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vol 63 / July, 2020
Article

DOI 10.17586/0021-3454-2019-62-10-875-885

UDC 004.052.42+681.518.5

TERNARY QUESTIONNAIRES WITH ERRORS AND UNCERTAINTIES IN THE ANSWERS

D. V. Ephanov
PSTU; Department of Automation and Telemechanics on the Railways


V. V. Khoroshev
Russian University of Transport, Department of Automation, Remote Control, and Communication in Railway Transport;


Abstract. A theory of questionnaires is development in the direction of studying the questionnaires features with questions with equal number of outcomes (homogeneous questionnaires). A special attention is given to ternary questionnaires in which the questions have three outcomes. Such questionnaires may be used to solve a wide range of discrete search, identification, and technical diagnostics tasks. Com-pared to binary questionnaires, ternary questionnaires may turn out to be questionnaires with a much lower cost for identical sets of identifiable events. The advantage is considered as a significant one when maximum cost of the questionnaire is limited, e. g., in the tasks of technical diagnostics with limited time for diagnosis. The questionnaires in which the questions allow for occurrence of errors, and the answers – for uncertainties, are studied. Methods of constructing questionnaires with errors and uncertainties for the matrix form of the task are described, and specifics of optimization of such questionnaires are con-sidered.
Keywords: event identification, technical diagnostics, theory of questionnaires, homogeneous questionnaires, binary questionnaires, ternary questionnaires, errors in answers, uncertain answers, questionnaire formation

References:
  1. Parkhomenko P.P. Automation and Remote Control, 1970, no. 4, pp. 140–159. (in Russ.)
  2. Picard C.F. Graphs and Questionnaires, Netherlands, North-Holland Publishing Company, 1980, 431 p.
  3. Parkhomenko P.P., Sogomonyan E.S. Osnovy tekhnicheskoy diagnostiki (optimizatsiya algoritmov di-agnostirovaniya, apparaturnyye sredstva) (Fundamentals of Technical Diagnostics (Optimization of Diagnostic Algorithms, Hardware)), Moscow, 1981, 320 р. (in Russ.)
  4. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V. Osnovy teorii nadezhnosti i tekhnicheskoy diagnosti-ki (Fundamentals of the Theory of Reliability and Technical Diagnostics), St. Petersburg, 2019, 588 р. (in Russ.)
  5. Parkhomenko P.P. Reports of the USSR Academy of Sciences, 1969, no. 1(184), pp. 51–54. (in Russ.)
  6. Chugaev B.N., Arzhenenko A.Yu. Statistics and Economics, 2013, no. 2, pp. 188–190. (in Russ.)
  7. Duncan G. SIAM Journal on Applied Mathematics, 1974, no. 1(27), pp. 59–71. DOI: 10.1137/0127005.
  8. Parkhomenko P.P. Automation and Remote Control, 2010, no. 6(71), pp. 1124–1134.
  9. Arzhenenko A.Yu., Vestyak V.A. Diskretnyy poisk. Teoriya voprosnikov (Discrete Search. Questionnaire Theory), Moscow, 2012, 159 р. (in Russ.)
  10. Efanov D.V., Khoroshev V.V., Osadchy G.V., Belyi A.A. Proceedings of 16th IEEE East-West Design & Test Symposium (EWDTS`2018), Kazan, Russia, September 14–17, 2018, pp. 237–245. DOI: 10.1109/EWDTS.2018.8524620.
  11. Arzhenenko A.Yu., Chugaev B.N. Optimal'nyye binarnyye voprosniki (Optimal Binary Questionnaires), Moscow, 1989, 128 р. (in Russ.)
  12. Arzhenenko A.Yu., Chugaev B.N. Automation and Remote Control, 1985, no. 2, pp. 159–164. (in Russ.)
  13. Arzhenenko A.Yu., Kazakova O.G., Chugayev B.N. Automation and Remote Control, 1985, no. 11, pp. 138–144. (in Russ.)
  14. Arzhenenko A.Yu., Kazakova O.G., Neyasov V.A. Automation and Remote Control, 1989, no. 6, pp. 139–149. (in Russ.)
  15. Arzhenenko A.Y., Bondarenko A.V. Electronic Modeling, 1990, no. 3, pp. 53–57. (in Russ.)
  16. Arzhenenko A.Y., Bondarenko A.V. Automation and Remote Control, 1991, no. 5, pp. 163–169. (in Russ.)
  17. Arzhenenko A.Y., Vestyak V.A. Automation and Remote Control, 2012, no. 7(73), pp. 1195–1201.
  18. Efanov D.V., Pavlov A.N. Proceedings of Petersburg Transport University, 2012, no. 4, pp. 125–134. (in Russ.)
  19.  Land A.H., Doig A.G. Econometrica, 1960, no. 3(28), pp. 497–520.
  20. Bellman R.E. Dynamic Programming, Princeton University Press, Princeton NJ, 1957, 392 p.
  21. Zadeh L.A. Information Sciences, 1975, vol. 1, рр. 119–249.
  22. Sapozhnikov Vl.V., Efanov D.V., Pavlov A.N. Automation, communication and Informatics, 2012, no. 1, pp. 30–33. (in Russ.)