nach oben

Pattern Recognition and Image Analysis

Erschienen in:

01.12.2023 | SCIENTIFIC SCHOOLS OF THE LOMONOSOV MOSCOW STATE UNIVERSITY (MSU), MOSCOW, THE RUSSIAN FEDERATION

Data Analysis and Interpretation: Methods of Computer-Aided Measuring Transducer Theory, Morphological Analysis, Possibility Theory, and Subjective Mathematical Modeling

verfasst von: Yu. P. Pyt’ev, A. I. Chulichkov, O. V. Falomkina, D. A. Balakin

Erschienen in: Pattern Recognition and Image Analysis | Ausgabe 4/2023

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This article provides an overview of the fundamental research directions being pursued at the Faculty of Physics of Lomonosov Moscow State University under the guidance of Professor Yuri Petrovich Pyt’ev. These research directions can be categorized into three primary areas: methods of morphological analysis of images and signals, theory of computer-aided measuring systems, and methods related to the theory of possibilities and subjective mathematical modeling. The article elucidates the foundational ideas and concepts of these directions, contemplates alternative approaches to address similar challenges, and offers both model-based and application-driven examples utilizing the methods corresponding to these directions and their combinations.

Vorheriger Artikel Image Analysis and Enhancement: General Methods and Biomedical Applications

Nächster Artikel I.G. Persiantsev’s Scientific School at the Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics: History of Development and Overview of Key Works

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

An ideal MT is an MT interacting with the measured object in the same way as an MT in a CAMT, whose output signal is equal to the Uf value of the characteristic of the SO of interest.

A measurement model is a mathematical model of the MT interacting with the measured object and with the environment, linking its input and output signals. The model of interpretation of the input signal of the MT is the mathematical model linking its input signal and CIMR of the object under study undisturbed by measurement.

\({{B}^{ - }}\) and \(B{\kern 1pt} \text{*}\) are the operators pseudoinverse to \(B\) and conjugate to \(B\), \({{B}^{ - }}\) = \(\mathop {\lim }\limits_{\alpha \to 0} B{\kern 1pt} \text{*}{\kern 1pt} {{(BB{\kern 1pt} \text{*} + \;\alpha I)}^{{ - 1}}}\) = \(\mathop {\lim }\limits_{\alpha \to 0} {{(B{\kern 1pt} \text{*}{\kern 1pt} B + \alpha I)}^{{ - 1}}}B{\kern 1pt} \text{*}\) [148].

M. N. Agapov, S. V. Klishin, V. V. Mikhailin, and Yu. P. Pyt’ev, “A reduction method for optical spectral analysis from photoemission data,” Moscow Univ. Phys. Bull. 43 (6), 87–89 (1988).MathSciNet

C. Antoniou, G. W. Harrison, M. I. Lau, and D. Read, “Subjective Bayesian beliefs,” SSRN Electron. J. 50, 403–420 (2015). https://doi.org/10.2139/ssrn.2247318

V. A. Antonyuk, N. V. Bulygina, and Yu. P. Pyt’ev, Methods of Morphological Analysis in Problem of Object Extraction (Nauka, Moscow, 1984).

V. A. Antonyuk, “An algorithm of rigorous consensus ranking,” Intellektual’nye Sist. Teoriya Prilozheniya 25 (3), 11–34 (2021).

V. K. Avilov, V. S. Aleshnovskii, A. V. Bezrukova, V. A. Gazaryan, N. A. Zyuzina, Yu. A. Kurbatova, D. A. Tarbaev, A. I. Chulichkov, and N. E. Shapkina, “Morphological and other research techniques for almost cyclic time series as applied to CO2 concentration series,” Comput. Math. Math. Phys. 61, 1106–1117 (1106). https://doi.org/10.1134/s0965542521070046

D. A. Balakin and Yu. P. Pyt’ev, “A comparative analysis of reduction quality for probabilistic and possibilistic measurement models,” Moscow Univ. Phys. Bull. 72, 101–112 (2017). https://doi.org/10.3103/s0027134917020047CrossRef

D. A. Balakin, “The empirical construction of mathematical models of measuring and optimal computing transducers,” Moscow Univ. Phys. Bull. 72, 168–175 (2017). https://doi.org/10.3103/s0027134917020059CrossRef

D. A. Balakin, “Improvement of measurement reduction of tomographic images using non-negativity of brightness,” Proc. SPIE 12084, 120841K (2022). https://doi.org/10.1117/12.2622648

D. A. Balakin and Yu. P. Pyt’ev, “Measurement reduction in the presence of subjective information,” Math. Models Comput. Simul. 11, 596–610 (2019). https://doi.org/10.1134/s2070048219040033MathSciNetCrossRef

10.

D. A. Balakin, “Order representation of distribution of possibility measure,” Intellektual’nye Sist. Teoriya Prilozheniya 20 (1), 4–27 (2017).

11.

D. A. Balakin, “Numerical methods for computing plausibility and belief distributions of consequences of a subjective model of object of research,” Comput. Math. Math. Phys. 58, 790–802 (2018). https://doi.org/10.1134/s0965542518050032MathSciNetCrossRef

12.

D. A. Balakin, “Reduction of images to the form typical for measuring the distribution of object transparency with subjective information about its sparsity in a given basis,” Moscow Univ. Phys. Bull. 75, 26–34 (2020). https://doi.org/10.3103/s0027134920010038CrossRef

13.

V. C. Bhavsar and A. M. Mironov, “Fuzzy modal logics,” in Proceedings of Workshop on Multi-Valued Logic Programming and Applications, MVLPA 2006 (Seattle, Wash., 2006), pp. 73–88.

14.

S. P. Bondarenko, Yu. P. Pyt’ev, and M. L. Serdobol’skaya, “On extreme possibilities of measurement-computer system as measuring device,” Matematicheskoe Model. 5 (9), 43–54 (1993).

15.

S. P. Bondarenko and Yu. P. Pyt’ev, “The effective rank of a model of linear measurement with an error,” Comput. Math. Math. Phys. 35 (1), 1–14 (1995).MathSciNet

16.

S. A. Brianskiy, S. V. Sidyakin, and Y. V. Vizilter, “Orientation spectrum algorithm development,” Int. Arch. Photogrammetry, Remote Sensing Spatial Inf. Sci. 40-5/W6 (6), 13–18 (2015). https://doi.org/10.5194/isprsarchives-xl-5-w6-13-2015

17.

A. G. Bronevich and A. V. Goncharov, “An axiomatic approach to measuring of information of sign-based image representations,” J. Comput. Syst. Sci. Int. 50, 51–66 (2011). https://doi.org/10.1134/s1064230710061012MathSciNetCrossRef

18.

A. G. Bronevich, A. N. Karkishchenko, and A. E. Lepskii, Analysis of Uncertainty in Extraction of Informative Attributes and Image Representation (Fizmatlit, Moscow, 2013).

