Geodesic
On a Method of Constructing Logical Neural Networks Based on Variable-Valued Logic Functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 154 (2018), pp. 43-48.

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

A method for constructing logical neural networks based on variable-valued logic functions is proposed. A theorem on the possibility of representing any logical function as a logical neural network is proved. The proof also contains an algorithm for constructing a logical neural network. The possibility of a generalization of the result obtained to the case of fuzzy logic is indicated.
Keywords: variable-valued predicate, data mining, variable-valued logical function, training sample, neural network approach, logical neural network, fuzzy logic. 
@article{INTO_2018_154_a4,
     author = {D. P. Dimitrichenko and R. A. Zhilov},
     title = {On a {Method} of {Constructing} {Logical} {Neural} {Networks} {Based} on {Variable-Valued} {Logic} {Functions}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {43--48},
     publisher = {mathdoc},
     volume = {154},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_154_a4/}
}
TY  - JOUR
AU  - D. P. Dimitrichenko
AU  - R. A. Zhilov
TI  - On a Method of Constructing Logical Neural Networks Based on Variable-Valued Logic Functions
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 43
EP  - 48
VL  - 154
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_154_a4/
LA  - ru
ID  - INTO_2018_154_a4
ER  - 
%0 Journal Article
%A D. P. Dimitrichenko
%A R. A. Zhilov
%T On a Method of Constructing Logical Neural Networks Based on Variable-Valued Logic Functions
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 43-48
%V 154
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2018_154_a4/
%G ru
%F INTO_2018_154_a4
D. P. Dimitrichenko; R. A. Zhilov. On a Method of Constructing Logical Neural Networks Based on Variable-Valued Logic Functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 154 (2018), pp. 43-48. http://geodesic.mathdoc.fr/item/INTO_2018_154_a4/

[1] Shibzukhov Z. M., Konstruktivnye metody obucheniya neironnykh setei, Nauka, M., 2006 | MR

[2] Lyutikova L. A., Timofeev A. V., Sgurev V. V., Iotsov V. I., “Razvitie i primenenie mnogoznachnykh logik i setevykh potokov v intellektualnykh sistemakh”, Trudy SPIIRAN, 2 (2005), 114-–126

[3] Zhilov R. A., “Primenenie metodov neirosetevogo obucheniya pri modelirovanii kognitivnykh kart”, Materialy XII Shkoly molodykh uchenykh «Nelokalnye kraevye zadachi i problemy sovremennogo analiza i informatiki», 2014, 27–28

[4] Zhilov R. A., “K voprosu o postroenii kognitivnykh kart dlya intellektualnoi obrabotki dannykh”, Vestnik KRAUNTs. Fiz. Mat. Nauki, 2016, no. 4–1 (16), 99-104

[5] Lyutikova L. A., Modelirovanie i minimizatsiya baz znanii v terminakh mnogoznachnoi logiki predikatov, Nalchik, 2006

[6] Barskii A. B., Logicheskie neironnye seti, INTUIT-BINOM, 2007

[7] Dimitrichenko D. P., “Mnogokriterialnyi poisk topologicheskikh struktur dlya optimalnogo postroeniya lokalnykh vychislitelnykh setei”, Doklady Adygskoi (Cherkesskoi) mezhdunarodnoi akademii nauk, 14:2 (2012), 68–73