Alcantud, José Carlos R.Campión Arrastia, María JesúsInduráin Eraso, EstebanMunárriz Iriarte, Ana2023-11-072023Alcantud, J. C. R., Campión, M. J., Induráin, E., & Munárriz, A. (2023). Scores of hesitant fuzzy elements revisited: “Was sind und was sollen”. Information Sciences, 648, 119500. https://doi.org/10.1016/j.ins.2023.1195000020-025510.1016/j.ins.2023.119500https://academica-e.unavarra.es/handle/2454/46707This paper revolves around the notion of score for hesitant fuzzy elements, the constituent parts of hesitant fuzzy sets. Scores allow us to reduce the level of uncertainty of hesitant fuzzy sets to classical fuzzy sets, or to rank alternatives characterized by hesitant fuzzy information. We propose a rigorous and normative definition capable of encapsulating the characteristics of the most important scores introduced in the literature. We systematically analyse different types of scores, with a focus on coherence properties based on cardinality and monotonicity. The hesitant fuzzy elements considered in this analysis are unrestricted. The inspection of the infinite case is especially novel. In particular, special attention will be paid to the analysis of hesitant fuzzy elements that are intervals.application/pdfeng© 2023 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0.Hesitant fuzzy elementsHesitant fuzzy setsScoresinfo:eu-repo/semantics/article2023-11-07info:eu-repo/semantics/embargoedAccess