Geodesic
Bayesian logical-probabilistic model of fuzzy inference: stages of conclusions obtaining and defuzzification
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 14 (2019) no. 2, pp. 92-110.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article presents the Bayesian logical-probabilistic model of fuzzy inference, which differs from the traditionally used model at the content of the stages of the conclusions obtaining, and defuzzification. The proposed model of fuzzy inference is based on the application of the apparatus of probabilistic logic and Bayes formula. The set of fuzzy implication rules is transformed into a set of probabilistic logical functions, the arguments of which are values of membership functions of the input linguistic variables and the calculated values are used as conditional probabilities in determining the posterior distribution on the set of hypotheses corresponding to the values of the output linguistic variable. The resulting posterior probability distribution is used for defuzzification of the output linguistic variable value. The features of the proposed method of defuzzification are revealed and specified in comparison with the traditionally used approach. The distinctive properties and effectiveness of the proposed Bayesian logical-probabilistic model of fuzzy inference are shown in the examples.
Keywords: fuzzy inference, linguistic variable, Bayesian logical-probabilistic model, Bayesian logical-probabilistic approach, probabilistic logic, Bayes formula, stage of conclusions obtaining, stage of defuzzification. 
@article{FSSC_2019_14_2_a1,
     author = {G. I. Kozhomberdieva and D. P. Burakov},
     title = {Bayesian logical-probabilistic model of fuzzy inference: stages of conclusions obtaining and defuzzification},
     journal = {Ne\v{c}etkie sistemy i m\^agkie vy\v{c}isleni\^a},
     pages = {92--110},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FSSC_2019_14_2_a1/}
}
TY  - JOUR
AU  - G. I. Kozhomberdieva
AU  - D. P. Burakov
TI  - Bayesian logical-probabilistic model of fuzzy inference: stages of conclusions obtaining and defuzzification
JO  - Nečetkie sistemy i mâgkie vyčisleniâ
PY  - 2019
SP  - 92
EP  - 110
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FSSC_2019_14_2_a1/
LA  - ru
ID  - FSSC_2019_14_2_a1
ER  - 
%0 Journal Article
%A G. I. Kozhomberdieva
%A D. P. Burakov
%T Bayesian logical-probabilistic model of fuzzy inference: stages of conclusions obtaining and defuzzification
%J Nečetkie sistemy i mâgkie vyčisleniâ
%D 2019
%P 92-110
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FSSC_2019_14_2_a1/
%G ru
%F FSSC_2019_14_2_a1
G. I. Kozhomberdieva; D. P. Burakov. Bayesian logical-probabilistic model of fuzzy inference: stages of conclusions obtaining and defuzzification. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 14 (2019) no. 2, pp. 92-110. http://geodesic.mathdoc.fr/item/FSSC_2019_14_2_a1/

[1] Zade L. A., The concept of a linguistic variable and its application to making approximate decisions, Mir Publ., Moscow, 1976, 165 pp. (in Russian)

[2] Lange F., Fuzzy logic, Strata Publ., SPb., 2018, 116 pp. (in Russian)

[3] Leonenkov A. V., Fuzzy simulation in MATLAB and fuzzyTECH, BKhV-Peterburg, SPb., 2005, 736 pp. (in Russian)

[4] Kudinov Yu. I., Kelina A. Yu., Kudinov I. Yu., Pashchenko A. F., Pashchenko F. F., Fuzzy models and control systems, LENAND Publ., Moscow, 2017, 328 pp. (in Russian)

[5] Kozhomberdieva G. I., Burakov D. P., “O primenenii modeli nechetkogo vyvoda dlya otsenivaniya vypolneniya praktik CMMI”, Intelligent systems in transport. IntellectTrans-2012: Sat materials II international scientific and practical conf. (St. Petersburg, March 28-31, 2012), 199–206 (in Russian)

[6] Kozhomberdieva G. I., Garina M. I., Burakov D. P., “Ob ispolzovanii apparata teorii prinyatiya reshenij v zadachakh otsenivaniya soglasno modeli CMMI”, Software and Systems, 2013, no. 4, 117–124 (in Russian)

[7] Kozhomberdieva G. I., Burakov D. P., Garina M. I., “Ispolzovanie formuly Bajesa pri otsenivanii vypolneniya praktik modeli CMMI”, Software and Systems, 2017, no. 1, 67–74 (in Russian)

[8] Kozhomberdieva G. I., Burakov D. P., “Bajesovskij podkhod k resheniyu zadach otsenivaniya kachestva”, Soft measurements and calculations, 2018, no. 5, 15–26 (in Russian)

[9] Kozhomberdieva G. I., “Bajesovskaya logiko-veroyatnostnaya model nechetkogo vyvoda”, International Conference on Soft Computing and Measurement, v. 1, 2019, 35–38 (in Russian)

[10] Burakov D. P., “Etap defazzifikatsii nechetkogo vyvoda: traditsionnyj i bajesovskij logiko-veroyatnostnyj podkhody”, International Conference on Soft Computing and Measurement, v. 1, 2019, 39–42 (in Russian)

[11] Fedorov R. F., Yakovlev V. V., Dobris G. V., Stochastic Information Converters, Mashinostroyeniye, Leningrad, 1978, 304 pp. (in Russian)

[12] Ryabinin I. A., “Logical and probabilistic method and its history”, Risk Analysis Issues, 11:3 (2014), 6–12 (in Russian)

[13] Tulupev A. L., Nikolenko S. I., Sirotkin A. V., Bayesian Networks: A Probabilistic Logic Approach, Nauka Publ., SPb., 2006, 607 pp. (in Russian)

[14] Burakov D. P., The logical basis of intelligent systems, Tutorial, v. 1, FGBOU VO PGUPS, SPb., 2018, 56 pp. (in Russian)

[15] Merekin Yu. V., “Reshenie zadach veroyatnostnogo rascheta odnotaktnykh skhem metodom ortogonalizatsii”, Computing Systems, 1963, no. 5, 10–21 (in Russian)

[16] Utkin L. V., Risk analysis and decision making with incomplete information, Nauka Publ., SPb., 2007, 404 pp. (in Russian)

[17] Venttsel E. S., Ovcharov L. A., Probability Theory and Its Engineering Applications, Nauka Publ., Moscow, 1988, 480 pp. (in Russian)

[18] Petukhov O. A., Brigadnov I. A., Khamidullin R. R., Petukhova E. O., Fuzzy patterns, Tutorial, SZTU, SPb., 2007, 92 pp. (in Russian)