Mathematical Foundations of Probabilistic Estimation in Fuzzy Bayesian Belief Networks

Specific problems arising in the creation of Bayesian networks for processing fuzzy information are considered. Conditions are obtained that ensure the probabilistic correctness of a priori data and results of network computing. For the case of nondeterministic states of network vertices, a fuzzy li...

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Veröffentlicht in:	Cybernetics and systems analysis Jg. 52; H. 2; S. 206 - 218
Hauptverfasser:	Parasyuk, I. M., Verovka, O. V.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.03.2016 Springer Springer Nature B.V
Schlagworte:	Artificial Intelligence Bayesian analysis Belief networks Computer science Control Cybernetics Estimates Fuzzy Fuzzy logic Interpolation Mathematics Mathematics and Statistics Networks Probabilistic methods Probability Probability theory Processor Architectures Software Engineering/Programming and Operating Systems Studies Systems Theory fuzzy probability estimate correctness of fuzzy computations binary network nondeterministic state Bayesian belief network
ISSN:	1060-0396, 1573-8337
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Abstract	Specific problems arising in the creation of Bayesian networks for processing fuzzy information are considered. Conditions are obtained that ensure the probabilistic correctness of a priori data and results of network computing. For the case of nondeterministic states of network vertices, a fuzzy linear interpolation procedure is proposed. The presented results make it possible to perform correct probabilistic Bayesian estimation over fuzzy networks of any configuration.
AbstractList	Specific problems arising in the creation of Bayesian networks for processing fuzzy information are considered. Conditions are obtained that ensure the probabilistic correctness of a priori data and results of network computing. For the case of nondeterministic states of network vertices, a fuzzy linear interpolation procedure is proposed. The presented results make it possible to perform correct probabilistic Bayesian estimation over fuzzy networks of any configuration. Specific problems arising in the creation of Bayesian networks for processing fuzzy information are considered. Conditions are obtained that ensure the probabilistic correctness of a priori data and results of network computing. For the case of nondeterministic states of network vertices, a fuzzy linear interpolation procedure is proposed. The presented results make it possible to perform correct probabilistic Bayesian estimation over fuzzy networks of any configuration. Keywords: Bayesian belief network, fuzzy probability estimate, correctness of fuzzy computations, binary network, nondeterministic state.
Audience	Academic
Author	Parasyuk, I. M. Verovka, O. V.
Author_xml	– sequence: 1 givenname: I. M. surname: Parasyuk fullname: Parasyuk, I. M. organization: V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine – sequence: 2 givenname: O. V. surname: Verovka fullname: Verovka, O. V. email: verovka.olga@gmail.com organization: V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine
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Cites_doi	10.1007/s10559-008-9067-z
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References	A. N. Borisov, A. V. Alekseev, G. V. Merkuryeva, N. N. Slyadz’, and V. I. Glushkov, Processing Fuzzy Information in Decision-Making Systems [in Russian], Radio i Svyz’, Moscow (1989). O. V. Verovka, “Epure representation of information in fuzzy Bayesian networks,” Computer Mathematics, No. 1, 52–60 (2013). S. V. Matsiyevskii, Fuzzy Sets [in Russian], Izd-vo Kaliningr. Un-ta, Kaliningrad (2004). I. V. Sergienko, I. N. Parasyuk, and S. V. Yershov, “Fuzzy transformational approach to the development of software systems,” Problems in Programming, Nos. 2–3, 122–132 (2004). O. V. Verovka and E. S. Karpinka, “Information filling of a fuzzy Bayesian network,” Computer Mathematics, No. 2, 57–63 (2014). O. V. Verovka, “Consideration of nondeterministic evidences during a posteriori estimation in fuzzy Bayesian networks,” Computer Mathematics, No. 