Evaluation of Decision-Making Chains and their Fractal Dimensions

Abstract

A decision-making process is a part of the decision-making theory, reasonably placing a major research interest on the question how the process is conducted and what affects the process itself in general. Naturally it is perceived as a sequence of steps, where things are moving forward little-by-little towards to the settled goal. An analysis could be done before (planning), during the process (control + adaption) or afterwards (analysis and evaluation). Also, we can just study someone’s decision process first, mainly trying to avoid making “their” mistakes. Anyway, making decisions or just observing and studying them is a part of life. Either one assumes evaluation of the current situation and of the expected outcomes, assigning to each decision some “quality” according to the fixed set of criteria (like probabilistic), or the flexible ones (different heuristics). Thus, from the mathematical and the philosophic points of view we will face three principle questions applicable to any particular decision-making theory: (1) How many criteria do we need? (2) How well they are defined/described? (3) Are there any relations between them, or we can consider them to be independent ones? Besides, any admissible theory also will consider some kind of underground efficiency questions (at least not to over-complicate and postpone a decision-making process), possibility to track and secure the major and intermediate goals and et cetera. It is clear that theoretical research and even the hated ad-hoc hypothesis use some reasonable assumptions about criteria selection and their quantity: pure or context oriented, but we want to consider the presented problem without restrictions of any specific theory, domain or context; using just common sense and analogies between exact and human sciences detected in twentieth century an later. Therefore, we created a hypothesis on how many evaluation criteria do we really need to operate inside an abstract decision domain—regardless the nature of criteria and their relations with real-world processes. Actually, it was not a big surprise that it resulted to be related with concepts of fractals, chaos and the notion of the fractal dimension. Their clear presence was discovered in many social and biological sciences recently, so an investigation was continued not only in terms of finding “deep” arguments to prove our postulates: recent results in math and physics also showed that most dynamic processes could be described differently considering an analysis of the current situation, short-term and long-term runs. Hence, the nature and the quantity of the involved criteria may vary (they could be implicitly time-dependent) and we need to study this kind of relation also.