Yuri P. Pavlov

Decision Control, Management, and Support in Adaptive and Complex Systems: Quantitative Models

Yuri Pavlov is an associate professor in the Institute of Information and Communication Technologies in Bulgarian Academy of Sciences, Bulgaria. He has received DUES from Paris VI France, MSc degree in Automation from Technical University of Sofia, and holds a PhDs from the Bulgarian Academy of Sciences. His research has been published in international journals Proceedings of Bulgarian Academy of Sciences, International online journal Bioautomation, European Journal of OR, E-learning III, and the knowledge society-Belgium, Proceedings in Manufacturing Systems, Romania. He has both research and practical expertise in innovative and creative decision-making, optimal control, and control design of complex systems. He is also a member of International Institute of Informatics and Systemics (IIIS). Yuri P. Pavlov (Bulgarian Academy of Sciences, Bulgaria) and Rumen D. Andreev (Bulgarian Academy of Sciences, Bulgaria)

Machine learning and expert utility assessment

The theory of utility allows for the expert preferences being taken account of in complex systems and problems. The expert values are not directly oriented to the problem under consideration and due to that specific algorithms have to be developed for constructing the utility. This imposes the need of developing specific approaches and methods for the analysis and evaluation of qualitative, conceptual information. The subjects of this article are the recurrent algorithms for constructing the utility function on the basis of stated preferences. The algorithms are theoretically based on the stochastic programming. The expert-computer dialogue has been modelled numerically. A prototype of information decision support system for assessment of individuals utility functions is elaborated on the base of the developed mathematical approach.

Preferences and Determination of the Nominal Growth Rate of a Fed-Batch Process: Control Design of Complex Processes

ABSTRACT The expected utility theory is the approach to measurement and utilization of qualitative, conceptual information. The subject of this paper is the design of methodology and algorithms for evaluation of expert utility that permit development of value-driven decision support in complex control and management systems. The approach is based on stochastic programming, the potential function method and on control theory. In the paper a control design for optimal control and stabilization of the specific growth rate of fed-batch biotechnological processes is presented. The control design is based on the Wang-Monod and Wang-Yerusalimsky kinetic models and their equivalent Brunovsky normal form. The control is written based on information of the growth rate. The mathematical formulations, presented here serve as basis for the tool development. The evaluation leads to the development of preferences-based decision support in machine learning environments and iterative complex control descriptions and design.

Subjective Probability and Expected Utility, A Stochastic Approximation Evaluation

The topic of this article is stochastic algorithms for evaluation of the utility and subjective probability based on the decision maker’s preferences. The main direction of the presentation is toward development of mathematically grounded algorithms for subjective probability and expected utility evaluation as a function of both the probability and the rank of the alternative. The stochastic assessment is based on mathematically formulated axiomatic principles and stochastic procedures and on the utility theory without additivity. The uncertainty of the human preferences is eliminated as is typical for the stochastic programming. Numerical presentations are shown and discussed. Indian Journ l of Applied Re earch Website: www.theglobaljournals.com (ISSN 2249-555X) INTRODUCTION The representation of complex systems including human decisions as objective function needs mathematical tools for evaluation of qualitative human knowledge. In decision making theory the primitive are preferences relations as description of peoples strategies, guided both by internal expectations about their own capabilities of getting results, and by external feedback of this result (Keeney & Raiffa, 1993). Such modeling addresses theory of measurement (scaling), utility theory and Bayesian approach in decision making. The Bayesian statistical technique in decision making is applicable when the information and uncertainty in respect of problems, hypothesis and parameters can be expressed by probability distribution and functional representation of human preferences (Griffiths & Tenenbaum, 2006). Such an approach needs careful analysis of the terms measurement, formalization and admissible mathematical operations in the modeling. This is a fundamental level that requires the use of basic mathematical terms like sets, relations and operations over them, and their gradual elaboration to more complex and specific terms like value and utility functions, operators on mathematically structured sets and harmonization of these descriptions with set of axioms. In this aspect we enter the theory of measurements and the expected utility theory (Fishburn, 1970). The evaluation of qualitative human knowledge and the mathematical inclusion of the subjective probabilities and utility posed many difficulties and needs a special attention. Generally the human notions and preferences have qualitative or verbal expression. The wisely merge of the qualitative and verbal expression as human preferences and quantitative mathematical description causes many efforts. The violations of transitivity of the preferences lead to declinations in utility and subjective probability assessment (Cohen & al., 1988; Kahneman & Tversky, 1979; Fishburn, 1988; Machina, 2009). Such declinations explain the DM behavior observed in the Allais Paradox (Allais, 1953). A long discussion for the role of the mathematic and the Bayesian theory in the human decision making reality has been started yet. New extensions of axiomatic bases of the developed mathematical theories are considered for further wide developments of von Neumann’s theory. Fruitful directions of researches are development of a nonadditive subjective utility theory. The mathematical results of Schmeidler in respect of subjective probability and utility description make a great impression on this development (Shmeidler, 1989). The paper suggests a reasonable wellfounded mathematical approach and methods for subjective probability and utility evaluation based on the von Neumann’s utility theory and the Kahneman’s and Schmeidler’s findings. We propose and discuss a stochastic programming for subjective probability and utility polynomial evaluation as machine learning based on the human preferences. Numerical presentations are shown and discussed. MATHEMATICAL FORMULATIONS AND BACKGROUND The difficulties that come from the mathematical approach are due to the probability and subjective uncertainty of the DM expression and the cardinal character of the expressed human’s preferences. The mathematical description is the following. Let X be the set of alternatives (X⊆R). From practical point of view the empirical system of human preferences relations is a algebraic system with relations SR (X,(≈),()), where (≈) can be considered as the relation “indifferent or equivalent”, and () is the relation “prefer”. We look for equivalency of the empirical system with the numbered system of relations SR (R-real numbers, (=), (>)). The “indifference” relation (≈) is based on () and is defined by ((x≈y) ¬((xy)∨(xy))). We introduce a set S, which elements are named state of nature, following Schmaidler’s exposition (Shmeidler, 1989). Let Ω be algebra of subset of S. Denote by Do the set of all measurable finite step valued functions from S to P and denote by Dc the constant functions in Do. Let D be a convex subset of P which includes Dc, (Dc ⊆ Do ⊆ D). In the neo-Bayesian nomenclature elements of X are deterministic finite outcome (alternatives), elements of P are random outcomes or lotteries connected with the objective probabilities, and elements of D are acts connected with the uncertainty of human operations described with subjective probabilities. Elements of S

Preferences, Utility Function, and Control Design of Complex Cultivation Process

This chapter demonstrates the flexibility and the diversity of the potential functions method and its conjunction with the utility theory when it describes completely analytically the complex system “decision maker-dynamical process.” The utility analytical descriptions have been built concerning the attitude of the technologist toward the dynamic process. Using these approach factors as ecology, financial perspective, social effect can be taken into account. They are included in the expert preferences via the expert attitude towards them. The analytic construction of the utility function is an iterative “machine-learning” process. This interactivity allows a new strategy in the process of control design and in the control of the system with human participation in the final solution. The first and the most important effect of this strategy is the possibility for the analytical description of such complex systems. This has been achieved for the first time in scientific practice. The second effect is the introduction of the iterativity in the process of forming the control as is used naturally and harmonically computer and analytical mathematical techniques. The third effect is the fact that the process of training can be reversed towards the trainer technology expert with the aim of additional analysis and corrections. In the control design are overcome restrictions connected with the observability of the Monod kinetics and with the singularities of the optimal control of Monod kinetic models. DOI: 10.4018/978-1-4666-2967-7.ch009