Geodesic
Generalized Edgeworth–Pareto principle
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2015-2021

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The general multicriteria choice problem with m individual preference relations and an asymmetric collective preference relation is considered. The concept of a $k$-effective alternative is introduced, which coincides with an effective alternative for $k=1$ and represents a weakly effective alternative for $k=m$. For the other integer values of $k$, it lies somewhere in between. In terms of the general multicriteria choice problem, the Pareto axiom and the exclusion axiom for dominated alternatives are stated. Assuming that these axioms hold, a generalized Edgeworth–Pareto principle is established, which was earlier introduced by the author in the special case $k=1$. The results are extended to a fuzzy collective preference relation and to a fuzzy set of initial alternatives. 
@article{ZVMMF_2015_55_12_a3,
     author = {V. D. Nogin},
     title = {Generalized {Edgeworth{\textendash}Pareto} principle},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2015--2021},
     publisher = {mathdoc},
     volume = {55},
     number = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a3/}
}
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V. D. Nogin. Generalized Edgeworth–Pareto principle. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2015-2021. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a3/