19.

E. A. Cheremukhin and A. I. Chulichkov, “On the application of computer measurement systems in tomography,” Comput. Math. Math. Phys. 45, 716–726 (2005).MathSciNet

20.

G. Choquet, “Theory of capacities,” Ann. Inst. Fourier 5, 131–295 (1954). https://doi.org/10.5802/aif.53MathSciNetCrossRef

21.

A. I. Chulichkov and E. M. Mol’kov, “Improving the resolution for an image of nonnegative brightness distorted by a linear transform,” in Proc. 6th Int. Conf. and Youth School on Information Technologies and Nanotechnologies, Ed. by V. V. Myasnikov (Samarsk. Nats. Issled. Univ. im. Akademika S.P. Koroleva, Samara, 2020), pp. 565–571. https://doi.org/10.17223/9785946219242/192

22.

A. I. Chulichkov and B. Yuan, “Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals,” Comput. Res. Model. 6, 189–202 (2014). https://doi.org/10.20537/2076-7633-2014-6-2-189-202CrossRef

23.

G. de Cooman, “Possibility theory I: The measure- and integral-theoretic groundwork,” Int. J. Gen. Syst. 25, 291–323 (1997). https://doi.org/10.1080/03081079708945160MathSciNetCrossRef

24.

G. de Cooman, “Possibility theory II: Conditional possibility,” Int. J. Gen. Syst. 25, 325–351 (1997). https://doi.org/10.1080/03081079708945161MathSciNetCrossRef

25.

G. de Cooman, “Possibility theory III: Possibilistic independence,” Int. J. Gen. Syst. 25, 353–371 (1997). https://doi.org/10.1080/03081079708945162MathSciNetCrossRef

26.

R. G. Cowell, A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter, Probabilistic Networks and Expert Systems (Springer-Verlag, Berlin, 1999).

27.

D. S. Demin and A. I. Chulichkov, “Filtering of monotonic convex noise-distorted signals and estimates of positions of special points,” J. Math. Sci. 172, 770–781 (2011). https://doi.org/10.1007/s10958-011-0220-2MathSciNetCrossRef

28.

A. P. Dempster, “Upper and lower probabilities induced by a multivalued mapping,” Ann. Math. Stat. 38, 325–339 (1967). https://doi.org/10.1214/aoms/1177698950MathSciNetCrossRef

29.

A. P. Dempster, “A generalization of Bayesian inference,” J. R. Stat. Soc.: Ser. B (Methodological) 30, 205–232 (1968). https://doi.org/10.1111/j.2517-6161.1968.tb00722.xMathSciNetCrossRef

30.

E. R. Dougherty, “The dual representation of gray-scale morphological filters,” in Proceedings CVPR ‘89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, Calif., 1989 (IEEE, 1989), Vol. 172, p. 177. https://doi.org/10.1109/cvpr.1989.37846

31.

D. Dubois and E. Hüllermeier, “Comparing probability measures using possibility theory: A notion of relative peakedness,” Int. J. Approximate Reasoning 45, 364–385 (2007). https://doi.org/10.1016/j.ijar.2006.06.017MathSciNetCrossRef

32.

D. Dubois and H. Prade, Fuzzy Sets and Systems—Theory and Applications, Mathematics in Science and Engineering, Vol. 144 (Academic, 1980). https://doi.org/10.1016/S0076-5392(13)60164-2

33.

D. Dubois and H. Prade, “A note on measures of specificity for fuzzy sets,” Int. J. Gen. Syst. 10, 279–283 (1985). https://doi.org/10.1080/03081078508934893MathSciNetCrossRef

34.

D. Dubois and H. Prade, Possibility Theory: An Approach to Computerized Processing of Uncertainty (Plenum Press, New York, 1988).

35.

D. Dubois and H. Prade, “Fuzzy sets and probability: Misunderstandings, bridges and gaps,” in Second IEEE Int. Conf. on Fuzzy Systems, San Francisco, 1993 (1993), pp. 1059–1068. https://doi.org/10.1109/FUZZY.1993.327367

36.

D. Dubois, “Possibility theory and statistical reasoning,” Comput. Stat. Data Anal. 51, 47–69 (2006). https://doi.org/10.1016/j.csda.2006.04.015MathSciNetCrossRef

37.

D. Dubois, H. T. Nguyen, and H. Prade, “Possibility theory, probability and fuzzy sets misunderstandings, bridges and gaps,” in Fundamentals of Fuzzy Sets, Ed. by D. Dubois and H. Prade, The Handbooks of Fuzzy Sets Series, Vol. 7 (Springer, 2000), pp. 343–438. https://doi.org/10.1007/978-1-4615-4429-6_8CrossRef

38.

D. Dubois and H. Prade, “Formal representations of uncertainty,” in Decision-Making Process, Ed. by D. Bouyssou, D. Dubois, M. Pirlot, and H. Prade (Wiley-ISTE, London, 2009), pp. 85–156. https://doi.org/10.1002/9780470611876.ch3CrossRef

39.

D. Dubois and H. Prade, “Possibility theory, probability theory and multiple-valued logics: a clarification,” Ann. Math. Artif. Intell. 32, 35–66 (2001). https://doi.org/10.1023/A:1016740830286MathSciNetCrossRef

40.

I. V. D’yakonova, T. V. Matveeva, and Yu. P. Pyt’ev, “Reduction of measurements of fuzzy sets,” Pattern Recognit. Image Anal. 11, 711–717 (2001).

41.

N. G. Efimkin, B. S. Ishkhanov, and Yu. P. Pyt’ev, “The use of the reduction method to increase the resolution of photonuclear experiments,” Moscow Univ. Phys. Bull. 43 (6), 46–52 (1988).

42.

I. S. Emel’yanenko, Yu. V. Lazarev, and Yu. P. Pyt’ev, “Tracing the line and extraction of small singularities in the problem of analyzing ridge patterns,” in Identification of Ridge Patterns on Optical-Digital Complex (Dal’nevostochnyi Gos. Univ., Vladivostok, 1980), pp. 40–49.

43.

A. G. Ermolaev and Yu. P. Pyt’ev, “The problem of noisekilling for the special type images,” Moscow Univ. Phys. Bull. 36 (6), 82 (1981).

44.

I. K. Ermolaev and A. A. Chulkov, “Physical principles for combining images acquired with remote probing,” Moscow Univ. Mech. Bull. 41 (6), 115–118 (1986).

45.

A. G. Ermolaev and Yu. P. Pyt’ev, “A priori estimates of useful signal for morphological analysis of resolving algorithms,” Avtometriya, No. 5, 118–120 (1984).

46.

