Munárriz Iriarte, Ana

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https://academica-e.unavarra.es/handle/2454/52177

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Munárriz Iriarte

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Ana

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Estadística, Informática y Matemáticas

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INARBE. Institute for Advanced Research in Business and Economics

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1173018

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812493

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2023 - 20242
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Author: Induráin Eraso, Esteban × End date: 2024 ×

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    PublicationOpen Access
    Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories
    (MDPI, 2024-08-13) Induráin Eraso, Esteban; Munárriz Iriarte, Ana; Sara Goyen, Martín Sergio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2
    We deal with two apparently disparate theories. One of them studies extensions of orderings from a set to its power set. The other one defines suitable scores on hesitant fuzzy elements. We show that both theories have the same mathematical substrate. Thus, important possibility/impossibility results concerning criteria for extensions can be transferred to new results on scores. And conversely, conditions imposed a priori on scores can give rise to new extension criteria. This enhances and enriches both theories. We show examples of translations of classical results on extensions in the context of scores. Also, we state new results concerning the impossibility of finding a utility function representing some kind of extension order if some restrictions are imposed on the utility function considered as a score.
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    Scores of hesitant fuzzy elements revisited: "Was sind und was sollen"
    (Elsevier, 2023) Alcantud, José Carlos R.; Campión Arrastia, María Jesús; Induráin Eraso, Esteban; Munárriz Iriarte, Ana; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBE
    This 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.