečan, B., Neubrunn, T.: Integral, Measure and Ordering. Kluwer, Dordrecht (1997)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–358 (1965)
Zadeh, L.A.: Probability measures on fuzzy sets. J. Math. Abal. Appl. 23, 421–427 (1968)
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Riečan, B., Michalíková, A. (2015). On the Continuity of Probability on IF Sets. In: Grzegorzewski, P., Gagolewski, M., Hryniewicz, O., Gil, M. (eds) Strengthening Links Between Data Analysis and Soft Computing. Advances in Intelligent Systems and Computing, vol 315. Springer, Cham. https://doi.org/10.1007/978-3-319-10765-3_8
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DOI: https://doi.org/10.1007/978-3-319-10765-3_8
Publisher Name: Springer, Cham
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