A. P. Ershov, A. A. Kuzovnikov, and S. E. Ponomareva, “Application of the reduction method to the microwave interferometry of shock waves in a weakly ionized plasma,” Zh. Tekh. Fiz. 59 (8), 142–145 (1989).

47.

S. O. Evsegneev and Yu. P. Pyt’ev, “Analysis and recognition of piecewise constant texture images,” Pattern Recognit. Image Anal. 16, 398–405 (2006). https://doi.org/10.1134/s1054661806030096CrossRef

48.

E. P. Fadeev and A. V. Zubyuk, “On the algebraic properties of the operations used at constructing modern convolutional neural networks,” in Mathematical Methods of Pattern Recognition: Proc. 19th All-Russian Conf. with Int. Participation (2019), pp. 102–105.

49.

I. I. Falomkin and Yu. P. Pyt’ev, “Algorithm of adaptive morphological filtering of images,” Pattern Recognit. Image Anal. 17, 408–420 (2007). https://doi.org/10.1134/s105466180703008xCrossRef

50.

O. V. Falomkina, Yu. P. Pyt’ev, and A. I. Chulichkov, “A new method for determining the velocity of a heavy ion based on the mathematical formalism of subjective modeling,” in Mathematical Methods of Pattern Recognition: Proc. 20th All-Russian Conf. with Int. Participation (Moscow, 2021), pp. 440–441.

51.

O. V. Zhuchko and Yu. P. Pyt’ev, “Reconstruction of functional dependences by possibility-theoretic methods,” Comput. Math. Math. Phys. 43, 733–749 (2003).MathSciNet

52.

K. S. Fu, Syntactic Pattern Recognition and Application (Prentice Hall, Upper Saddle River, N.J., 1982).

53.

M. V. Glazoff, S. N. Rashkeev, Yu. P. Pyt’ev, J.-W. Yoon, and S. Sheu, “Interplay between plastic deformations and optical properties of metal surfaces: A multiscale study,” Appl. Phys. Lett. 95, 84106 (2009). https://doi.org/10.1063/1.3213391CrossRef

54.

M. Goldstein, “Subjective Bayesian analysis: Principles and practice,” Bayesian Anal. 1, 403–420 (2006). https://doi.org/10.1214/06-ba116MathSciNetCrossRef

55.

P. V. Golubtsov, Yu. P. Pytev, and A. I. Chulichkov, “Problems of optimal measuring of a Gaussian signal,” Moscow Univ. Phys. Bull. 40 (6), 17–21 (1985).

56.

P. V. Golubtsov, Yu. P. Pytev, and A. I. Chulichkov, “Optimal data reduction in physics experiments,” Moscow Univ. Phys. Bull. 41 (2), 7–11 (1986).

57.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, Upper Saddle River, N.J., 2002).

58.

R. C. Gonzalez, R. E. Woods, and S. L. Eddings, Digital Image Processing Using MATLAB (Pearson Prentice Hall, 2003).

59.

E. A. Cheremukhin, A. I. Chulichkov, and E. A. Grachev, “An estimation of electron beam current density based on ricking up curves subject to scattering in a diaphragm,” Matematicheskoe Model. 15 (3), 83–91 (2003).

60.

P. V. C. Hough, “Method and means for recognizing complex patterns,” US Patent 3069654 (1962).

61.

Picture Processing and Digital Filtering, Ed. by T. S. Huang, Topics in Applied Physics, Vol. 6 (Springer, Berlin, 1975). https://doi.org/10.1007/978-3-662-41612-9CrossRef

62.

M. Hussain, D. Chen, A. Cheng, H. Wei, and D. Stanley, “Change detection from remotely sensed images: From pixel-based to object-based approaches,” ISPRS J. Photogrammetry Remote Sensing 80, 91–106 (2013). https://doi.org/10.1016/j.isprsjprs.2013.03.006CrossRef

63.

A. Jøsang, “A logic for uncertain probabilities,” Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 9, 279–311 (2001). https://doi.org/10.1142/S0218488501000831MathSciNetCrossRef

64.

A. Jøsang, Subjective Logic: A Formalism for Reasoning Under Uncertainty, Artificial Intelligence: Foundations, Theory, and Algorithms (Springer, Cham, 2016). https://doi.org/10.1007/978-3-319-42337-1

65.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

66.

A. N. Karkishchenko and A. V. Goncharov, “Stability investigation of the sign representation of images,” Autom. Remote Control 71, 1793–1803 (2010). https://doi.org/10.1134/s0005117910090043MathSciNetCrossRef

67.

K. V. Kirillov and A. I. Chulichkov, “Measurement reduction in a fuzzy experimental model as a solution of linear programming problems,” Moscow Univ. Phys. Bull. 54 (2), 83–86 (1999).

68.

A. A. Kozlov, V. I. Nikolaev, Yu. P. Pyt’ev, V. S. Rusakov, and A. Yu. Selina, “On the dialogue approach to the solution of the problem of analyzing and interpreting a Mössbauer spectrum,” Moscow Univ. Phys. Bull. 1989 (6), 27–31 (1989).

69.

A. A. Kozlov and Yu. P. Pyt’yev, “The efficiency of reduction of measurements and some problems of metering-computing assembly design,” USSR Comput. Math. Math. Phys. 27 (2), 1–6 (1987). https://doi.org/10.1016/0041-5553(87)90146-7CrossRef

70.

V. N. Kozlov, Elements of the Mathematical Theory of Visual Perception (Izd-vo Mosk. Gos. Univ., Moscow, 2001).

71.

S. N. Kulichkov, A. I. Chulichkov, and D. S. Demin, Morphological Analysis of Ultrasonic Signals in Acoustics (Novyi Akropol’, Moscow, 2010).

72.

S. Lal, M. Chandra, G. K. Upadhyay, and D. Gupta, “Removal of additive Gaussian noise by complex double density dual tree discrete wavelet transform,” MIT Int. J. Electron. Commun. Eng. 1 (1), 8–16 (2011).

73.

Yu. V. Lazarev and Yu. P. Pyt’ev, “Morphological method in the problem of ridge pattern coding automation,” in Interuniversity Thematic Collection of Sci. Papers on Identification of Ridge Patterns on Optical-Digital Complex (Dal’nevostochnyi Gos. Univ., Vladivostok, 1980), pp. 17–23.

74.

J. Li and R. Mesiar, “Lusin’s theorem on monotone measure spaces,” Fuzzy Sets Syst. 175, 75–86 (2011). https://doi.org/10.1016/j.fss.2011.03.004MathSciNetCrossRef

75.

M.-H. Masson and T. Denœux, “Inferring a possibility distribution from empirical data,” Fuzzy Sets Syst. 157, 319–340 (2006). https://doi.org/10.1016/j.fss.2005.07.007MathSciNetCrossRef

76.

