Analysis and Decision Making in Uncertain Systems by Professor Zdzislaw Bubnicki PhD (auth.)

By Professor Zdzislaw Bubnicki PhD (auth.)

A unified and systematic description of research and determination difficulties inside a large category of doubtful structures, defined by way of conventional mathematical tools and by way of relational wisdom representations.

With specific emphasis on doubtful keep an eye on platforms, Professor Bubnicki provides a distinct method of formal types and layout (including stabilization) of doubtful structures, in response to doubtful variables and similar descriptions.

• creation and improvement of unique options of doubtful variables and a studying procedure inclusive of wisdom validation and updating.

• Examples in regards to the keep an eye on of producing platforms, meeting approaches and activity distributions in desktops point out the probabilities of useful functions and techniques to determination making in doubtful systems.

• contains specific difficulties equivalent to attractiveness and keep watch over of operations lower than uncertainty.

• Self-contained.

If you have an interest in difficulties of doubtful keep watch over and selection aid structures, this may be a worthy addition in your bookshelf. Written for researchers and scholars within the box of keep watch over and knowledge technological know-how, this ebook also will profit designers of knowledge and keep watch over systems.

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Extra resources for Analysis and Decision Making in Uncertain Systems

Sample text

U,u(z) all possible values ii,:X2, ... ,xm and introduce the set Denote by values u corresponding to the Then P[u = u;(z)] ~ Pui = LPxj jESui and where q = argmax/Jui· i Version//. m ubd = Eu(u;z) =Lf[Jd(z,xj)Pxj· j=I Now the detenninistic decision algorithms '~'ad and 'P,d are based directly on the knowledge of the decision making KD obtained from KP for the given y *, and are the results of two different detenninizations ofKD. 4 Empirical Interpretations Proper empirical interpretations of the probabilistic data and the results of the Analysis and Decision Making in Uncertain Systems 42 decision problems under consideration are very important from a practical point of view.

30) is as follows: J = {j E Su : / \ (Xjik =1 ~ i E/)}. 1. e. i = / for R which is not a function. The solution has the form J : Sy(j,k) =i *} . 6. Let a=5 P=6 ' ' x= 0 0 0 0 27 Relational Systems and the requirement is I= {3,4,5}, which means that determined by D y = {ji3, y4, y5} . 29) Sy(l) = {1,6}, Sy(2) = {4,5}, Sy(3) = {3,4,6}, Sy(4) = {4}, Sy(5) = {2,3,4,6}. Then J = {2, 4}, which means that the requirement is satisfied for the decisions and u4 . It is easy to see that for x= the solution does not exist.

Let us determine the optimal decision ud* following data: D for a one-dimensional plant and the 53 Application of Random Variables fx(x) = { . -k 0 for x~O for X s; 0. 9. 37) is determined by the inequality 2u u Y2 -z Yl -z --s;xs;--. 4--). 41) Analysis and Decision Making in Uncertain Systems 54 dpd(u,z) = 0 du we obtain the deterministic decision algorithm * _ ITf ( ) _ ud- rd z - (YI- z)(Y2- z){ln(y2- z) -ln[2(yl- z)]} . 1, - ~ Dy] = u * . e. the existence of u for which Pd(u,z) -:1- 0: 2 1 O:S--:S--.

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