scholarly journals On Self-Aggregations of Min-Subgroups

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 201
Author(s):  
Carlos Bejines ◽  
Sergio Ardanza-Trevijano ◽  
Jorge Elorza
Keyword(s):  
Mathematical Morphology ◽  
Level Sets ◽  
Aggregation Function ◽  
Active Area ◽  
Translation Invariance ◽  
Subgroup Structure ◽  
Input Size ◽  
Aggregation Functions ◽  
Self Aggregation

Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions . However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.

scholarly journals Mixed aggregation functions for outliers detection

2021 ◽  
pp. 1-14
Author(s):  
Hengshan Zhang ◽  
Chunru Chen ◽  
Tianhua Chen ◽  
Zhongmin Wang ◽  
Yanping Chen
Keyword(s):  
Aggregation Function ◽  
Outliers Detection ◽  
Aggregation Functions ◽  
Novel Approach ◽  
Consensus Measure

A scenario that often encounters in the event of aggregating options of different experts for the acquisition of a robust overall consensus is the possible existence of extremely large or small values termed as outliers in this paper, which easily lead to counter-intuitive results in decision aggregation. This paper attempts to devise a novel approach to tackle the consensus outliers especially for non-uniform data, filling the gap in the existing literature. In particular, the concentrate region for a set of non-uniform data is first computed with the proposed searching algorithm such that the domain of aggregation function is partitioned into sub-regions. The aggregation will then operate adaptively with respect to the corresponding sub-regions previously partitioned. Finally, the overall aggregation is operated with a proposed novel consensus measure. To demonstrate the working and efficacy of the proposed approach, several illustrative examples are given in comparison to a number of alternative aggregation functions, with the results achieved being more intuitive and of higher consensus.

GENERATION OF WEIGHTING TRIANGLES ASSOCIATED WITH AGGREGATION FUNCTIONS

2000 ◽  
Vol 08 (04) ◽  
pp. 417-451 ◽  
Author(s):  
T. CALVO ◽  
G. MAYOR ◽  
J. TORRENS ◽  
J. SUÑER ◽  
M. MAS ◽  
...  
Keyword(s):  
Aggregation Function ◽  
Weighted Averaging ◽  
Fractal Structures ◽  
Weighted Mean ◽  
Averaging Operators ◽  
Ordered Weighted Averaging ◽  
Aggregation Functions ◽  
Different Types ◽  
Ordered Weighted Averaging Operators

In this work, we present several ways to obtain different types of weighting triangles, due to these types characterize some interesting properties of Extended Ordered Weighted Averaging operators, EOWA, and Extended Quasi-linear Weighted Mean, EQLWM, as well as of their reverse functions. We show that any quantifier determines an EOWA operator which is also an Extended Aggregation Function, EAF, i.e., the weighting triangle generated by a quantifier is always regular. Moreover, we present different results about generation of weighting triangles by means of sequences and fractal structures. Finally, we introduce a degree of orness of a weighting triangle associated with an EOWA operator. After that, we mention some results on each class of triangle, considering each one of these triangles as triangles associated with their corresponding EOWA operator, and we calculate the ornessof some interesting examples.

scholarly journals Learning Aggregation Functions

2021 ◽  
Author(s):  
Giovanni Pellegrini ◽  
Alessandro Tibo ◽  
Paolo Frasconi ◽  
Andrea Passerini ◽  
Manfred Jaeger
Keyword(s):  
Machine Learning ◽  
Learning Community ◽  
State Of The Art ◽  
Real Data ◽  
Universal Function ◽  
Aggregation Function ◽  
Function Representation ◽  
Aggregation Functions ◽  
Complex Functions ◽  
Latent Dimension

Learning on sets is increasingly gaining attention in the machine learning community, due to its widespread applicability. Typically, representations over sets are computed by using fixed aggregation functions such as sum or maximum. However, recent results showed that universal function representation by sum- (or max-) decomposition requires either highly discontinuous (and thus poorly learnable) mappings, or a latent dimension equal to the maximum number of elements in the set. To mitigate this problem, we introduce LAF (Learning Aggregation Function), a learnable aggregator for sets of arbitrary cardinality. LAF can approximate several extensively used aggregators (such as average, sum, maximum) as well as more complex functions (e.g. variance and skewness). We report experiments on semi-synthetic and real data showing that LAF outperforms state-of-the-art sum- (max-) decomposition architectures such as DeepSets and library-based architectures like Principal Neighborhood Aggregation, and can be effectively combined with attention-based architectures.

