Abstract
The inclusion of organizational knowledge in the process of modeling of complex systems is an essential step in the decision-making. This needs normative description of the system structure in terms of objective and sub-objectives. In phenomena with human participation, the emphasis is on the cardinal significance as preferences. The approach to modeling such information is the utility theory. This chapter demonstrates a value-driven approach and presents two mathematical models of complex processes. The normative approach is based on stochastic-approximation methods for analytical representation of qualitative preferences. The approach is illustrated in two practical oriented applications. The first one represents modeling of exhaustible timber production by reflecting socio-economic and forest-related ecological factors. The second one concerns the determining of the optimal usage of active and passive technology-based resources in classroom teaching. The approach permits mathematical modeling and even control and prescriptive decision support in complex processes.
TopBackground
A reasonable approach to the mathematical description of human beings is an analytical representation of their preferences. Preference representation as value or utility function enables value-based modeling. Value-based decision-making based on human preferences and their inclusion in complex systems is a challenge and a modern research trend simultaneously. It is the first step in the implementation of human-centered value-driven design in a decision-making process (Keeney & Raiffa, 1999). The main objective is to avoid the contradictions in human’s decisions in complex processes and to permit mathematical calculations in these fields.
The complex phenomena and the characteristics of human thinking raise uncertainty in the expressed human preferences. The mathematical approach to modeling such type of thinking and acquired information includes the theory of measurement, utility theory, theory of probability and various aspects of operational researches (Keeney & Raiffa, 1999; Clarke, 1983; Aubin, 2007). Especially promising in this direction is the stochastic approximation theory and the potential functions method. The latter, by its nature, allows machine learning and is used in various fields, including a mathematical description of perceptions (Aizerman et al, 1970; Mandel, 2018).
Key Terms in this Chapter
Util: A microeconomics’ standard unit of measurement of the utility.
Active Teaching Resource: A resource used in active teaching approach – both the teacher and learner actively participates in the process of knowledge acquiring (e.g., discussion, laboratory experiment, simulation, group project, educational game).
Utility Theory: A normative approach to the issue of how people should rationally choose in conditions of uncertainty.
Utility Independence: An attribute A1 is utility-independent of attribute A2, if conditional preferences on lotteries on A1, given at a fixed value of A2, do not depend on that fixed point. The utility independence is not symmetrical.
Passive Teaching Resource: A resource used in passive teaching approach – teacher presents learning matter, the learner only passively receives knowledge (e.g., narrative, presentation, lecture, demonstration, text).
Model-Driven Decision-Making and Control: An emphasized access to and manipulation of a statistical, financial, optimization, or simulation model. It uses data and parameters provided by users to assist decision process in analyzing a situation.
Machine Learning: A computational methodology for automatic information collection and knowledge descriptions aimed at improving solutions of tasks from real practice and experience.
Complexity: A condition of a system or situation integrated with some degree of order but with too many elements and relationships to be understood in a simple analytic or logical way. In the extreme, the complex system or situation is with multiple and diverse connections with dynamic and interdependent relationships, events, and processes.
Value-Driven Design: A system engineering strategy, which enables multidisciplinary design optimization. It creates an environment for optimization by providing designers with a value function as objective or as part of the mathematical model.