Mixture functions and their monotonicity

Abstract

We consider mixture functions, which are a type of weighted averages for which the corresponding weights are calculated by means of appropriate continuous functions of their inputs. In general, these mixture function need not be monotone increasing. For this reason we study sucient conditions to ensure standard, weak and directional monotonicity for specic types of weighting functions. We also analyze directional monotonicity when dierentiability is assumed.

A fusion method for multi-valued data

“…It is worth mentioning that via deviation-based approaches there is possible to catch several types of mixture operators and their generalizations (more in [17], [18], [19], [20], [21]).…”

Multiple Optimal Solutions and the Best Lipschitz Constants Between an Aggregation Function and Associated Idempotized Aggregation Function

“…More details can be seen in the excellent reviews on the state of the art by Grabisch et al [3][4][5], group decision making by Mohd and Abdullah [7] and Del Moral et al [2], and construction methods by Khameneh and Kilicman [6]. Recently, many papers have been dedicated to an aggregation function in group decision making [11][12][13], multi-criteria decision making [14], two-side matching decision making [15], and others [16,17].…”

Some Construction Methods of Aggregation Operators in Decision-Making Problems: An Overview

“…We usually need to develop the class of aggregation functions by constructing new ones based on the existing operators. There are a number of techniques to construct different classes of aggregation operators with different properties [23,[27][28][29][30][31][32][33][34] where they start from given aggregation functions and continue by constructing new ones. A review paper over such techniques allows us to have an insight of not only the problems that can be solved by them, but also situations that cannot be handled by these methods.…”