T. V. Matveeva and Yu. P. Pyt’ev, “Nonlinear reduction of measurements in problems of remote atmosphere probing,” Moscow Univ. Phys. Bull. 46 (4), 99–101 (1991).

77.

T. V. Matveeva and Yu. P. Pyt’ev, “On possibility-theoretic methods for measurement interpretation,” Pattern Recognit. Image Anal. 12, 316–325 (2002).

78.

L. M. Mestetskii, Continuous Morphology of Binary Images: Figures, Skeletons, and Conference Circuits (Fizmatlit, Moscow, 2009).

79.

N. G. Mikheev, A. I. Chulichkov, and V. A. Antonyuk, “Piecewise constant signal estimation by the recording of signal measurements in a linear scheme,” Moscow Univ. Phys. Bull. 76, 73–79 (2021). https://doi.org/10.3103/S0027134921020089CrossRef

80.

I. V. Mitin and A. I. Chulichkov, “Reliability of parametrically specified model of measurements,” Moscow Univ. Phys. Bull. 44 (4), 7–13 (1989).MathSciNet

81.

I. V. Mitin and T. D. Shodmonkulov, “The problem of mathematical processing of experimental results from semiconductor nuclear radiation detectors,” Moscow Univ. Phys. Bull. 42 (3), 28–33 (1987).

82.

S. K. Mohideen, “Denoising of images using complex wavelet transform,” Int. J. Adv. Sci. Tech. Res. 1 (2), 176–184 (2012).

83.

T. Muller, D. Wang, and A. Jøsang, “Information theory for subjective logic,” in Modeling Decisions for Artificial Intelligence, Ed. by V. Torra and T. Narukawa, Lecture Notes in Computer Science, Vol. 9321 (Springer, Cham, 2015), pp. 230–242. https://doi.org/10.1007/978-3-319-23240-9_19CrossRef

84.

T. Murofushi, K. Uchino, and S. Asahina, “Conditions for Egoroff’s theorem in non-additive measure theory,” Fuzzy Sets Syst. 146, 135–146 (2004). https://doi.org/10.1016/j.fss.2003.09.006MathSciNetCrossRef

85.

F. T. Nguen, “On the possibility approach to information analysis,” in Fuzzy Sets and Possibility Theory, Ed. by R. Yager (Radio i Svyaz’, Moscow, 1986), pp. 285–292.

86.

V. I. Nikolaev, Yu. P. Pyt’ev, V. S. Rusakov, A. G. Sveshnikov, and E. N. Terent’ev, “A new principle of organization for a "spectrometer-computer” complex in Mössbauer spectroscopy,” Sov. Phys. Dokl. 26, 950 (1981).

87.

D. M. Novitsky, Yu. P. Pyt’ev, and B. I. Volkov, “On the measurement computer-aided systems based on the gauges of first and second orders,” Mat. Model. 18 (6), 15–28 (2006).MathSciNet

88.

S. A. Orlovskii, Decision-Making Problems at Fuzzy Original Information (Nauka, Moscow, 1981).

89.

S. A. Orlovski, Calculus of Decomposable Properties, Fuzzy Sets, and Decisions (Allerton Press, New York, 1994).

90.

S. S. Papilin and Yu. P. Pyt’ev, “Probability and possibility models of matrix games of two subjects,” Math. Models Comput. Simul. 3, 528–540 (2011). https://doi.org/10.1134/s2070048211040077MathSciNetCrossRef

91.

Fuzzy Sets in Control and Artificial Intelligence Models, Ed. by D. A. Pospelov (Nauka, Moscow, 1986).

92.

W. K. Pratt, Digital Image Processing, 3rd ed. (John Wiley and Sons, New York, 2001).

93.

Yu. V. Pyatkov, D. V. Kamanin, O. V. Falomkina, Yu. P. Pyt’ev, B. M. Herbst, and W. H. Trzaska, “Estimating the reliability of revealing the fine structure in mass-kinetic energy distributions of nuclear reaction products,” Pattern Recognit. Image Anal. 21, 82–87 (2011). https://doi.org/10.1134/s1054661811010111CrossRef

94.

Yu. P. Pyt’ev, E. N. Terent’ev, and V. V. Tekin, “Comparative analysis of some resolving algorithms on computer,” Izv. Akad. Nauk SSSR. Tekh. Kibern. 4, 528–539 (1976).

95.

Yu. P. Pyt’ev, S. S. Zadorozhnyi, and A. E. Luk’yanov, “On automation of comparative morphological analysis of electron-microscopic images,” Izv. Akad. Nauk SSSR. Ser. Fiz. 41, 2436–2441 (1977).

96.

Yu. P. Pyt’ev and E. N. Terent’ev, “Numerical analysis of projection image processing methods,” Izv. Akad. Nauk SSSR. Tekh. Kibern., No. 1, 204–214 (1977).

97.

Yu. P. Pyt’ev, E. N. Terent’ev, and S. S. Zadorozhnyi, “Morphological analysis of integrated circuit images,” Vestn. Mosk. Univ. Ser. 3: Fiz., Astron., No. 6, 749–750 (1976).

98.

Yu. P. Pyt’ev, A. V. Kalinin, E. O. Loginov, and V. V. Smolovik, “Morphological analysis of color images in the Chebyshev and quadratic metrics,” Pattern Recognit. Image Anal. 8, 234–236 (1998).

99.

Yu. P. Pyt’ev, A. V. Kalinin, E. O. Loginov, and V. V. Smolovik, “Comparison of black-and white and Lambertian morphologies in the problem of pattern recognition,” Pattern Recognit. Image Anal. 8, 239–241 (1998).

100.

Yu. P. Pyt’ev and S. S. Zadorozhnyi, “Morphological method of adaptive correction of image sensor array elements,” Moscow Univ. Phys. Bull. 53 (5), 23–28 (1998).

101.

Yu. P. Pyt’ev, A. V. Kalinin, E. O. Loginov, and V. V. Smolovik, “On the problem of object detection by black-and-white and color morphologies,” Pattern Recognit. Image Anal. 8, 532–536 (1998).

102.

Yu. P. Pyt’ev, I. I. Falomkin, and A. I. Chulichkov, “Morphological compression of grayscale images of text,” Pattern Recognit. Image Anal. 16 (3), 523–528 (2006).CrossRef

103.

Yu. V. Pyt’ev and G. S. Zhivotnikov, “On the methods of possibility theory for morphological image analysis,” Pattern Recognit. Image Anal. 14 (1), 60–71 (2004).

104.

Yu. P. Pyt’ev and A. I. Chulichkov, Methods of Morphological Image Analysis (Fizmatlit, Moscow, 2010).

105.

Yu. P. Pyt’ev and A. I. Chulichkov, “Estimating the parameters of images and signals by morphological analysis,” Meas. Tech. 59, 584–588 (2016). https://doi.org/10.1007/s11018-016-1012-3CrossRef

106.

