Applications of Intuitionistic Multi L–Fuzzy Sets in Decision-Making Problems by Using the Normalized Euclidean Distance Approach

Abstract

Intuitionistic Multi L-Fuzzy Sets (IMLFS) offer a powerful framework for handling uncertainty and hesitation in decision-making. They incorporate degrees of membership, non-membership, and hesitation over a multi-level lattice structure. This paper explores the application of IMLFS in multi-criteria decision-making (MCDM) problems, offering a flexible and comprehensive framework for evaluating alternatives under uncertainty. To measure the similarity or dissimilarity between different alternatives in the IMLFS context, distance measures play a pivotal role. We examine four commonly used distance metrics: Hamming distance, Euclidean distance, Normalized Hamming distance, and Normalized Euclidean distance. Among these, the Normalized Euclidean distance emerges as the most effective in decision-making scenarios due to its ability to account for relative deviations while mitigating the impact of scale differences. It maintains sensitivity to changes in fuzzy values and supports a balanced evaluation in ranking alternatives. Thus, the integration of IMLFS with Normalized Euclidean distance provides a robust decision-making tool, enabling improved handling of uncertainty, ambiguity, and linguistic variability.