Geodesic
The Edgeworth–Pareto principle in terms of a fuzzy choice function
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 583-592 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Edgeworth–Pareto Principle, the simplest version of which has been known since the 19th century, is stated in general terms of a fuzzy choice function. The application of the principle is justified for a wide class of fuzzy multicriteria choice problems described by certain axioms of the rational behavior. These results bring the axiomatic substantiation of the Edgeworth–Pareto principle performed previously by the author to the most general form and make it possible to reveal the boundaries of that class of multicriteria choice problems for which the application of this principle is required. Based on scalarization methods as applied to multicriteria problems, upper bounds are derived for the unknown set of selected vectors. 
@article{ZVMMF_2006_46_4_a3,
     author = {V. D. Nogin},
     title = {The {Edgeworth{\textendash}Pareto} principle in terms of a~fuzzy choice function},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {583--592},
     year = {2006},
     volume = {46},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a3/}
}
TY  - JOUR
AU  - V. D. Nogin
TI  - The Edgeworth–Pareto principle in terms of a fuzzy choice function
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 583
EP  - 592
VL  - 46
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a3/
LA  - ru
ID  - ZVMMF_2006_46_4_a3
ER  - 
%0 Journal Article
%A V. D. Nogin
%T The Edgeworth–Pareto principle in terms of a fuzzy choice function
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 583-592
%V 46
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a3/
%G ru
%F ZVMMF_2006_46_4_a3
V. D. Nogin. The Edgeworth–Pareto principle in terms of a fuzzy choice function. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 583-592. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a3/

[1] Nogin V. D., “Logicheskoe obosnovanie printsipa Edzhvorta–Pareto”, Zh. vychisl. matem. i matem. fiz., 42:7 (2002), 951–957 | MR | Zbl

[2] Nogin V. D., Prinyatie reshenii v mnogokriterialnoi srede: kolichestvennyi podkhod, Izd. 2-e, ispr. i dop., Fizmatlit, M., 2002 | Zbl

[3] Nogin V. D., “Obobschennyi printsip Edzhvorta–Pareto i granitsy ego primenimosti”, Ekonomika i matem. metody, 41:3 (2005), 128–131 | MR

[4] Nogin V. D., “Printsip Edzhvorta–Pareto i otnositelnaya vazhnost kriteriev v sluchae nechetkogo otnosheniya predpochteniya”, Zh. vychisl. matem. i matem. fiz., 43:11 (2003), 1666–1676 | MR | Zbl

[5] Aizerman M. A., Aleskerov F. T., Vybor variantov. Osnovy teorii, Nauka, M., 1990 | MR

[6] Makarov I. M., Vinogradskaya T. M., Rubchinskii A. A., Sokolov V. B., Teoriya vybora i prinyatiya reshenii, Nauka, M., 1982 | MR

[7] Mulen E., Kooperativnoe prinyatie reshenii: aksiomy i modeli, Mir, M., 1991 | MR

[8] Sen A., Ob etike i ekonomike, Nauka, M., 1996

[9] Podinovskii V. V., Nogin V. D., Pareto-optimalnye resheniya mnogokriterialnykh zadach, Nauka, M., 1982 | MR

[10] Jahn J., “Scalarization in vector optimization”, Math. Program., 29 (1984), 203–218 | DOI | MR | Zbl

[11] Jahn J., “Some characterization of the optimal solutions of a vector optimization problem”, Operat. Res. Spektrum., 7 (1985), 7–17 | DOI | MR | Zbl