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Article collection "Mathematical Problems of Cybernetics" №5, Moscow, 1994
Authors: Sholomov L.A.
Research of relations in criterion spaces and design of group choice operators
The ordinal relation x ̃ρy ̃, x ̃=(x1,…,xn), y ̃=(y1…,yn)ϵ Rn is completely determined by the relations (more, less, equal) of components xi and yi, i= 1,…,n. In terms of the representing functions gρ, a complete description of the ordinal relations ρ for the main classes used in multi-criteria choice problems is found. These are classes of L linear orders, W weak orders, S semi-orders, I interval orders, P partial orders, and A acyclic relations, L⊂W⊂S⊂I⊂P⊂A. We also studied the problem of design of (R1n→R2)-operators of group choice. It consists in describing the operators that aggregate any n-tuple of individual relations from the class R1 into a group relation of the class R2. The article solves this problem for all pairs of classes (R1,R2), R1,R2∈ {L,W,S,I,P,A} satisfying a naturally occurring condition R1⊆R2. Recognition problems of whether operator in question is a (R1n→R2)-operator of a given type, are investigated for NP-hardness and polynomiality.
multi-criteria choice, group choice, ordinal relation, description of ordinal relations, group choice operator, design of operators
Publication language: russian,  pages: 35 (p. 109-143)
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Sholomov Lev Abramovich,  ,  Федеральный исследовательский центр ''Информатика и управление'' РАН