Measurement reduction in the presence of subjective information
Matematičeskoe modelirovanie, Tome 30 (2018) no. 12, pp. 84-110.

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The article considers an application of the mathematical formalism of subjective modeling to improve the quality of measurement data interpretation by using a researcher's incomplete and unreliable subjective information about the research object. It is shown the mathematical formalism of subjective modeling allows the researcher to use measurement data to test the adequacy of the subjective model for the research objective, to correct the subjective model, to combine the observation data and his subjective notions about the research object to optimize his conclusions about the researched features of the research object and how to check the information about the research object for misinformation. Obtained results are illustrated by computer experiments.
Keywords: measurement reduction, subjective modeling
Mots-clés : information fusion, information verification.
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D. A. Balakin; Yu. P. Pyt'ev. Measurement reduction in the presence of subjective information. Matematičeskoe modelirovanie, Tome 30 (2018) no. 12, pp. 84-110. http://geodesic.mathdoc.fr/item/MM_2018_30_12_a5/

[1] T. Terano, K. Asano, M. Sugeno (red.), Prikladnye nechetkie sistemy, Mir, M., 1993, 368 pp.

[2] K. Tanaka, “Resume on dealing with uncertainty/ambiguity in conjunction with knowledge engineering”, Fuzzy Set and Possibility Theory. Recent Developments, Pergamon Press, NY., 1982, 633 pp.

[3] Yu.P. Pyt'ev, “Modeling of Subjective Judgments Made by a Researcher-Modeler about the Model of the Research Object”, Math. Mod. and Comp. Simul., 5:6 (2013), 538–557 | DOI | MR | Zbl

[4] Iu.P. Pyt'ev, Veroiatnost, vozmozhnost i subiektivnoe modelirovanie v nauchnykh issledovaniiakh. Matematicheskie, empiricheskie osnovy, prilozheniia, Fizmatlit, M., 2017, 280 pp.

[5] Iu. P. Pyt'ev, Vozmozhnost kak alternativa veroiatnosti, 2 izd., pererab. i dopoln., Fizmatlit, M., 2016, 600 pp.

[6] A.L. Tulupev, S.I. Nikolenko, A.V. Sirotkin, Baiesovskie seti: Logiko-veroiatnostnyi podkhod, Nauka, Saint Petersburg, 2006, 607 pp.

[7] R.G. Cowell et al., Probabilistic Networks and Expert Systems, Springer-Verlag, New York, 1999, 324 pp. | MR | Zbl

[8] C. Antoniou et al., “Subjective Bayesian beliefs”, Journal of Risk and Uncertainty, 50:1 (2015), 35–54 | DOI | MR

[9] M. Goldstein, “Subjective Bayesian Analysis: Principles and Practice”, Bayesian Analysis, 1 (2006), 403–420 | DOI | MR | Zbl

[10] D. Williamson, M. Goldstein, “Posterior Belief Assessment: Extracting Meaningful Subjective Judgements from Bayesian Analyses with Complex Statistical Models”, Bayesian Analysis, 10:4 (2015), 877–908 | DOI | MR | Zbl

[11] G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ, 1976, 302 pp. | MR | Zbl

[12] J. Kohlas, P.-A. Monney, A Mathematical Theory of Hints: An Approach to the Dempster–Shafer Theory of Evidence, Springer-Verlag, Berlin–Heidelberg, 1995, 422 pp. | MR | Zbl

[13] R.R. Yager, N. Alajlan, “Dempster-Shafer belief structures for decision making under uncertainty”, Knowledge-Based Systems, 80 (2015), 58–66 | DOI

[14] A. Josang, “A Logic for Uncertain Probabilities”, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9:3 (2001), 279–311 | DOI | MR | Zbl

[15] A. Josang, “Multi-Agent Preference Combination using Subjective Logic”, 11th Workshop on Preferences and Soft Constraints (SofT'11) (Perugia, 2011)

[16] A. Josang, P.C.G. Costa, “Determining Model Correctness for Situations of Belief Fusion”, 16th International Conference on Information Fusion (FUSION 2013) (Istanbul, 2013)

[17] T. Muller, D. Wang, A. Josang, “Information Theory for Subjective Logic”, Modeling Decisions for Artificial Intelligence, Springer Nature, 2015, 230–242 | DOI | MR | Zbl

[18] A. Josang, Subjective Logic: A Formalism for Reasoning Under Uncertainty, Springer International Publishing, Heidelberg, 2016, 337 pp. | Zbl

[19] A. Josang, L. Kaplan, “Principles of subjective networks”, 19th International Conference on Information Fusion (FUSION), IEEE, 07/2016, 1292–1299

[20] R.R. Yager, “On the Dempster-Shafer framework and new combination rules”, Information Sciences, 41:2 (1987), 93–137 | DOI | MR | Zbl

[21] T. Inagaki, “Interdependence between safety-control policy and multiple-sensor schemes via Dempster-Shafer theory”, IEEE Transactions on Reliability, 40:2 (1991), 182–188 | DOI | Zbl

[22] T. Denoeux, “Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence”, Artificial Intelligence, 172:2/3 (2008), 234–264 | DOI | MR | Zbl

[23] M.E. Cattaneo, “Belief functions combination without the assumption of Independence of the information sources”, Intern. J. of Approximate Reasoning, 52:3 (2011), 299–315 | DOI | MR | Zbl

[24] D. Dubois, H. Prade, “On the Combination of Evidence in Various Mathematical Frameworks”, Reliability Data Collection and Analysis, v. 3, Springer Nature, Dordrecht, 1992, 213–241 | DOI

