ISSN 2071-8594

Russian academy of sciences


Gennady Osipov

V.D. Nogin Composed approach to reduce the Pareto set using linear or multiplicative scalarization


A multi-criteria choice problem including a DM’s binary preference relation is considered. Two combined two-stage approaches are proposed. According these methods firstly we have to reveal some information on the DM’s preference relation and then to apply scalarization methods based on linear or multiplicative functions. Justification of both combined two-stage approaches are given.


multicriteria choice, axiomatic approach, quant of information, linear scalarization, multiplicative scalarization, Edgeworth-Pareto principle, Pareto set reducing.

PP. 70-77.


1. Nogin V.D. Problema suzheniya mnozhestva Pareto: podkhody k resheniyu// Iskusstvennyy intellekt i prinyatie resheniy, № 1, 2008.S. 98-112.
2. Nogin V.D. Prinyatie resheniy v mnogokriterialnoy srede: kolichestvennyy podkhod. M.: Fizmatlit, 2005.
3. Nogin V.D. Suzhenie mnozhestva Pareto: aksiomaticheskiy podkhod. M.: Fizmatlit, 2016.
4. Nogin V.D. Lineynaya svertka v mnogokriterialnoy optimizatsii//Iskusstvennyy intellekt i prinyatie resheniy,№ 4, 2014. S. 73-82.
5. Nogin V.D. Obobshchennyy printsip Edzhvorta-Pareto//Zhurnal vychislitelnoy matematiki i matematicheskoy fiziki, t. 55, № 12, 2015.S. 2015–2021.
6. Petrovskiy A.B. Teoriya prinyatiya resheniy. M.: Izdatelskiy tsentr Akademiya, 2009, 400 s.
7. Podinovskiy V.V., Nogin V.D. Pareto-optimalnye resheniya mnogokriterialnykh zadach. M.: Fizmatlit, 2007.
8. Trends in multiple criteria decision analysis (Greco S., Ehrgott M., Figueira, J., eds.) Springer, New York,2010, 412 p.