Yu. P. Pyt’ev, “Lie groups in recognition problems,” Vopr. Radioelektroniki, Ser. Obshchetekhnicheskaya, No. 8, 141–158 (1970).

107.

Yu. P. Pyt’ev, “Algorithm of signal preprocessing in recognition systems generalizing by similarity,” Kibernetika, No. 3, 23–31 (1971).

108.

Yu. P. Pyt’ev, “Parametric and group generalized sequences,” Izv. Akad. Nauk SSSR. Tekh. Kibern., No. 4, 157–163 (1971).

109.

Yu. P. Pyt’ev, “(G,G)-Invariant transformations and estimation of images,” Kibernetika, No. 6 (1973).

110.

Yu. P. Pyt’ev, “Signal preprocessor algorithm for recognition systems with similarity generalization,” Cybern. Syst. Anal., No. 7, 415–424 (1971). https://doi.org/10.1007/BF01070450

111.

Yu. P. Pyt’ev, “Projective analysis of transforms,” Cybern. Syst. Anal., No. 11, 488–498 (1975). https://doi.org/10.1007/BF01069477

112.

Yu. P. Pyt’ev, “Morphological concepts in problems of image analysis,” Sov. Phys. Dokl. 20, 646 (1976).

113.

Yu. P. Pyt’ev, “Morphological analysis of images,” Sov. Phys., Dokl. 28, 308–310 (1983).

114.

Yu. P. Pyt’ev, “Problems of morphological image analysis,” in Mathematical Methods for Studying Earth’s Mineral Resources from Space, Ed. by V. G. Zolotukhin (Nauka, Moscow, 1984), pp. 41–82.

115.

Yu. P. Pyt’ev, “Morphological image analysis,” Pattern Recognit. Image Anal. 3, 19–28 (1993).

116.

Yu. P. Pyt’ev, “The morphology of color (multispectral) images,” Pattern Recognit. Image Anal. 7, 467–473 (1997).

117.

Yu. P. Pyt’ev, “Methods for morphological analysis of color images,” Pattern Recognit. Image Anal. 8, 517–531 (1998).

118.

Yu. P. Pyt’ev, “Oblique projectors and relative forms in image morphology,” Comput. Math. Math. Phys. 53, 1916–1937 (2013). https://doi.org/10.1134/S0965542513120105MathSciNetCrossRef

119.

Yu. P. Pyt’ev, Probability, Possibility, and Subjective Modeling in Scientific Research (Fizmatlit, Moscow, 2018).

120.

Yu. P. Pyt’ev, “Oblique projectors, relative forms, and subjective models in image morphology,” in Intellectualization of Information Processing: 10th Int. Conf., Crete Island, Greece (Torus Press, Moscow, 2020), p. 153.

121.

Yu. P. Pyt’ev, Mathematical Methods of Experiment Interpretation (Vysshaya Shkola, Moscow, 1989).

122.

Yu. P. Pyt’ev, Methods for Analysis and Interpretation of Experiment (Izd-vo Mosk. Univ., Moscow, 1990).

123.

Yu. P. Pyt’ev, Methods of Mathematical Modeling of Measurement-Computational Systems, 3rd ed. (Fizmatlit, Moscow, 2012).

124.

Yu. P. Pyt’ev, “Subjective models, oblique projectors, and optimal decisions in image morphology,” Pattern Recognit. Image Anal 27, 213–233 (2017). https://doi.org/10.1134/S1054661817020080CrossRef

125.

Yu. P. Pyt’ev, “Measurement-computational trancducer as a universal measurement tool,” Mir Izmerenii, No. 6, 3–8 (2013).

126.

Yu. P. Pyt’ev, K. S. Sobolev, A. I. Chulichkov, and V. A. Antonjuk, “On the problem of superresolution of blurred images,” Pattern Recognit. Image Anal. 14, 50–59 (2004).

127.

Yu. P. Pyt’ev, “Reduction problems in experimental investigations,” Math. USSR Sb. 48, 237–272 (1984). https://doi.org/10.1070/SM1984v048n01ABEH002673CrossRef

128.

Yu. P. Pyt’ev, Possibility As an Alternative of Probability, 2nd ed. (Fizmatlit, Moscow, 2016).

129.

Yu. P. Pyt’ev, “Methods of the theory of possibilities in the problems of optimal estimation and decision making, Part 1,” Pattern Recognit. Image Anal. 7, 338–346 (1997).

130.

Yu. P. Pyt’ev, Possibility: Elements of the Theory and Applications (Editorial URSS, Moscow, 2000).

131.

Yu. P. Pyt’ev, “Foundations of possibility theory. Methods of optimal estimation and decision making. 1. Measure of possibility: Definition and properties,” Moscow Univ. Phys. Bull. 52 (3), 1–7 (1997).

132.

Yu. P. Pyt’ev, “Foundations of possibility theory. Methods of optimal estimation and decision making. 2. Measure of necessity: Definition, properties, integration over possibility and necessity,” Moscow Univ. Phys. Bull. 52 (4), 1–7 (1997).

133.

Yu. P. Pyt’ev, “Methods of the theory of possibilities in the problems of optimal estimation and decision making. Part 3,” Pattern Recognit. Image Anal. 9, 416–426 (1999).

134.

Yu. P. Pyt’ev, “On stochastic models of possibility,” Intellektual’nye Sist. 6 (1–4), 25–62 (2001).

135.

Yu. P. Pyt’ev, “Foundations of possibility theory. Methods of optimal estimation and decision making. Estimation of fuzzy elements and their distribution parameters,” Moscow Univ. Phys. Bull. 53 (6), 1–8 (1998).

136.

Yu. P. Pyt’ev, “Possibility-theoretic method of measurement reduction,” Moscow Univ. Phys. Bull. 54 (1), 1–7 (1999).

137.

Yu. P. Pyt’ev, “On meaningful interpretation of possibility and necessity,” Moscow Univ. Phys. Bull. 54 (5), 1–7 (1999).

138.

Yu. P. Pyt’ev, “Optimal decisions in the theory of possibilities,” Moscow Univ. Phys. Bull. 54 (6), 1–6 (1999).

139.

Yu. P. Pyt’ev and I. V. Mazaeva, “Possibility theoretical prediction of mean monthly temperature,” Moscow Univ. Phys. Bull. 57 (5), 27–31 (2002).

140.

Yu. P. Pyt’ev, V. A. Gazaryan, and P. B. Rosnitskiy, “A comparative analysis of the efficiency of probabilistic and possibilistic algorithms for medical diagnostics,” Moscow Univ. Phys. Bull. 69, 210–217 (2014). https://doi.org/10.3103/S0027134914030138CrossRef

141.

