TOPSISort-L: An extended likelihood-based interval-valued intuitionistic fuzzy TOPSIS-sort method and its application to multi-criteria group decision-making

In real-world multi-criteria group decision making challenges, decision makers typically provide imprecise or ambiguous information due to a lack of knowledge, time constraints, or restrictions regarding information disclosure. In order to deal with this sort of imprecision caused by experts' subjective evaluation, fuzzy sets have been suggested. When compared to traditional fuzzy sets, interval-valued intuitionistic fuzzy sets, also known as IVIFSs, are superior when it comes to dealing with subjective ambiguity and incomplete information. For these reasons, this work provides a novel extension for the TOPSIS technique by employing likelihoods of IVIFSs, and introduces a methodology named as TOPSISort-L that is capable of classifying alternatives under a variety of circumstances. We begin by developing the conventional fuzzy TOPSIS technique by using a newly proposed decision matrix, a novel selection mechanism for ideal solutions, and a generalized likelihood-based closeness metric for the purpose of alternative ranking. After that, the TOPSISort-L algorithms are presented to obtain an accurate classification for the alternatives when there are information about the characteristic profiles, and also obtain an approximate classification when information about the characteristic profiles is missing. Eventually, by contrasting the approach with various different methodologies now in use, we exhibit the validity and adaptability of the method.