By Professor Zdzislaw Bubnicki PhD (auth.)

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

With certain emphasis on doubtful keep watch over platforms, Professor Bubnicki supplies a different method of formal versions and layout (including stabilization) of doubtful structures, in response to doubtful variables and comparable descriptions.

• creation and improvement of unique strategies of doubtful variables and a studying procedure such as wisdom validation and updating.

• Examples about the keep watch over of producing structures, meeting tactics and activity distributions in computers point out the chances of sensible functions and ways to choice making in doubtful systems.

• comprises certain difficulties equivalent to popularity and keep watch over of operations less than uncertainty.

• Self-contained.

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

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Extra info for Analysis and Decision Making in Uncertain Systems

Example text

39) is satisfied. D We can consider other approaches to the determinization of KP or KD under consideration, consisting in two successive determinizations: the determinization at the relational level analogous to that described in Sect. 4 and the determinization concerning uncertainty described by the probability distribution of :X at the second level. A. Determinization for the given D y In this case we may use the mean value uM in the determinization of the relational and random decision algorithm < Du (z; x )Jx > ~ KD 1 at the first level: uM = fudu·[ Du(z;x) fdur1~ct>d(z,x).

2. ' using the different ways of the determinization described above. It is also important to note that the results '~'ad and 'f'bd in points A and B have no evident empirical interpretation. 4. 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)]} .

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. The second level denotes the expert's uncertainty, and is described by the probability distribution fx(x).

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