Person: Miguel Turullols, Laura de
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Miguel Turullols
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Laura de
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EstadĆstica, InformĆ”tica y MatemĆ”ticas
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ISC. Institute of Smart Cities
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0000-0002-7665-2801
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810922
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Publication Open Access Strengthened ordered directional and other generalizations of monotonicity for aggregation functions(Springer, 2018) Sesma Sara, Mikel; Miguel Turullols, Laura de; Lafuente LĆ³pez, Julio; Barrenechea Tartas, Edurne; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; EstadĆstica, InformĆ”tica y MatemĆ”ticas; Universidad PĆŗblica de Navarra / Nafarroako Unibertsitate PublikoaA tendency in the theory of aggregation functions is the generalization of the monotonicity condition. In this work, we examine the latest developments in terms of different generalizations. In particular, we discuss strengthened ordered directional monotonicity, its relation to other types of monotonicity, such as directional and ordered directional monotonicity and the main properties of the class of functions that are strengthened ordered directionally monotone. We also study some construction methods for such functions and provide a characterization of usual monotonicity in terms of these notions of monotonicity.Publication Open Access Local properties of strengthened ordered directional and other forms of monotonicity(Springer, 2019) Sesma Sara, Mikel; Miguel Turullols, Laura de; Mesiar, Radko; FernĆ”ndez FernĆ”ndez, Francisco Javier; Bustince Sola, Humberto; EstadĆstica, InformĆ”tica y MatemĆ”ticas; Estatistika, Informatika eta Matematika; Universidad PĆŗblica de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13In this study we discuss some of the recent generalized forms of monotonicity, introduced in the attempt of relaxing the monotonicity condition of aggregation functions. Specifically, we deal with weak, directional, ordered directional and strengthened ordered directional monotonicity. We present some of the most relevant properties of the functions that satisfy each of these monotonicity conditions and, using the concept of pointwise directional monotonicity, we carry out a local study of the discussed relaxations of monotonicity. This local study enables to highlight the differences between each notion of monotonicity. We illustrate such differences with an example of a restricted equivalence function.