Geodesic
Reduction of the Pareto set based on closed information about fuzzy DM's preference relation
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2012), pp. 33-47
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Pareto set reduction axiomatic approach generalized on a fuzzy preference relation case is considered. So-called fuzzy closed information is used in this paper to reduce the compromise set. It is shown how to construct a fuzzy set, which is an upper estimate for the unknown fuzzy set of selected vectors. The results obtained generalize previous states, where preference relation and selected vectors are crisp. Numerical illustration of using fuzzy closed information in decision process is given.
Keywords: multicriteria choice problem, the Pareto set, fuzzy preference relation, the Pareto set reduction axiomatic approach. 
@article{VSPUI_2012_3_a3,
     author = {A. O. Zakharov},
     title = {Reduction of the {Pareto} set based on closed information about fuzzy {DM's} preference relation},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {33--47},
     year = {2012},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2012_3_a3/}
}
TY  - JOUR
AU  - A. O. Zakharov
TI  - Reduction of the Pareto set based on closed information about fuzzy DM's preference relation
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2012
SP  - 33
EP  - 47
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2012_3_a3/
LA  - ru
ID  - VSPUI_2012_3_a3
ER  - 
%0 Journal Article
%A A. O. Zakharov
%T Reduction of the Pareto set based on closed information about fuzzy DM's preference relation
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2012
%P 33-47
%N 3
%U http://geodesic.mathdoc.fr/item/VSPUI_2012_3_a3/
%G ru
%F VSPUI_2012_3_a3
A. O. Zakharov. Reduction of the Pareto set based on closed information about fuzzy DM's preference relation. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2012), pp. 33-47. http://geodesic.mathdoc.fr/item/VSPUI_2012_3_a3/

[1] Nogin V. D., Prinyatie reshenii v mnogokriterialnoi srede: kolichestvennyi podkhod, Izd. 2-e, ispr. i dop., Fizmatlit, M., 2005, 176 pp.

[2] Nogin V. D., “Printsip Edzhvorta–Pareto i otnositelnaya vazhnost kriteriev v sluchae nechetkogo otnosheniya predpochteniya”, Zhurn. vychisl. matematiki i mat. fiziki, 43:11 (2003), 1666–1676

[3] Bogdanova A. V., Nogin V. D., “Suzhenie mnozhestva Pareto na osnove prosteishikh naborov nechetkoi informatsii ob otnositelnoi vazhnosti kriteriev”, Vestn. S.-Peterb. un-ta. Ser. 10: Prikladnaya matematika, informatika, protsessy upravleniya, 2007, no. 2, 3–17

[4] Klimova O. N., “Suzhenie mnozhestva Pareto na osnove naborov vzaimno zavisimoi informatsii o nechetkom otnoshenii predpochteniya”, Iskusstvennyi intellekt i prinyatie reshenii, 2009, no. 2, 34–44

[5] Zakharov A. O., “Suzhenie mnozhestva Pareto na osnove zamknutoi informatsii ob otnoshenii predpochteniya LPR”, Vestn. S.-Peterb. un-ta. Ser. 10: Prikladnaya matematika, informatika, protsessy upravleniya, 2009, no. 4, 69–83 | MR

[6] Zadeh L. A., “Fuzzy sets”, Information and Control, 8 (1965), 338–353 | DOI | MR | Zbl

[7] Kaufmann A., Introduction a la theorie des sous-ensemblis flous

[8] Zakharov A. O., “Suzhenie mnozhestva Pareto na osnove vzaimno zavisimoi informatsii zamknutogo tipa”, Iskusstvennyi intellekt i prinyatie reshenii, 2011, no. 1, 95–109