2, 98–109 (2011). O. V. Verovka, “Probability distribution in fuzzy treelike Bayesian networks,” Computer Mathematics, No. 2, 10–17 (2012). O. V. Verovka and I. N. Parasyuk, “Probability propagation in fuzzy Bayesian belief networks with nondeterministic states,” Cybernetics and Systems Analysis, 44, No. 6, 925–940 (2008). L. A. Zadeh, The Concept of a Linguistic Variable and its Application to Approximate Reasoning [Russian translation], Mir, Moscow (1976). O. V. Verovka and I. N. Parasyuk, “A multilevel approach to the representation of Bayesian networks,” Computer Mathematics, No. 1, 83–93 (2010). I. N. Parasyuk and F. V. Kostukevich, “Methods of transformation of a Bayesian network for constructing a nodal tree and their modification,” Computer Mathematics, No. 1, 70–80 (2008). O. V. Verovka, “Using network methods of organization of Bayesian estimation as applied to fuzzy information,” Computer Mathematics, No. 2, 57–63 (2013). I. N. Parasyuk and S. V. Yershov, “Model-oriented architecture of fuzzy multiagent systems,” Computer Mathematics, No. 2, 62–74 (2010). 9816_CR13 9816_CR12 9816_CR1 9816_CR11 9816_CR10 9816_CR4 9816_CR5 9816_CR2 9816_CR3 9816_CR8 9816_CR9 9816_CR6 9816_CR7
References_xml	– reference: O. V. Verovka, “Probability distribution in fuzzy treelike Bayesian networks,” Computer Mathematics, No. 2, 10–17 (2012). – reference: O. V. Verovka and E. S. Karpinka, “Information filling of a fuzzy Bayesian network,” Computer Mathematics, No. 2, 57–63 (2014). – reference: O. V. Verovka and I. N. Parasyuk, “A multilevel approach to the representation of Bayesian networks,” Computer Mathematics, No. 1, 83–93 (2010). – reference: O. V. Verovka, “Epure representation of information in fuzzy Bayesian networks,” Computer Mathematics, No. 1, 52–60 (2013). – reference: O. V. Verovka, “Consideration of nondeterministic evidences during a posteriori estimation in fuzzy Bayesian networks,” Computer Mathematics, No. 2, 98–109 (2011). – reference: A. N. Borisov, A. V. Alekseev, G. V. Merkuryeva, N. N. Slyadz’, and V. I. Glushkov, Processing Fuzzy Information in Decision-Making Systems [in Russian], Radio i Svyz’, Moscow (1989). – reference: L. A. Zadeh, The Concept of a Linguistic Variable and its Application to Approximate Reasoning [Russian translation], Mir, Moscow (1976). – reference: I. N. Parasyuk and F. V. Kostukevich, “Methods of transformation of a Bayesian network for constructing a nodal tree and their modification,” Computer Mathematics, No. 1, 70–80 (2008). – reference: O. V. Verovka, “Using network methods of organization of Bayesian estimation as applied to fuzzy information,” Computer Mathematics, No. 2, 57–63 (2013). – reference: S. V. Matsiyevskii, Fuzzy Sets [in Russian], Izd-vo Kaliningr. Un-ta, Kaliningrad (2004). – reference: O. V. Verovka and I. N. Parasyuk, “Probability propagation in fuzzy Bayesian belief networks with nondeterministic states,” Cybernetics and Systems Analysis, 44, No. 6, 925–940 (2008). – reference: I. V. Sergienko, I. N. Parasyuk, and S. V. Yershov, “Fuzzy transformational approach to the development of software systems,” Problems in Programming, Nos. 2–3, 122–132 (2004). – reference: I. N. Parasyuk and S. V. Yershov, “Model-oriented architecture of fuzzy multiagent systems,” Computer Mathematics, No. 2, 62–74 (2010). – ident: 9816_CR6 – ident: 9816_CR7 – ident: 9816_CR5 – ident: 9816_CR4 – ident: 9816_CR13 – ident: 9816_CR12 – ident: 9816_CR1 doi: 10.1007/s10559-008-9067-z – ident: 9816_CR10 – ident: 9816_CR11 – ident: 9816_CR2 – ident: 9816_CR3 – ident: 9816_CR9 – ident: 9816_CR8
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SubjectTerms	Artificial Intelligence Bayesian analysis Belief networks Computer science Control Cybernetics Estimates Fuzzy Fuzzy logic Interpolation Mathematics Mathematics and Statistics Networks Probabilistic methods Probability Probability theory Processor Architectures Software Engineering/Programming and Operating Systems Studies Systems Theory
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Title	Mathematical Foundations of Probabilistic Estimation in Fuzzy Bayesian Belief Networks
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