Value Based Decision Control for Complex Systems

Introduction

The mathematical description of Decision maker (DM) analytically as utility function together with the model description of the investigated process could give a complete mathematical representation of the complex system “Technologist (DM) – dynamic process.” Such models ensure exact mathematical descriptions of problems in various areas which quantitative modeling is difficult: economics, biotechnology, ecology, and so on. These models guarantee that the powerful optimal control theory could be applied in such complex areas and exact mathematical solutions could be determined in agreement with the DM preferences. Here complexity is understood as inclusion of the DM as inseparable part of the complex system and as inclusion of the DM in the model description. The focus is analytical inclusion of the decision maker in the modeling and in the main objective function. Following from this, the orientation of the approach is toward the branch of the Model driven decision making in the taxonomy created by Daniel Power (Power, 2002). A model-driven decision making emphasizes access to and manipulation of a statistical, financial, optimization or simulation model. Model-driven decision making uses data and parameters provided by technologists to assist the DM in analyzing a situation.

Human thinking and preferences have qualitative nature which makes the problems in the domain of the complex systems with human participation to be considered as qualitative, i.e. difficult for analytical description. People’s preferences contain characteristics of subjective and probabilistic uncertainty. This makes the mathematical incorporation of human preferences in complex systems difficult. Possible approach for resolving these problems is the stochastic approximation (Aizerman et al., 1970; Kivinen et al., 2004; Pavlov & Andreev, 2013). The uncertainty of the subjective preferences could be viewed as a noise which can be eliminated as is typical for stochastic approximation. A main requirement of the stochastic assessment is the analytical presentation of the qualitative nature of the human’s preferences and notions (Keeney & Raiffa, 1993).

The main assumption in each management or control decision is that the values of the subject making the decision are the guiding force and as such they are the main moment in supporting the decisions (Keeney, 1988). In complex system with human participation the DM’s values are implicitly and heuristically included. This means that there is no explicit objective function to allow for flexible behavior of the decision maker when forming the decisions. Such objective value function allows for quantitative analysis and removal of logical inconsistencies and errors (Castagne et al., 2009; Collopy & Hollingsworth, 2009). Value driven design can be defined as a development paradigm, in which required human value considerations are engineered into best practices, activities and management (Collopy, 2009). Value-driven control design enables design optimization by providing designers with an objective function. The value based presentation of objective function includes all the important attributes of a system being designed, and outputs a score (Hall & Davis, 2007; Castagne et al., 2009). At the whole system level, the objective function which performs this assessment of value is called a value model.

The main focus of the paper is the productive merger of mathematical exactness with the empirical uncertainty in the human notions. A mathematical methodology that is useful for dealing with the uncertainty of human behavior in complex problems and mathematical description of the complex system “technologist-process” is presented here. The described approach permits representation of the individual’s preferences as value/utility function, evaluated as machine learning and inclusion of this function in the value model as objective function.