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

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.

Preferences-Based Performance Measurement Models

It is shown that the human subjective expectations for the uncertainty events can be described mathematically with the terms of the probability theory and can be inserted into the mathematical theory of von Neumann and Morgenstern. Some examples of utility functions are shown.

Extrapolation Methods in Control and Adaptive System

In the initial stages of the choice of approaches and methods, the heuristic of the investigator is very important, because in most of the cases there is a lack of measurements or even clear scales under which to implement these measurements and computations. This stage is often outside of the strict logic and mathematics and is close to the art, in the widest sense of the word. For complex systems and practical problems, the explicit description of such an algorithm is a difficult problem; often it is not solvable, but the existence of beforehand solutions and realizations allow one to make meaningful prognosis estimates. Such an approach is the method of “Multidimensional Linear Extrapolation” (MLE) described in this chapter. The main idea is that close situations give close solutions. The method is very efficient and gives many good solutions for difficult modeling problems.

Elements of Stochastic Programming

In the second part of the chapter is discussed the “potential functions method,” a very fruitful area of the stochastic programming. Even though it is called method, this field is actually a mathematical theory whose practical results are a large number of stochastic recurrent procedures for pattern recognition, approximating algorithms for functions in noisy conditions, development of unified mathematical approach for machine learning on the basis of human preference, proof of the perceptron theory, etc. The stochastic algorithms based on the “potential functions method” have stable convergence and flexibility, and these properties permit fruitful application in utility and value function evaluations and polynomial approximations. The last part of the chapter gives an example of pattern recognition of two sets of positive and negative answers as machine learning procedure.

Mathematical Preliminaries

The correct assessment of the level of informativity and usability of these types of knowledge requires careful analysis of the terms measurement, formalization, uncertainty, probability, and admissible mathematical operations, under the respective scale, which does not distort the initial empirical information. This chapter is of an introductory nature in one of the vastest fields of mathematics, namely “probability theory and mathematical statistics” and their application in decision-making. After the discussion of fundamental notions and theorems in Probability theory, the authors reveal some of the fundamental techniques establishing the convergence of the recurrent stochastic procedures in the Stochastic programming, which will permit analytical description of the value and utility functions. The analytical description of the expert’s preferences as value or utility function will allow mathematically the inclusion of the decision maker in the description of the complex system “Technologist-process”.

A Preference Utility-Based Approach for Qualitative Knowledge Discovery

This chapter gives a short description of a prototype Decision Support System (DSS), which assesses the value and/or utility functions of the individual user. This DSS allows de-facto training of the computer in the same preferences as that of the individual user without the need of additional participant or mediator in the process of utility evaluation. It is mathematically backed up by the methods described in the preceding chapters. The presented methodology and mathematical procedures allow for the creation of such individually oriented DSS for analytic representation of the preferences as objective function based on direct comparisons or on the gambling approach. Such systems may be autonomous or parts of a larger information decision support system.

Decision Support in Bird’s Production Farms

In order to achieve this aim, methods and theoretical studies in the area of expert or decision support systems are used in the area of bird production. The investigation includes development of the methodology (approach and algorithms) for such systems and its testing on the level of modeling and data simulation.

Stochastic Utility Evaluation

A mathematically grounded method is offered in the chapter that could be used at the stage of expressing the preferences and constructing the value and utility functions. In this case, it is necessary to take account of some important characteristics of the DM-Computer dialogue such as the conceptual, qualitative nature of the subject’s thinking and the probable and subjective indefiniteness of expressing the expert’s preferences. The utility functions are constructed by the means of stochastic recurrent procedures as a recognition of a set by learning the computer in the same preferences as these of the expert.

Decision Support Fundamentals

Rational approaches to decision-making are classified in one of the following categories: descriptive, normative, or prescriptive. The main normative models that are presented concern value functions, expected utility and subjective expected utility. Several alternative normative frameworks that have appeared in the literature of the last thirty years particularly for attacking the problem of conflicting objectives—the analytic hierarchical process, multi-criteria decision-making movement, outranking—are described. A Framework to align decision support-driven initiatives with the decision-making vision is given in the chapter. It divides the objective-oriented systems that determine the structure of decision-making domain from the strategic actions in this domain that have to determine the decision-making process. The latter serves as the basis for defining the main objectives, which have to be achieved in the development of Decision-Making Support Systems (DMSS). A classification scheme of the main categories of such systems is suggested. The development of DMSSs depends on the accepted implementation method, architectural representation of these systems, implementation approaches and used information, communication and computer technologies. They guarantee not only the capabilities of decision-making support systems, but its characteristics as well.

Personalized E-Learning Systems

After presentation of a technique for measurement of human preferences and its implementation in an instrument for measurement, several attempts to reveal the great potential of evaluation of human preferences in learner modeling are described.