Annals of Systems Research: Publikatie van de Systeemgroep by Henk Koppelaar (auth.), B. Van Rootselaar (eds.)

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

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Structure System LetE = {ei' e2 , ••• , em} be a nomenpty set of identifiers of elements involved in a structure system and let eo stand for the environment of the system. Let r N be a nonempty set of neutral generative systems. Each element of the structure 36 G. J. KLIR, H. J. J. UYTTENHOVE system is one of these generative systems; the identification of a particular system for each element is given in terms of function fN : E-+r N Let Xi denote the set of external (observed) variables involved in the generative system associated with element ei (i = 1, 2, ...

J' Moreover, ifthere is no C(! k ~ C(! j' then C(! i will be called an immediate successor of C(! l' 4 are given in previous papers [1, 2]. l' 6 are given in Figures 2, 3 and Table 2. Each of them shows all types of structure candidates involved and their 'immediate successor' relationship. , it is obvious that its successors are derivable by modifying subsets identifying elements ofC(! into smaller subsets. " ~ C(!. ; indeed, if two or more elements are modified, the obtained successors are derivable from other successors obtained by modifying only one of the elements.

COMPUTERIZED METHODOLOGY FOR STRUCTURE MODELLING 35 One convenient representation of the various forms of GN , which is used in all our computer programs, are probabilistic matrices. ' The various forms of GN are modified to forms of GD • They can conveniently be represented either by three-dimensional arrays [3] or in terms of matrices with the following characteristics AD d D BD fJl D Rows Columns Entries Matrix symbol e e, c e e, Cr c, c' c' c" Cr Cr p(c, c' 1 e) p(c' 1 e, c) peer' c, I e) p(cr 1 e, cr) Pcc'le Pc'lec Perc, Ie P Cr 1eCr The directed generative system //' 2D is then defined as a triple //' 2D = (//'OD' M, GD), (4) where //' OD is an directed source system, M is a sampling mask and GD is an element taken from the set {AD' d D' B D, fJl D}.

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