ISSN 2071-8594

Russian academy of sciences

Editor-in-Chief

Gennady Osipov

O.V. Baskov. Algorithm for Pareto set reduction using fuzzy information on the DM preference relation

Abstract.

A model of multicriteria choice including a set of possible variants, numerical vector criterion, and a fuzzy preference relation of a decision maker (DM) is considered. The problem of multicriteria choices is to select one or several variants from the Pareto set, i.e. to reduce this set. Axiomatic approach to this problem is adopted. In this paper, we consider an algorithm for reducing the Pareto set based on an arbitrary finite collection of fuzzy information quanta on the DM preference relation.

Keywords:

multicriteria choice, the Pareto set reduction, axiomatic approach, fuzzy logic.

PP. 57-65.

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REFERENCES

1. Nogin V.D., Baskov O.V. Suzhenie mnozhestva Pareto na osnove ucheta proizvolnogo konechnogo nabora chislovoy informatsii ob otnoshenii predpochteniya // Doklady Akademii Nauk, 2011, t. 438, № 4, S. 1-4.
2. Nogin V.D. Prinyatie resheniy v mnogokriterialnoy srede: kolichestvennyy podkhod. M.: FIZMATLIT, 2002. 176 s.
3. Nogin V.D. Problema suzheniya mnozhestva Pareto: podkhody k resheniyu // Iskusstvennyy intellekt i prinyatie resheniy, 2008, № 1, S. 98-112.
4. Nogin V.D. Printsip Edzhvorta-Pareto i otnositelnaya vazhnost kriteriev v sluchae nechetkogo otnosheniya predpochteniya // Zhurnal vychislitelnoy matematiki i matematicheskoy fiziki, 2003, t. 43, № 11, s. 1676-1686.
5. Baskov O.V. Algoritm perescheta obrazuyushchikh konechnoporozhdennogo nechetkogo konusa pri dobavlenii obrazuyushchey k ego dvoystvennomu konusu // Zhurnal vychislitelnoy matematiki i matematicheskoy fiziki, v pechati.
6. Baskov O.V. Dvoystvennye nechetkie konusy // Protsessy upravleniya i ustoychivost: Trudy XLIII mezhdunarodnoy nauchnoy konferentsii aspirantov i studentov / Pod red. A.S.Yeremina, N.V.Smirnova. Spb.: Izdat. Dom S.-Peterb. gos. un-ta, 2012. S. 449 — 453.