Download e-book for iPad: Annals of Systems Research: Publikatie van de Systeemgroep by Henk Koppelaar (auth.), B. Van Rootselaar (eds.)

By Henk Koppelaar (auth.), B. Van Rootselaar (eds.)

ISBN-10: 1461342430

ISBN-13: 9781461342434

ISBN-10: 9020706578

ISBN-13: 9789020706574

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Extra resources for Annals of Systems Research: Publikatie van de Systeemgroep Nederland Publication of the Netherlands Society for Systems Research

Example text

A directed coupling D i, j between elements e i' e j is defined by (8) where Zi' Y j stand for the set of output variables of element e i and the set of input variables of element ej' respectively. Clearly, we have to require Z·=uD .. l j ld (9) The directed structure systemY 3D is defined as quintuple (10) where r D is a set of directed generative systems,fD is a mapping E----'>-r D' and D is a matrix [Di) of directed couplings between all pairs of elements including the environment; it will be called the directed coupling matrix.

None of the axioms ofstruc- 46 G. J. KLIR, H. J. J. UYTIENHOVE ture candidates is violated. The new candidate rt' = (rt - {Ea}) u {E~, E~/} is a successor of rt based on the p-modification. As such, it is an immediate successor of rt. All immediate successors are produced since step (1) is repeated for all pairs vj' Vk E Ea and the order of variables vj' Vk is not significant: the same successor is clearly produced by either order. Alternative II: Applicable only if Ua '" 0 and Wa '" 0· Case 1: vj is not related (directly or indirectly) to any other variable of Wa through elements of set (rt - {Ea} ).

Then, (11) indicates how much the data system represented by ((j k differs from the given data system with respect to the chosen mask; it will be called the distance of ((j k from the perfect candidate CC 0 for the data system and given mask. Its normalized version IXk dk (12) =-, I;d. I I defined within a specified set of candidates CCi (i = I, 2, ... ), will be called the degree ofdiscrepancy. Clearly (13) and where the lower bounds, dk = didates; do = by definition. ° ° and (14) IXk = 0, represent perfect structure can- 50 G.

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Annals of Systems Research: Publikatie van de Systeemgroep Nederland Publication of the Netherlands Society for Systems Research by Henk Koppelaar (auth.), B. Van Rootselaar (eds.)


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