A New Total Order Relation for Modal Intervals with Application to Multi-Attribute Decision Making

Decision making, an inherent process in daily and professional life, involves selecting among multiple alternatives and establishing preferences. This task is often approached using various applied models to evaluate the available options. Generally, these models rely on valuation functions that compare alternatives using real numbers. However, in environments characterized by uncertainty and imprecision, it is necessary to adapt these methodologies. To this end, this article focuses on the use of modal intervals, which allow for the retention of information related to the uncertainty present in the decision-making context. The article proposes a new total interval order relation, enabling the use of interval-valued valuation functions while preserving uncertainty information. Furthermore, it presents a generalization of the total interval order relation by incorporating the decision-maker's degree of pessimism or optimism.