Yu. P. Pyt’ev, “Mathematical modeling of randomness and fuzziness phenomena in scientific studies. II. Applications,” Moscow Univ. Phys. Bull. 72 (2), 113–127 (2017).CrossRef

142.

Yu. P. Pyt’ev, “Modeling of subjective judgments made by a researcher-modeler about the model of the research object,” Math. Models Comput. Simul. 5, 538–557 (2013). https://doi.org/10.1134/S2070048213060094MathSciNetCrossRef

143.

Yu. P. Pyt’ev, O. V. Falomkina, S. A. Shishkin, and A. I. Chulichkov, “Mathematical formalism of subjective modeling,” Mash. Obuchenie Anal. Dannykh 4 (2), 108–121 (2018).

144.

Yu. P. Pyt’ev, O. Falomkina, and S. Shishkin, “Subjective restoration of mathematical models for a research object, its measurements, and measurement-data interpretation,” Pattern Recognit. Image Anal. 29, 577–591 (2019). https://doi.org/10.1134/S1054661819040138CrossRef

145.

Yu. P. Pyt’ev, O. V. Falomkina, and A. I. Chulichkov, “Subjective restoration of omissions in the measurement data of an object of study and its mathematical model,” Pattern Recognit. Image Anal. 32, 743–754 (2022). https://doi.org/10.1134/S1054661822040101CrossRef

146.

Yu. P. Pyt’ev, “Mathematical methods of subjective modeling in scientific research: I. The mathematical and empirical basis,” Moscow Univ. Phys. Bull. 73, 1–16 (2018). https://doi.org/10.3103/S0027134918010125CrossRef

147.

Yu. P. Pyt’ev, “Mathematical methods of subjective modeling in scientific research: 2. Applications,” Moscow Univ. Phys. Bull. 73, 125–140 (2018). https://doi.org/10.3103/S0027134918020145CrossRef

148.

Yu. P. Pyt’ev, “Pseudoinverse operators. Properties and applications,” Math. USSR Sb. 46, 17–50 (1983). https://doi.org/10.1070/SM1983v046n01ABEH002743CrossRef

149.

Yu. P. Pyt’ev and O. V. Falomkina (Zhuchko), “The methods of the possibility theory in the problems of optimal estimation and decision making: VII. Reconstruction of functional dependences from experimental data,” Pattern Recognit. Image Anal. 12, 116–129 (2002).

150.

Yu. P. Pyt’ev, “Stochastic models of possibility,” Pattern Recognit. Image Anal. 12, 376–396 (2002).

151.

Yu. P. Pyt’ev, “Foundations of possibility theory. Methods of optimal estimation and decision making: 5. Fuzzy elements, independence, and conditional distributions,” Moscow Univ. Phys. Bull., No. 2, 1–8 (1998).

152.

Yu. P. Pyt’ev, “Image reconstruction,” Sov. Phys., Dokl. 24, 147–150 (1979).

153.

Yu. P. Pyt’ev, “Image-quality improvement,” Sov. Phys., Dokl. 24, 154–156 (1979).

154.

Yu. P. Pyt’ev, “Suppression of false signals in the problem of raising resolution,” Sov. Phys., Dokl. 25, 898–900 (1980).

155.

Yu. P. Pyt’ev, “Measuring Computational complex. Models of the linear measuring scheme,” Moscow Univ. Phys. Bull. 38 (4), 26–30 (1983).

156.

Yu. P. Pyt’ev, “Measuring-computational complex. Problems of reduction of the results of measurements,” Moscow Univ. Phys. Bull. 38 (5), 23–27 (1983).

157.

Yu. P. Pyt’ev and A. I. Chulichkov, “Recursive methods of measurement reduction,” Mat. Model. 1 (8), 22–44 (1989).MathSciNet

158.

Yu. P. Pyt’ev, “Methods of reduction of measurements in hilbert spaces,” Math. USSR-Sb. 54, 525–549 (1986). https://doi.org/10.1070/SM1986v054n02ABEH002983CrossRef

159.

Yu. P. Pyt’ev, A. I. Chulichkov, and N. M. Chulichkova, “Reduction of images distorted by a turbulent atmosphere,” Moscow Univ. Phys. Bull. 42 (3), 22–27 (1987).

160.

Yu. P. Pyt’ev, G. V. Sukhorukova, and A. I. Chulichkov, “The remote sensing problems: Mathematical modelling, analysis and interpreting of the results,” Mat. Model. 6 (11), 113–127 (1994).MathSciNet

161.

Yu. P. Pyt’ev, V. A. Gazaryan, G. V. Sukhorukova, and T. V. Matveeva, “Interval estimation of measurement model parameters in remote sounding problems,” Moscow Univ. Phys. Bull. 48 (2), 1–6 (1993).

162.

Yu. P. Pyt’ev and P. V. Golubtsov, “The distribution of the time resource of measurements in an experiment,” Moscow Univ. Phys. Bull. 38 (5), 57–62 (1983).

163.

Yu. P. Pyt’ev, “Accuracy and reliability of experimental interpretation,” Moscow Univ. Phys. Bull. 41 (3), 14–19 (1986).

164.

Yu. P. Pyt’ev, “The precision and reliability of interpreting a series of measurements,” Moscow Univ. Phys. Bull. 41 (5), 1–5 (1986).

165.

Yu. P. Pyt’ev, “On the precision and reliability of the interpretation of indirect measurements,” Dokl. Math. 36, 96–100 (1987).

166.

Yu. P. Pyt’ev and M. L. Serdobol’skaya, “Reduction problems in the case of an unknown correlation operator,” Moscow Univ. Phys. Bull. 43 (6), 87–89 (1988).MathSciNet

167.

Yu. P. Pyt’ev, “Reliability of experiment interpretation based on an approximate model,” Mat. Model. 1 (2), 49–64 (1989).MathSciNet

168.

Yu. P. Pyt’ev and M. L. Serdobol’skaya, “A maximum-reliability method in model choice,” Moscow Univ. Phys. Bull. 43 (5), 19–24 (1988).MathSciNet

169.

Yu. P. Pyt’ev, “Reliability of measurement reduction,” Dokl. Math. 34, 1056–1058 (1989).MathSciNet

170.

Yu. P. Pyt’ev, “Nonlinear reduction of measurement,” Mat. Model. 1 (5), 44–59 (1989).MathSciNet

171.

Yu. P. Pyt’ev, “On the theory of measuring-computational systems of minimax type,” Mat. Model. 3 (10), 65–79 (1991).MathSciNet

172.

Yu. P. Pyt’ev, “For theory of nonlinear measure computer systems,” Mat. Model. 4 (2), 76–94 (1992).MathSciNet

173.

A. Yu. Pyt’ev and Yu. P. Pyt’ev, “The effective dimension of a set of measurement data,” Comput. Math. Math. Phys. 38 (4), 657–671 (1998).MathSciNet

174.

