Geodesic
Mathematical models for performing unified arithmetic operations with fuzzy numbers in the formalization of expert knowledge
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 4, pp. 75-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper considers fuzzy representation and manipulation of explicit and implicit expert knowledge. It proposes to use fuzzy numbers that allow describing uncertainty factors. It also presents a new form of specifying symmetrized forms of representation of fuzzy numbers, as well as extended and additional arithmetic operations on them which preserve the original level of fuzzy knowledge of experts and simplify the process of their formalization in solving applied problems.
Keywords: fuzzy numbers, extended and additional arithmetic operations, simulation modeling, accuracy, reliability, adequacy of the model, complex technical system. 
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A. V. Spesivtsev; B. V. Sokolov. Mathematical models for performing unified arithmetic operations with fuzzy numbers in the formalization of expert knowledge. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 4, pp. 75-84. http://geodesic.mathdoc.fr/item/VYURM_2024_16_4_a8/

[1] U.R. Eshbi, Vvedenie v kibernetiku, ed. V.A. Uspenskii, IL, M., 1959, 432 pp. | MR

[2] A.V. Spesivtsev, N.G. Domshenko, “Ekspert kak «intellektualnaya izmeritelno-diagnosticheskaya sistema»”, Sb. dokladov. KhIII Mezhdunarodnoi konferentsii po myagkim vychisleniyam i izmereniyam SCM (23-25 iyulya 2010, Sankt-Peterburg), v. 2, Izdatelstvo SPbGETU «LETI», SPb, 2010, 28–34

[3] A.V. Spesivtsev, Upravlenie riskami chrezvychainykh situatsii na osnove formalizatsii ekspertnoi informatsii, Izd-vo Politekhn. un-ta, SPb, 2004, 237 pp.

[4] A.N. Averkin, S.V. Prokopchina, “Myagkie vychisleniya i izmereniya”, Intellektualnye sistemy (MGU), 2:1–4 (1997), 93–114

[5] V.B. Tarassov, “General Approaches to the Modelling of Soft Estimates and Beliefs in Strategic Decision Engineering”, Proceedings of 2002 IEEE International Conference on Artificial Intelligence Systems, ICAIS 2002 (Divnomorskoe, Russia, 5-10 September), IEEE, Los Alamitos CA, 2002, 45–49 | MR

[6] A.I. Orlov, “Prikladnaya teoriya izmerenii”, Prikl. mnogomern. stat. analiz, M., 1978, 68–138

[7] M.B. Ignatev, V.E. Marlei, V.V. Mikhailov, A.V. Spesivtsev, Modelirovanie slabo formalizovannykh sistem na osnove yavnykh i neyavnykh ekspertnykh znanii, POLITEKh-PREESS, SPb., 2018, 500 pp.

[8] M. Mizumoto, K. Tanaka, “Some Properties in Fuzzy Sets on Type 2”, Information and Control, 31:4 (1976), 312–340 | DOI | MR

[9] A.A. Gvozdik, “Reshenie nechetkikh uravnenii”, Izv. AN SSSR. Tekhnicheskaya kibernetika, 1984, no. 5, 176–183

[10] A.V. Alekseev, “Primenenie nechetkoi matematiki v zadachakh prinyatiya reshenii”, Prikladnye zadachi analiza reshenii v organizatsionno-tekhnicheskikh sistemakh, Rizh. politekhn. In-t, Riga, 1983, 38–42

[11] A.N. Borisov, A.V. Alekseev, G.V. Merkurev i dr., Obrabotka nechetkoi informatsii v sistemakh prinyatiya reshenii, Radio i svyaz, M., 1989, 304 pp.

[12] L.A. Zade, Ponyatie lingvisticheskoi peremennoi i ego primenenie k prinyatiyu priblizhennykh reshenii, Mir, M., 1976, 162 pp.

[13] A.M. Astankov, A.V. Spesivtsev, A.V. Vagin, “Snizhenie riskov vozniknoveniya opasnykh posledstvii pri ekspluatatsii nasosnykh agregatov zapravochnogo oborudovaniya raketno-kosmicheskikh kompleksov”, Problemy upravleniya riskami v tekhnosfere, 2016, no. 1, 6–14

[14] I.A. Khodashinskii, R.V. Mescheryakov, I.V. Gorbunov, “Metody nechetkogo izvlecheniya znanii v zadachakh obnaruzheniya vtorzhenii”, Voprosy zaschity informatsii, 2012, no. 1 (96), 45–50

[15] Z.I. Rezanova, A.S. Romanov, R.V. Mescheryakov, “Zadachi avtorskoi atributsii teksta v aspekte gendernoi prinadlezhnosti (k probleme mezhdistsiplinarnogo vzaimodeistviya lingvistiki i informatiki)”, Vestnik Tomskogo gosudarstvennogo universiteta, 2013, no. 370, 24–28

[16] I.A. Rakhmanenko, R.V. Mescheryakov, “Analiz identifikatsionnykh priznakov v rechevykh dannykh s pomoschyu gmm-ubm sistemy verifikatsii diktora”, Trudy SPIIRAN, 2017, no. 3 (52), 32–50 | DOI

[17] A.S. Romanov, R.V. Mescheryakov, Z.I. Rezanova, “Metodika proverki odnorodnosti teksta i vyyavleniya plagiata na osnove metoda opornykh vektorov i filtra bystroi korrelyatsii”, Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2014, no. 2 (32), 264–269

[18] R.V. Mescheryakov, Ya.A. Turovskii, “Perspektivnye napravleniya razvitiya cheloveko-mashinnykh interfeisov”, Sbornik trudov IX Mezhdunarodnoi nauchno-tekhnicheskoi konferentsii « Informatsionnye tekhnologii v nauke, obrazovanii i proizvodstve» (ITNOP-2023) (Belgorod, 2023), 2023, 23–29