New Decision-Making Process Based on Set Theory: Towards Application of Set Theory

Generating consistent and appropriate choices is essential for any decision-making process that deals with ambiguity or uncertainty. Throughout history, various mathematicians have devised distinct methodologies for resolving decision-making problems. This study presents a novel approach, referred to as the Decision-Making Process Algorithm (DMPA), that is grounded in the principles of set theory. The objective of this technique is to enhance the process of resolving decision-making problems. To illustrate the mathematical process, we will address two problems. The first concern is about the availability of different brands of a specific product, each having equally important distinct features. The second issue pertains to medical diagnosis and the handling of uncertainty. The Decision-Making Process Algorithm (DMPA) is based on the principle of a co-evolutionary algorithm that is specifically designed to handle non-linear constraints. In the field of co-optimization, it is necessary to tackle challenges that are not commonly encountered in traditional optimization methods. The paper presents the findings of the Decision-Making Process Algorithm (DMPA), which suggests that the algorithm is highly effective in tackling real-world problems. This is supported by the successful implementation of the algorithm in two separate case studies. The first case study involved the selection of a specific product variety or brand, while the second case study focused on the management of uncertainty in medical diagnosis.