Local Properties of Strengthened Ordered Directional and Other Forms of Monotonicity
In 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.
This work is supported by the project TIN2016-77356-P (AEI/FEDER, UE), by the Public University of Navarra under the project PJUPNA13 and by Slovak grant APVV-14-0013.
- 13.Lucca, G., Sanz, J., Dimuro, G., Bedregal, B., Asiain, M.J., Elkano, M., Bustince, H.: CC-integrals: Choquet-like Copula-based aggregation functions and its application in fuzzy rule-based classification systems. Knowl.-Based Syst. 119, 32–43 (2017). https://doi.org/10.1016/j.knosys.2016.12.004CrossRefGoogle Scholar
- 17.Sesma-Sara, M., De Miguel, L., Roldán López de Hierro, A.F., Lafuente, J., Mesiar, R., Bustince, H.: Pointwise directional increasingness and geometric interpretation of directionally monotone functions. Information Sciences (Submitted)Google Scholar
- 20.Sesma-Sara, M., Mesiar, R., Bustince, H.: Weak and directional monotonicity of functions on Riesz spaces to fuse uncertain data. Fuzzy Sets Syst. (In press). https://doi.org/10.1016/j.fss.2019.01.019