Analysis and Decision Making in Uncertain Systems

Citation

Vallée, R. (2006), "Analysis and Decision Making in Uncertain Systems", Kybernetes, Vol. 35 No. 1/2, pp. 242-243. https://doi.org/10.1108/03684920610640362

This book, by Professor Academician Zdzislaw Bubnicki, Head of the Institute of Control and Systems Engineering of the Wroclaw University of Technology (Poland), belongs to the Communications and control Engineering Series edited by Professor Manfred Thoma. It may be considered as an extension of the author's monograph Uncertain Logics, Variables and Systems (Springer‐Verlag, 2002). It is useful for graduate students, researchers and readers interested in control, information and decision in the case of uncertain systems that is to say systems whose description involves any form of uncertainty.

The purpose of this book is to provide a unified description of analysis and decision problems in uncertain static or dynamical systems involving random or fuzzy variables and also “uncertain variables” (a concept proposed by the author) or more generally so‐called soft variables. The uncertain systems considered are described either as functional (classical) models, or by relational knowledge representations or logical knowledge representations. In the last case relations are logical formulas concerning inputs, outputs and additional variables. It has been introduced by the author and its treatment called “logic‐algebraic method”. Another original contribution, in the case of a system with relational knowledge representation, is a learning process obtained by a step to step knowledge validation and up‐dating. Each time it is necessary, basic prerequisites are given (random and fuzzy variables for example) making the book self‐contained. Moreover many examples are given in each of the 14.

For a static functional system, the problem of analysis, is to find the output (result) corresponding to a given input (decision) and the problem of decision is to find the set of possible inputs (decisions) corresponding to a given output (desired results). In case of a static relational system, the analysis problem consists in finding the set of outputs corresponding to a given set of inputs and the decision problem consists in finding the set of possible inputs corresponding to a given set of acceptable outputs. The problems of analysis and decision are also defined and solved when the function or relation is affected by an unknown variable which may be random, fuzzy or “uncertain” (parametric uncertainty). In the case of a static system with logical knowledge representation, analysis and decision problems are also considered, even if the logical knowledge representation is random, fuzzy or “uncertain” (non‐parametric uncertainty). The above methods may be applied to dynamical systems (functional, relational or with relational knowledge representations), even in the random, fuzzy or “uncertain” cases, for parametric and non‐parametric uncertainty. Problems of optimization or stability of uncertain systems are also considered as well as the complex of operations, with uncertain execution times, and pattern recognition under uncertainty.

The learning process concerns a static system with relational knowledge representation involving unknown parameters. At each step of the process one must check (validation) if what is observed is compatible with the knowledge representation admitted at the precedent step. If it is not the case, the current estimation of the parameters must be modified (up‐dating).

This book represents the synthesis of around 60 papers of the author generally devoted to the impact of the many kinds of uncertainties which can affect a system both at the level of the knowledge of its structure and the level of decision making. It is a very interesting and important contribution to what I call “esistemo‐praxiology”.