Enhancing Fuzzy Decision-Making Models with an Extended Interval-Valued Comparison

Uncertainty is always present in the real world. In the case of information, uncertainty can be described as imprecise, vague, or incomplete, which is where the fuzzy approach becomes relevant. The fuzzy logic, by handling degrees of truth rather than the usual true or false values, offers a robust framework for dealing with such uncertainties. An interval number, embodying this fuzzy principle, can be used alternatively to reduce uncertainty in certain models. For example, in decision-making models, there is often a step where the models are required to rank output values. As intervals can exhibit partial overlap, a novel extended measure, grounded in fuzzy logic, is proposed to compare the resulting interval- valued output from various cases (i.e., overlapping and non- overlapping) of the interval, considering uncertainty. The existing methods, which use the acceptability index and probabilistic approach, are not applicable when the intervals have the same midpoint. Thus, an extended measure was proposed to address this issue, leveraging the fuzzy approach to enable comparison even when the intervals compared have the same midpoint.