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

By Professor Zdzislaw Bubnicki PhD (auth.)

A unified and systematic description of study and selection difficulties inside a large category of doubtful structures, defined via conventional mathematical tools and by means of relational wisdom representations.

With unique emphasis on doubtful regulate structures, Professor Bubnicki promises a different method of formal versions and layout (including stabilization) of doubtful structures, in accordance with doubtful variables and comparable descriptions.

• creation and improvement of unique recommendations of doubtful variables and a studying approach along with wisdom validation and updating.

• Examples in regards to the keep watch over of producing structures, meeting strategies and job distributions in desktops point out the chances of useful purposes and methods to determination making in doubtful systems.

• contains precise difficulties equivalent to reputation and keep an eye on of operations less than uncertainty.

• Self-contained.

If you have an interest in difficulties of doubtful regulate and determination aid platforms, this can be a necessary addition for your bookshelf. Written for researchers and scholars within the box of keep an eye on and knowledge technology, this publication also will gain designers of data and keep watch over systems.

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Extra resources for Analysis and Decision Making in Uncertain Systems

Example text

The probability distribution fu (u) may not exist) and in the description KP= it is not necessary to assume that y is the value of a random variable. In the discrete case we have finite sets of possible input and output vectors: uE {ui,iJi, ... ,ua }, The knowledge representation K(p) analogous to f(u,y) now has a form of the matrix where pif denotes the joint probability that u =uj and Pij y = Yi: =P[(u=uj)A(y=y;)]. J z-1,2, ... , , j = l,2, ... ] l - 1,2, ... , ' j = l,2, ... 4) The forms of KP presented above may be called non-parametric descriptions of the uncertain plant.

Zk E Dz ~ k E K. The decision problem consists in finding the largest set J implication (j E J) 1\ (k E K) ~ i E such that the I is satisfied. 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}.

The problem may be extended to a set of output values DY c Y , given by a user. e. the probability that every y belonging to the set D Y may occur at the output (may be a possible output). Note that where Then fJx given by an expert and the set Dy c Y given by a user, one should determine the optimal decision u* maximizing the probability P[Dy(u;x) ~ Dy] ~ p(u).

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