By Sköldstam 1975- Markus

Research of the section house of heavy symmetric most sensible (ISBN 9173739944)

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**Example text**

Then the y is called possible in technology A if there exists an activity level x such that y = Ax, When the x ) o. 11) (A) denote a cone spanned by the column vectors a j E Rm A. 10). x" j = ajEA. ajERm. Xj ~ 0, j=l J J 1 •••• ,n). Then a normal vector to (A) exists. 1 (Koopmans). 12) 0. This theorem implies as a necessary condition that boundary vector point; to p (A) of (A) for all nonacute angle (A). 1 in that the In (A)~ should be included in the orthogonal complement (A), in aj (A) E which the makes p on the efficient point p particular, an orthogonal yt.

Because the preference function of DM and thus the shape of his indifference loci corresponding to it are assumed to be globally unknown, the marginal rates of substitution of DM can be only locally assessed as the trade-off rates among objectives at some point. In many cases where the convexity is not assumed, search for the preferred solution requires selecting as most desirable the marginal rates of substitution coinciding with the trade-off ra tes of DM from among the local non inferior marginal rates of substitution.

Existence of the core has been examined by Scarf (1967), Shaplay and Shubik (1969), and others. 1) maximal or is reduced noninferior to solutions. 1) is to convert it to a scalar-valued optimization problem. 27) maximize x E X x ERn, f i : Rn .. R1, i = 1, ••• ,m, and n 1 g J: R .. •• , J , X E Rn). 27) problem (MDP) , problem. The is or called in the short, function multiple X ~ {x I gj < 0, criteria decision the multiobjective decision V: Rm .. R1, is called the V(f(x», scalarized, vector-valued (multidimensional) valuation function, or alternatively, criteria the scalarized (multiobjective) ( sca lar-va 1 ued) valuation function.