Modeling of complex processes with human participations causes difficulties due to the lack of precise measurement coming from the qualitative nature of the human notions. This provokes the need of utilization of empirical knowledge expressed cardinally. An approach for solution of these problems is utility theory. As cyber-physical systems are integrations of computation, networking, and physical processes in interaction with the user is needed feedback loops, the aim of the chapter is to demonstrate the possibility to describe quantitatively complex processes with human participation. This approach permits analytical representations of the users' preferences as objective utility functions and modeling of the complex system “human-process.” The mathematical technique allows CPS users dialog and is demonstrated by two case studies, portfolio allocation, and modeling of a competitive trade by a finite game and utility preference representation of the trader. The presented formulations could serve as foundation of development of decision support tools and decision control.
Top Introduction
The principles of rationality in the human behavior and the determination of the best decision solutions require a meaningful mathematical approach relevant to the problems under consideration. The meaning of best varies from problem to problem (Keeney & Raiffa, 1999; Keeney, 1988). The variety of the complex processes with human participations as social obligations, financial and engineering problems e.g. causes difficulties due to the inherent time variant properties and the lack of precise measurement coming from the qualitative nature of the human notions. This complexity of problems pose in question the needs of development of decision support methods and tools for design of advanced contemporary systems as Cyber-Physical Systems (Lee, 2008; Bradley & Atkins, 2015; Hahn & Kuhn, 2012).
Cyber-Physical Systems (CPS) are integrations of computation, networking, and physical processes in interaction with the user. In fact, such kind of systems are information and computer based systems supporting processes of control, management, decision making with supporting organizational, managing and/or business information and decisions (Lee, 2008; Bradley & Atkins, 2015). These systems maintain operational levels in which the human interaction and decisions could be crucial for the final result. In general, CPS are interactive software systems with the purpose of supporting the decision-maker with information and accompanying optimal solutions. In such kind of systems empirical knowledge can be taken into account, introduced in a convenient way even in cardinal form. Additionally, CPS could maintain data bases, sorting of sequential data, monitoring of dynamical processes, mathematical analysis etc. Such design needs feedback loops and interaction with the human (user) participating in the process. Physical and software components and the dialog with the users are deeply intertwined, each operating on different special mathematical scales (Keeney, 1988; Lee, 2008; Pfanzagl, 1971).
The incomplete human acquired information could be compensated by expressions of qualitative human preferences in dialog with the users. The preferences are expressed in regard to the main purpose and the related sub-objectives to the problem under consideration and are external manifestations of the human estimations (Keeney & Raiffa, 1999; Keeney, 1988; Pavlov & Andreev, 2013; Pavlov, 2005). Possible approach for solution of these problems is the Theory of measurement, the Utility theory and the Stochastic programming (Keeney & Raiffa, 1999; Pfanzagl, 1971; Fishburn, 1970, 1978). The Utility theory basically deals with the expressed subjective user preferences. Possible criteria for “the meaning of best” can be an expert (decision maker-DM) utility function (Keeney, 1988; Pavlov & Andreev, 2013; Fishburn, 1978).