Axiomatic Approach to Rankings Techniques of Decision Analysis

Abstract

Decision-making constitutes an integral part of human life, encompassing daily activities such as shopping and travel planning, as well as political elections. The decision-making process relies on the analysis of available options based on various criteria, enabling hierarchical ordering and the selection of the optimal alternative. In the case of decisions with long-term consequences, such as choosing the location of a production plant or investment strategy, spontaneity is unacceptable. With the increasing availability of information, the necessity of considering numerous potential options becomes a challenge.
In decision-making theory, various methods for evaluating objects have been developed, categorized as methods of total order or partial order, aligning with the mathematical concept of linear order. There are many natural, intuitive and desired properties of ranking techniques of multi-criteria decision-making. These properties can be expressed in terms of functional equations and inequalities. In such setting, the desired properties can be investigated with straightforward proof. With an approach of the functional equations and inequalities, ranking techniques can be evaluated in terms of the desired properties what enables a choice of an optimal ranking method for a given task.
The article presents a short review of ranking techniques of multi-criteria decision-making. It makes conclusions about the common ideas shared among most of presented ranking techniques. In final, four properties of selected ranking techniques are investigated, namely: symmetry, scale-invariance, shift-invariance, and boundness.