Yu. P. Pyt’ev and A. I. Chulichkov, “Measurement computer systems: Modeling, reliability, algorithms,” Pattern Recognit. Image Anal. 1, 212–223 (1991).

175.

Yu. P. Pyt’ev, “Measurement computer systems of superhigh resolution,” Pattern Recognit. Image Anal. 1, 54–76 (1991).

176.

Yu. P. Pyt’ev, “On meaningful interpretation of possibility and necessity,” Moscow Univ. Phys. Bull. 54 (5), 1–6 (1999).

177.

Yu. P. Pyt’ev, “Optimal decisions in the theory of possibilities,” Moscow Univ. Phys. Bull. 54 (6), 1–5 (1999).

178.

Yu. P. Pyt’ev, “Foundations of possibility theory. Methods of optimal estimation and decision making. 4. Maximal extension of possibility,” Moscow Univ. Phys. Bull. 53 (1), 3–6 (1998).MathSciNet

179.

Yu. P. Pyt’ev, “Fuzzy computer-aided measuring systems,” Pattern Recognit. Image Anal. Syst. 3, 150–157 (1993).

180.

Yu. P. Pyt’ev, “Methods of the theory of possibilities in the problems of optimal estimation and decision making: II. Independence and conditional possibility and necessity,” Pattern Recognit. Image Anal. 8, 1–7 (1998).

181.

Yu. P. Pyt’ev, “Uncertain fuzzy sets: Theory and applications,” Pattern Recognit. Image Anal. 5, 13–34 (1995).

182.

Yu. P. Pyt’ev, “Mathematical methods and algorithms of empirical reconstruction of stochastic and fuzzy models,” Intellektual’nye Sist. 11 (1–4), 277–327 (2007).MathSciNet

183.

Yu. P. Pyt’ev, “Uncertain fuzzy models and their applications,” Intellektual’nye Sist. 8 (1–4), 147–310 (2004).

184.

Yu. P. Pyt’ev, “Empirical restoration of the measures of possibility and possibility likelihood in models of expert decisions,” Autom. Remote Control 71, 486–500 (2010). https://doi.org/10.1134/S0005117910030100MathSciNetCrossRef

185.

Yu. P. Pyt’ev and G. S. Zhivotnikov, “Theoretical-probabilistic and theoretical-possibilistic recognition models: Comparative analysis,” Intellektual’nye Sist. 6 (1–4), 63–90 (2002).

186.

Yu. P. Pyt’ev and I. A. Shishmarev, Probability Theory, Mathematical Statistics, and Elements of the Possibility Theory for Physicists (Izd-vo Mosk. Univ., Moscow, 2010).

187.

Yu. P. Pyt’ev, “The methods of the possibility theory in the problems of optimal estimation and decision making: IV. The Methods of measurement reduction. The principle of relativity in the possibility theory,” Pattern Recognit. Image Anal. 10, 43–52 (2000).

188.

Yu. P. Pyt’ev, “The methods of the possibility theory in the problems of optimal estimation and decision making: V. The possibility-theory methods of measurement. Reduction of measurement of fuzzy sets,” Pattern Recognit. Image Anal. 10, 447–459 (2000).

189.

Yu. P. Pyt’ev, “The methods of the possibility theory in the problems of optimal estimation and decision Making: VI. Fussy sets. Independence. P-Complection. Methods for estimation of fuzzy sets and their parameters,” Pattern Recognit. Image Anal. 12, 107–115 (2002).

190.

Yu. P. Pyt’ev, “Uncertain fuzzy models and their applications: 1. Uncertain, fuzzy and uncertain fuzzy elements and sets,” Pattern Recognit. Image Anal. 14, 541–570 (2004).

191.

C. R. Rao, Shalabh, H. Toutenburg, and C. Heumann, in Linear Models and Generalizations: Least Squares and Alternatives, 3rd ed., Springer Series in Statistics (Springer-Verlag, Berlin, 2008).

192.

L. J. Savage, The Foundations of Statistics (Dover, New York, 1972).

193.

J. Serra, Image Analysis and Mathematical Morphology (Academic, New York, 1982).

194.

G. Shafer, A Mathematical Theory of Evidence (Princeton Univ. Press, 1976). https://doi.org/10.1515/9780691214696CrossRef

195.

R. Slowinski, Fuzzy Sets and Possibility Theory, Operations Research and Statistics (Kluwer Academic, 1998).

196.

Methods of Computer Image Processing, Ed. by V. A. Soifer (Fizmatlit, Moscow, 2003).

197.

M. Sugeno, “Theory of fuzzy integral and its applications,” in PhD Thesis (1974).

198.

M. Sugeno, “Fuzzy decision-making problems,” Trans. Soc. Instrum. Control Eng. 11, 709–714 (1975). https://doi.org/10.9746/sicetr1965.11.709CrossRef

199.

M. Sugeno, “Fuzzy measure and fuzzy integral,” Trans. Soc. Instrum. Control Eng. 8, 218–226 (1972). https://doi.org/10.9746/sicetr1965.8.218CrossRef

200.

M. Sugeno, “Inverse operation of fuzzy integrals and conditional fuzzy measures,” Trans. Soc. Instrum. Control Eng. 11, 32–37 (1975). https://doi.org/10.9746/sicetr1965.11.32CrossRef

201.

V. Yu. Terebizh, “Image restoration under minimal a priori information,” Phys.-Usp. 38, 137–167 (1995). https://doi.org/10.1070/PU1995v038n02ABEH000068CrossRef

202.

S. Theodoridis and K. Koutroumbas, Pattern Recognition (Academic, 1999). https://doi.org/10.1016/B978-0-12-369531-4.X5000-8

203.

A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems (Nauka, Moscow, 1979).

204.

J. T. Tou and R. C. Gonzalez, Pattern Recognition Principles, Applied Mathematics and Computation (Addison-Wesley, Reading, Mass., 1974).

205.

A. L. Tulup’ev, S. I. Nikolenko, and A. V. Sirotkin, Bayesian Nets: Logico-Probabilistic Approach (Nauka, St. Petersburg, 2006).

206.

E. R. Urbach, J. B. T. M. Roerdink, and M. H. F. Wilkinson, “Connected shape-size pattern spectra for rotation and scale-invariant classification of gray-scale images,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 272–285 (2007). https://doi.org/10.1109/tpami.2007.28CrossRefPubMed

207.

V. N. Vapnik, Reconstruction of Dependences by Empirical Data (Nauka, Moscow, 1979).

208.

V. N. Vapnik and A. Ya. Chervonenkis, Theory of Pattern Recognition: Statistical Learning Problems (Nauka, Moscow, 1974).

209.

V. N. Vapnik, T. G. Glazkova, V. A. Koshcheev, A. I. Mikhal’skii, and A. Ya. Chervonenkis, Algorithms and Programs for Reconstruction of Dependences (Nauka, Moscow, 1984).

