Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Mathematical Model of the Problem of Distribution in Conditions of Uncertainty

Author(s):

Valery Borisovich Vilkov

The army general A.V. Khrulyov military academy of logistics
St.-Petersburg, Russia.
Candidate of physico-mathematical Sciences,
associate Professor of the Department of scientific and technical disciplines

amirusha@rambler.ru

Alexander Vladimirovich Flegontov

St-Petersburg State University, St.-Petersburg,
Herzen State Pedagogical University of Russia, St.-Petersburg, Russia.
Doctor of Sciences, Professor,
Head of the Department of computer engineering and software development

flegontoff@yandex.ru

Andey Kliment’evich Chernykh

St.-Petersburg military institute of armies of national
guards of Russian Federation,
St.-Petersburg, Russia.
Doctor of technical Sciences, Professor,
Department of Informatics and mathematics

nataliachernykh@mail.ru

Abstract:

A mathematical model of the problem of distribution in conditions of uncertainty is considered. The main problem is formulated on the example of the plan selection for specialist development programme implementation. The solution is based on approaches of the graph theory, fuzzy set theory and fuzzy logic, and linear programming. Theoretical principles are illustrated by meaningful examples. A natural generalization of the considered problem is proposed.

Keywords

• fuzzy decision
• fuzzy logic
• fuzzy sets
• the optimal plan for the problem solving
• training plan

References:

1. Vilkov V. B., Chernykh A. K. Theorya i practika optimizatsii upravlencheskikh rechenii v usloviyakh ChS na transporte: monografya. SPb. : Sant-Petersburg Universyti GPS MChS Rossii, 2016 - 162 s
2. Berg K. Theorya grafov i ee primenenya. - M. :IL, 1962. - 320 s
3. Ore O. Theorya grafov. - M. : Nauka, 1968. - 352 s
4. Zadeh L. Ponyatie lingvisticheskoi peremennoi i ego primenenie k prinyatiu pribligennykh rechenii. - M. : Mir, 1976. - 166 s
5. Kofman A. Vvedenie v theoriu nechetkikh mnogestv. - M. : Radio i svyaz, 1982. - 429 s
6. Leonenkov A. V. Nechetkoe modelirovanie v srede MATLAB i fuzzyTECH. - SPb. : BKhV-Peterburg, 2005. - 725 s
7. Orlovskii S. A. Problemy prinyatiya rechenii pri nechetkoi iskhodnoy informasei. - M. : Nauka, 1981. - 206 s
8. Yakhyaeva G. E. Nechetkie mnogestva i neyronnye seti. - M. : Binom, 2006. - 315 s
9. Zadeh L. A. Fuzzy sets. - Information and Control, 1965, vol. 8, N 3, p. 338-353
10. Chernykh A. K., Vilkov V. B. Upravlenye bezopastnostyu transportnykh perevozok pri organizasyi materialnogo obespecheniya sil i sredstv MChS Rossii v usloviakh chrezvychaynoy situasii// Pogarovzryvobezopastnost’. 2016. V. 25. Т 9. P. 52-59
11. Chernykh A. K., Kozlova I. V., Vilkov V. B. Voprosy prognozirovanya material’no-tekhnicheskogo obespechenya s ispolzovaniem nechetkikh mathematicheskikh modeley// Problemy upravlenya riskamy v thekhnosfere. 2015. N 4 (36). P. 107-117
12. Vilkov V. B., Chernykh A. K., Flegontov A. V. Theorya i practika optimizatsii rechenii na osnove nechetkikh mnogestv i nechetkoi logiki. SPb. : Izd. RGPU im. A. I. Gerzena. Monografya, 2017. -160 s
13. Terano T., Asai K., Sugeno M. Prikladnye nechetkie sistemy. - M. : Mir, 1993. - 368 s
14. Shtovba S. D. Vvedenie v theoriu nechetkikh mnogestv i nechetkuu logiku. - Vinniza: UNIVERSUM- Vinniza, 2001. - 71 s
15. Vagner G. Osnovy issledovanya operasyi. V. 1. - M. : Mir, 1972. -335 s

Full text (pdf)