Chain background and Demo

Explanation of „Show“ of spyout. Two matrices are relevant: zeta-matrix with entries z(x,y); x, y being objects and antichain-matrix, with the entry acm((q1,q2); (x,y)), with q1, q2 any two attributes (indicators).

- zeta-matrix

- ac-matrix

Beside the statistical characteristics (see textbooks of statistics) of each attribute (indicator) the connectivities are based on an evaluation of the zeta-matrix.

Connectivity:

Each object (i.e. each representative element x) gets its partial order coordinate (o(x),f(x),u(x)) as follows:

The ordered set of o,f,u of an element x is also called its “spectrum”.

Chainlist:

Let x,z be two elements from which we know that they are connected (either by inspecting the Hasse diagram, or by trial. A chain is the set of elements mutually comparable, providing a path from x to z or the other way round.

, then we define the length of the chain being k+1.

A list of all chains, connecting x and z ordered for decreasing length is given.

Conflicts:

Fix the elements x and y, but allow all pairs of indicators, possible for a set of indicators {q1,…,qm}. Then a check ist to be done for pairs. In all cases, where a list (ordered by the conflicting indicators) is provided, showing the actual indicator values and in order to facilitate the evaluation of the conflict the complete range qj1 and qj2, respectivly has.