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 choice difficulties inside a large classification of doubtful structures, defined by means of conventional mathematical tools and through relational wisdom representations.

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

• advent and improvement of unique innovations of doubtful variables and a studying technique inclusive of wisdom validation and updating.

• Examples about the keep watch over of producing structures, meeting methods and activity distributions in desktops point out the probabilities of sensible purposes and ways to choice making in doubtful systems.

• contains specific difficulties similar to popularity and keep watch over of operations lower than uncertainty.

• Self-contained.

If you have an interest in difficulties of doubtful regulate and determination help platforms, this may be a worthy addition for your bookshelf. Written for researchers and scholars within the box of regulate and data technology, this booklet also will gain designers of knowledge and keep watch over systems.

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5). 5. Consider a plant with u, z, y inequality E cu + z R 1 (one-dimensional variables), described by the :::> y :::> 2cu + z , For Dy = [Ymin•Ymaxl and the given c >0. 22) gives y =~cu + z =$(u,z). From the equation $(u,z) = y * we obtain the decision algorithm 2(y • -c) u = 'P(z) = - - ' - - - 3z 24 Analysis and Decision Making in Uncertain Systems z z -----;;. 6. 7. 5 Discrete Case Assume that Now the relation R (u, y) is a set of pairs Ciij, Y;) selected from U x Y, and may be described by the zero-one matrix Xji = { 1 if (iij,Y;)ER 0 if (iij,Y;)~R.

X=g(m) where x is a vector of features characterizing the element m. Q. A frequency of the event "x = xj " for the discrete case is defined as a ratio between the number of cases xi =xj in the sequence (xl>x 2 , ... ,xn) and n. In a similar way we define a frequency of the event" xeDx" for the continuous case as a ratio between the number of cases x j eDx in the sequence and n. If n is x sufficiently large then the first frequency is approximately equal to P( = x;) and the second frequency is approximately equal to P(x eDx).

21). Note that knowledge of fz(z) is not needed. e. that fz(z) exists. 1. e. the interpretations concerning the output y for which a user's D requirement is formulated. 26) where x denotes an unknown vector parameter which is assumed to be a value of a described by the probability density fx(x) (see Sect. 1). Now, random variable x we have the case of two-level uncertainty or second-order uncertainty. The first level denotes the uncertainty concerning the non-deterministic plant, described by a relation which is not a function.

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