210.

V. V. Varlamov, B. S. Ishkhanov, Yu. P. Pyt’ev, A. P. Chernyaev, and D. V. Yudin, “Reduction processing and photonuclear reaction cross section estimation,” Moscow University Physics Bulletin 39 (4), 62–69 (1984).

211.

J. Vejnarova, “Conditional independence relations in possibility theory,” Int. J. Uncertainty, Fuzziness Knowl.-Based Syst. 8, 253–269 (2000). https://doi.org/10.1142/s0218488500000186MathSciNetCrossRef

212.

Yu. V. Vizil’ter, S. Yu. Zheltov, A. V. Bondarenko, et al., Image Processing and Analysis in Machine Vision Problems (Fizmatkniga, Moscow, 2010).

213.

Yu. V. Vizil’ter, S. Yu. Zheltov, and V. I. Busurin, Modern Morphological Analysis and Its Application in Aviation Technical Vision Systems (Izd-vo Mosk. Inst., Moscow, 2020).

214.

B. I. Volkov and Yu. P. Pyt’ev, “Measuring-computing transducers based on sensors with lumped parameters,” Comput. Math. Math. Phys. 43, 1177–1191 (2003).MathSciNet

215.

T. Watanabe and T. Tanaka, “On Lusin’s theorem for non-additive measures that take values in an ordered topological vector space,” Fuzzy Sets Syst. 244, 41–50 (2014). https://doi.org/10.1016/j.fss.2013.07.021MathSciNetCrossRef

216.

O. Wolkenhauer, Possibility Theory with Applications to Data Analysis (Research Studies Press, 1998).

217.

R. R. Yager and N. Alajlan, “Dempster–Shafer belief structures for decision making under uncertainty,” Knowl.-Based Syst. 80, 58–66 (2015). https://doi.org/10.1016/j.knosys.2014.12.031CrossRef

218.

R. R. Yager, Fuzzy Sets and Possibility Theory (Pergamon Press, New York, 1982).

219.

R. R. Yager, “Conditional approach to possibility-probability fusion,” IEEE Trans. Fuzzy Syst. 20, 46–56 (2012). https://doi.org/10.1109/tfuzz.2011.2165847CrossRef

220.

R. R. Yager, “Entailment principle for measure-based uncertainty,” IEEE Trans. Fuzzy Syst. 20, 526–535 (2012). https://doi.org/10.1109/tfuzz.2011.2178029CrossRef

221.

L. P. Yaroslavskii, Introduction to Digital Image Processing (Sovetskoe Radio, Moscow, 1979).

222.

L. P. Yaroslavskii, Digital Signal Processing in Optics and Holography (Sovetskoe Radio, Moscow, 1987).

223.

B. Yuan and A. I. Chulichkov, “On the estimation of the maximum possibility for the parameters of a measurement model,” Moscow Univ. Phys. Bull. 70, 353–361 (2015). https://doi.org/10.3103/s002713491505015xCrossRef

224.

L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1965). https://doi.org/10.1016/s0019-9958(65)90241-xCrossRef

225.

L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets Syst. 1, 3–28 (1978). https://doi.org/10.1016/0165-0114(78)90029-5MathSciNetCrossRef

226.

S. S. Zadorozhnyi, Yu. P. Pyt’ev, and A. I. Chulichkov, “Morphological methods in automatic recognition of cars’ license plates from their video-images,” Pattern Recognit. Image Anal. 10, 288–292 (2000).

227.

S. S. Zadorozhnyi, A. A. Kozlov, and Yu. P. Pyt’ev, “Increasing the resolution of diffusion-type devices,” Moscow Univ. Phys. Bull. 41 (4), 17–21 (1986).

228.

Yu. I. Zhuravlev and I. B. Gurevich, Pattern Recognition and Image Recognition, Vol. 2: Models and Methods: Reference Book, Ed. by D. A. Pospelov (Radio i Svyaz’, Moscow, 1990).

229.

Yu. I. Zhuravlev, V. V. Ryazanov, and O. V. Sen’ko, Recognition: Mathematical Methods. Program Systems. Practical Application (Fazis, Moscow, 2005).

230.

Yu. I. Zhuravlev, “On the algebraic approach to solving recognition and classification problems,” Probl. Kibernetiki 33, 5–68 (1978).

231.

A. V. Zubyuk and V. G. Baikov, “Idempotent neural network as an implementation of the morphological method of object recognition by images,” in Technical Vision in Control Systems (Moscow, 2018), pp. 53–54.

232.

A. V. Zubyuk and V. G. Baykov, “Neural network implementation of the morphological method for recognizing objects in images,” in Proc. 25th Conf.: Mathematics. Computing. Education (2018), p. 135.

233.

A. V. Zubyuk, “A possibility model in the problems of morphological image analysis,” Moscow Univ. Phys. Bull. 67, 512–519 (2012). https://doi.org/10.3103/s002713491206015xMathSciNetCrossRef

234.

A. V. Zubyuk, “Image classification in fuzzy morphology: An algorithm for empirically reconstructing the decision rule,” Moscow Univ. Phys. Bull. 68, 6–12 (2013). https://doi.org/10.3103/s0027134913010189CrossRef

235.

A. V. Zubyuk and V. V. Asharin, “Using qualitative subjective information in the form of soft inequalities to solve some ill-posed inverse problems,” in Abstracts of the Fifteenth Int. Conf. on Fuzzy Set Theory and Applications (Printing House of the Armed Forces Academy of General M.R. Štefánik Liptovský, 2020), p. 97.

236.

A. V. Zubyuk, “A new approach to specificity in possibility theory: Decision-making point of view,” Fuzzy Sets Syst. 364, 76–95 (2019). https://doi.org/10.1016/j.fss.2018.06.017MathSciNetCrossRef

237.

A. V. Zubyuk, “The decision-making driven approach to specificity of possibilities in the Savage-style setting,” in 38th Linz Seminar on Fuzzy Set Theory Linz-2019: Set Functions in Games and Decisions: Abstracts (Johannes Kepler Univ. Linz, Linz, Austria, 2019), pp. 100–103.

Titel: Data Analysis and Interpretation: Methods of Computer-Aided Measuring Transducer Theory, Morphological Analysis, Possibility Theory, and Subjective Mathematical Modeling
verfasst von: Yu. P. Pyt’ev
A. I. Chulichkov
O. V. Falomkina
D. A. Balakin
Publikationsdatum: 01.12.2023
Verlag: Pleiades Publishing
Erschienen in: Pattern Recognition and Image Analysis / Ausgabe 4/2023
Print ISSN: 1054-6618
Elektronische ISSN: 1555-6212
DOI: https://doi.org/10.1134/S1054661823040351