A New Extension of Monotonicity: Ordered Directional Monotonicity
In this work, we discuss a recent generalization of the classical notion of monotonicity, with a special focus on the idea of directional monotonicity. This idea leads to the concepts of pre-aggregation functions and of ordered directional monotonicity. For the former, the direction along which monotonicity is considered is the same for all the points of the domain and the same boundary conditions as for aggregation functions are imposed. For the latter, different directions of monotonicity may be considered at different points.
KeywordsAggregation function Pre-aggregation function Directional monotonicity Ordered-directional monotonicity
The authors would like to thank research projects TIN2016-77356-P(AEI/FEDER, UE) and APVV-14-0013.
- 2.Bustince, H., Barrenechea, E., Lafuente, J., Mesiar, R., Kolesárová, A.: Ordered directionally monotone functions. Justification and application. IEEE Trans. Fuzzy Syst.Google Scholar
- 11.Canny, J.: Finding edges and lines in images. Technical report, Massachusetts Institute of Technology, Cambridge, MA, USA (1983)Google Scholar