[25] A. Martin, C. Osswald, J. Dezert, “General combination rules for qualitative and quantitative beliefs”, J. Adv. Inform. Fusion, 3:2 (2008), 67–89

[26] L. Zadeh, “A simple view of the Dempster-Shafer Theory of Evidence and its implication for the rule of combination”, The AI Magazine, 7:2 (1986), 85–90

[27] A. Bronevich, I. Rozenberg, “The choice of generalized Dempster-Shafer rules for aggregating belief functions”, International Journal of Approximate Reasoning, 56 (2015), 122–136 | DOI | MR | Zbl

[28] A. Josang, R. Hankin, “Interpretation and Fusion of Hyper Opinions in Subjective Logic”, 15th International Conference on Information Fusion (FUSION 2012) (Singapore, 2012)

[29] M.A. Klopotek, S.T. Wierzchon, “Empirical Models for the Dempster-Shafer-Theory”, Belief Functions in Business Decisions, Springer Nature, Heidelberg, 2002, 62–112 | DOI

[30] P. Wang, “A Defect in Dempster-Shafer Theory”, Uncertainty Proceedings 1994, Morgan Kaufmann Publishers, San Francisco, CA, 1994, 560–566 | DOI

[31] Iu.P. Pyt'ev, Metody matematicheskogo modelirovaniia izmeritelno-vychislitelnykh sistem, 3 ed., revised and extended, Fizmatlit, M., 2012, 428 pp.

[32] C.R. Rao et al., Linear Models and Generalizations: Least Squares and Alternatives, 3rd ed., Springer-Verlag, Berlin, 2007, 572 pp. | MR

[33] S. V. Huffel, P. Lemmerling (eds.), Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms and Applications, 1st ed., Springer Nature, Dordrecht, the Netherlands, 2002, 397 pp. | MR

[34] A.N. Tikhonov, V.Y. Arsenin, Solutions of ill-posed problems, Winston, New York, 1977, 258 pp. | MR | Zbl

[35] A.N. Tikhonov et al., Numerical Methods for the Solution of Ill-Posed Problems, Springer Netherlands, Dordrecht, 1995, 254 pp. | MR

[36] H.W. Engl, M. Hanke, A. Neubauer, Regularization of Inverse Problems, 1st ed., Springer Nature, Dordrecht, the Netherlands, 1996, 321 pp. | MR

[37] V.A. Morozov, Regularization Methods for Ill Posed Problems, CRC Press, Boca Raton, FL, 1993, 257 pp. | MR | Zbl

[38] U. Amato, W. Hughes, “Maximum entropy regularization of Fredholm integral equations of the first kind”, Inverse Problems, 7:6 (1991), 793–808 | DOI | MR | Zbl

[39] A.S. Leonov, “A generalization of the maximal entropy method for solving ill-posed problems”, Siberian Mathematical Journal, 41:4 (2000), 716–724 | DOI | MR | Zbl

[40] A.I. Chulichkov, B. Yuan, “The possibility of estimating the values of a function at given points of the measurement results of a finite number of its linear functionals”, Moscow University Physics Bulletin, 69:3 (2014), 218–222 | DOI | MR

[41] Iu.P. Pyt'ev, Matematicheskie metody interpretatsii eksperimenta, Vysshaia shkola, M., 1989, 352 pp.

[42] D.A. Balakin, Yu.P. Pyt'ev, “A Comparative Analysis of Reduction Quality for Probabilistic and Possibilistic Measurement Models”, Moscow University Physics Bulletin, 72:2 (2017), 101–112 | DOI

[43] D.A. Balakin, Iu.M. Nagorny, Iu.P. Pyt'ev, “Empiricheskaia verifikatsiia, vosstanovlenie i korrektsiia subieektivno modeli”, Beskonechnomerny analiz, stokhastika, matematicheskoe modelirovanie: novye zadachi i metody. Problemy matematicheskogo i estestvennonauchnogo obrazovaniia, Sb. st. Mezhd. konf., RUDN University, M., 2015, 190–195

[44] D.A. Balakin, Iu.P. Pyt'ev, “Empiricheskaia verifikatsiia, vosstanovlenie i korrektsiia subieektivno modeli issleduemogo obieekta v teorii izmeritelno-vychislitelnykh preobrazovatele”, XIII Vserossiskaia nauchno-tekhnicheskaia konferentsiia «Sostoianie i problemy izmereni», Sbornik materialov, Bauman Moscow State Technical University, M., 2015, 42–45

[45] D.A. Balakin, Iu.P. Pyt'ev, “Subieektivnaia interpretatsiia dannykh izmereni, polychennykh pri chastichno izvestno modeli izmereni”, Inzhenerno-fizicheskie problemy novo tekhniki. Sbornik materialov XII Vserossiskogo soveshchaniia-seminara, Bauman Moscow State Technical University, M., 2016, 45–48

[46] Yu.P. Pyt'ev, “Mathematical methods of subjective modeling in scientific research. 1. Mathematical and empirical basis”, Moscow University Physics Bulletin, 73:1 (2018), 1–16 | DOI

[47] Yu.P. Pyt'ev, “Mathematical methods of subjective modeling in scientific research. 2. Applications”, Moscow University Physics Bulletin, 73:2 (2017), 102

[48] D.A. Balakin, “The Empirical Construction of Mathematical Models of Measuring and Optimal Computing Transducers”, Moscow University Physics Bulletin, 72:2 (2017), 168–175 | DOI