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Abstrakty
We discuss the fuzzification of classical probability theory. In particular, we point out similarities and differences between the so-called fuzzy probability theory and the so-called operational probability theory.
Rocznik
Tom
Strony
179--188
Opis fizyczny
Bibliogr. 19 poz., rys.
Twórcy
autor
- Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01 Košice, Slovak Republic
- Catholic University in Ružomberok, Hrabovská cesta 1, 034 01 Ružomberok, Slovak Republic
autor
- Catholic University in Ružomberok, Hrabovská cesta 1, 034 01 Ružomberok, Slovak Republic
- Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01 Košice, Slovak Republic
Bibliografia
- [1] M. Beer, Fuzzy Probability Theory, In: Encyclopedia of Complexity and Systems Science, volume 6 (Editor-in-chief: R. A. Meyers), Springer, New York, 2009, 4047-4059.
- [2] S. Bugajski, Statistical maps I. Basic properties, Math. Slovaca 51 (2001), 321-342.
- [3] S. Bugajski, Statistical maps II. Operational random variables, Math. Slovaca 51 (2001), 343-361.
- [4] A. Colubi, J. S. Dominguez-Menchero, M. Lopez-Diaz, D. A. Ralescu, On the formalization of fuzzy random variables, Inform. Sci. 133 (2001), 3-6.
- [5] R. Frič, Remarks on statistical maps and fuzzy (operational) random variables, Tatra Mountains Mathematical Publ. 30 (2005), 21-34.
- [6] R. Frič, Extension of domains of states, Soft Comput. 13 (2009), 63-70.
- [7] R. Frič, M. Papčo, A categorical approach to probability theory, Studia Logica 94 (2010), 215-230.
- [8] R. Frič, M. Papčo, On probability domains II, Internat. J. Theoret. Phys. 50 (2011), 3778-3786.
- [9] R. Frič and M. Papčo, Fuzzification of crisp domains, Kybernetika 46 (2010), 1009-1024.
- [10] R. Frič, M. Papčo, Statistical maps and generalized random walks, Math. Slovaca 62 (2012), 1079-1090.
- [11] S. Gudder, Fuzzy probability theory, Demonstratio Math. 31 (1998), 235-254.
- [12] A. N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer, Berlin, 1933. (An English translation by N. Morrison appeared under the title Foundations of the Theory of Probability (Chelsea, New York) in 1950.)
- [13] H. Kwakernaak, Fuzzy random variables I. definitions and theorems. Inf. Sci. 15 (1978), 1-19.
- [14] R. Mesiar, Fuzzy sets and probability theory, Tatra Mountains Mathematical Publ. 1 (1992), 105-123.
- [15] M. Papčo, On measurable spaces and measurable maps, Tatra Mountains Mathematical Publ. 28 (2004), 125-140.
- [16] M. Papčo, On fuzzy random variables: examples and generalizations, Tatra Mountains Mathematical Publ. 30 (2005), 175-185.
- [17] M. Papčo, On effect algebras, Soft Comput. 12 (2007), 26-35.
- [18] M. R. Puri, D. A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (2007), 409-422.
- [19] L. A. Zadeh, Probability measures of fuzzy events, J. Math. Anal. Appl. 23 (1968), 421-427.
Typ dokumentu
Bibliografia
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