Geodesic
Completions for space of preferences
Contributions to game theory and management, Tome 7 (2014), pp. 290-299.

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A preferences structure is called a complete one if it axiom linearity satisfies. We consider a problem of completion for ordering preferences structures. In section 2 an algorithm for finding of all linear orderings of finite ordered set is given. It is shown that the indicated algorithm leads to construction of the lattice of ideals for ordered set. Further we find valuations for a number of linear orderings of ordered sets of special types. A problem of contraction of the set of linear completions for ordering preferences structures which based on a certain additional information concerning of preferences in section 4 is considered. In section 5, some examples for construction and evaluations of the number of all linear completions for ordering preferences structures are given.
Keywords: preferences structure, ordering preferences structure, completion of preferences structure, a valuation for the number of linear completions. 
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     author = {Victor V. Rozen},
     title = {Completions for space of preferences},
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Victor V. Rozen. Completions for space of preferences. Contributions to game theory and management, Tome 7 (2014), pp. 290-299. http://geodesic.mathdoc.fr/item/CGTM_2014_7_a26/

[1] Birkhoff G., Lattice theory, Coll. Publ., 25, Amer. Math. Soc., 1967 | MR | Zbl

[2] Rozen V., “Decision making under many quality criteria”, Collected papers presented on the Fifth International Conference Game Theory and management (SPb., 2011), Contribution to game theory and management, 5, Graduate School of Management, SPbU, 2012, 257–267

[3] Rozen V., Decision making under quality criteria, Palmarium Academic Publishing, Saarbrucken, Deutschland, 2013 (in Russian)