Geodesic
The problem of ranking nonreusable interval objects specified by three points
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 1, pp. 119-132 Cet article a éte moissonné depuis la source Math-Net.Ru

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Three methods for preference-based ranking of nonreusable objects are described in the case when the possible results of their use are represented as pessimistic, optimistic, and most likely estimates. The methods rely on the approximation of the binary probability preference relation by binary preference relations with respect to specially designed characteristics based on the above three estimates, namely, the median, dominant, and most likely values. The methods are verified using Monte Carlo simulation. It is shown that the median and dominant preference relations ensure a relatively high degree of approximation accuracy in most cases, while the binary preference relation with respect to the most likely value leads to a considerable reduction in the accuracy of approximation. 
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I. F. Shakhnov. The problem of ranking nonreusable interval objects specified by three points. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 1, pp. 119-132. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_1_a9/

[1] Ushakov I. A., “Zadacha o vybore predpochtitelnogo ob'ekta”, Izv. AN SSSR. Tekhn. kibernetika, 1971, no. 4, 3–8

[2] Moon J. W., Topics on Tournaments, Holt, New York, 1968 | MR | Zbl

[3] Shakhnov I. F., “Metod dominant v zadache uporyadocheniya intervalnykh trekhtochechno zadannykh ob'ektov”, Izv. RAN. Teoriya i sistemy upravleniya, 2012, no. 3, 84–97

[4] Tervonen T., Figueira J. R., “A survey on stochastic multicriteria acceptability analysis methods”, J. Multi-Criteria Decision Analysis, 15 (2008), 1–14 | DOI | Zbl

[5] Belton V., Stewart T., Multiple Criteria Decision Analysis: An Integrated Approach, Kluwer Academic Publishers, Dordrecht, 2002 | Zbl

[6] Shakhnov I. F., “Model dlya obrabotki rezultatov parnykh sravnenii ob'ektov, zadavaemykh v vide intervalnykh otsenok”, Elektronnaya tekhnika. Ser. “Ekonomika i sistemy upravleniya”, 1990, no. 4, 33–39

[7] Shakhnov I. F., “Metod median v zadache uporyadocheniya intervalnykh trekhtochechno zadannykh ob'ektov”, Zh. vychisl. matem. i matem. fiz., 51:8 (2011), 1390–1399 | MR | Zbl

[8] Shakhnov I. F., “Metod tsentralnogo lucha v zadache kvantifikatsii intensivnosti predpochtenii na osnove parnykh sravnenii”, Izv. RAN. Teoriya i sistemy upravleniya, 2009, no. 4, 96–108 | MR

[9] Podinovskii V. V., “Zadacha otsenivaniya koeffitsientov vazhnosti kak simmetricheski-leksikograficheskaya zadacha optimizatsii”, Avtomatika i telemekhanika, 2003, no. 3, 130–162 | MR

[10] Burkov V. N., Novikov D. A., Kak upravlyat proektami, SINTEG-GEO, M., 1997

[11] Poia D., Matematika i pravdopodobnye rassuzhdeniya, IIL, M., 1957

[12] Pytev Yu. P., Vozmozhnost kak alternativa veroyatnosti, Fizmatlit, M., 2007

[13] Kaiberg G., Veroyatnost i induktivnaya logika, Progress, M., 1979

[14] Aivazyan S. A., Mkhitaryan V. S., Prikladnaya statistika i osnovy ekonometriki, YuNEITI, M., 1998

[15] Orlov A. I., Prikladnaya statistika, Ekzamen, M., 2006