A New Medical Image Segmentation Method Based on Chan-Vese Model

2014 ◽  
Vol 513-517 ◽  
pp. 3750-3756 ◽  
Author(s):  
Yuan Zheng Ma ◽  
Jia Xin Chen
Keyword(s):  
Image Segmentation ◽  
Mathematical Morphology ◽  
Level Sets ◽  
Medical Image ◽  
Medical Image Segmentation ◽  
Experimental Results ◽  
Segmentation Method ◽  
Accuracy Requirement ◽  
Segmentation Accuracy ◽  
Segmentation Problem

The traditional segmentation method for medical image segmentation is difficult to achieve the accuracy requirement, and when the edges of the image are blurred, it will occurs incomplete segmentation problem, in order to solve this problem, we propose a medical image segmentation method which based on Chan-Vese model and mathematical morphology. The method integrates Chan-Vese model, mathematical morphology, composite multiphase level sets segmentation algorithm, first, through iterative etching operation to extract the outline of the medical image, and then the medical image is segmented by the Chan-Vese model based on the complex multiphase level sets, finally the medical image image is dilated iteratively by using morphological dilation to restore the image. The experimental results and analysis show that, this method improves the multi-region segmentation accuracy during the segmentation of medical image and solves the problem of incomplete segmentation.

scholarly journals Water quality indices and benefit-cost analysis

2013 ◽  
Vol 4 (1) ◽  
pp. 81-105 ◽  
Author(s):  
Patrick J. Walsh ◽  
William J. Wheeler
Keyword(s):  
Water Quality ◽  
Cost Analysis ◽  
Impact Analysis ◽  
Quality Parameters ◽  
Convincing Evidence ◽  
Aggregation Function ◽  
Benefit Cost Analysis ◽  
Regulatory Impact Analysis ◽  
Aggregation Functions ◽  
Benefit Cost

The water quality index (WQI) has emerged as a central way to convey water quality information to policy makers and the general public and is regularly used in US EPA regulatory impact analysis. It is a compound indicator that aggregates information from several water quality parameters. Several recent studies have criticized the aggregation function of the EPA WQI, arguing that it suffers from “eclipsing” and other problems. Although past papers have compared various aggregation functions in the WQI (usually looking at correlation), this is the first paper to examine these functions in the context of benefit-cost analysis. Using data from the 2003 EPA CAFO rule, the present paper examines four aggregation functions and their impact on estimated benefits. Results indicate that the aggregation method can have a profound effect on benefits, with total benefit estimates varying from $82 million to $504 million dollars. The net benefits of the rule vary from negative to positive over this range of estimates. Furthermore, a sensitivity analysis does not find convincing evidence to substitute the current aggregation function, although several changes to the underlying WQI methodology may be warranted.

scholarly journals Sub-Additive Aggregation Functions and Their Applications in Construction of Coherent Upper Previsions

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 2
Author(s):  
Serena Doria ◽  
Radko Mesiar ◽  
Adam Šeliga
Keyword(s):  
Linear Space ◽  
Random Variables ◽  
Aggregation Function ◽  
Full Characterization ◽  
Aggregation Functions ◽  
Bounded Below

In this paper, we explore the use of aggregation functions in the construction of coherent upper previsions. Sub-additivity is one of the defining properties of a coherent upper prevision defined on a linear space of random variables and thus we introduce a new sub-additive transformation of aggregation functions, called a revenue transformation, whose output is a sub-additive aggregation function bounded below by the transformed aggregation function, if it exists. Method of constructing coherent upper previsions by means of shift-invariant, positively homogeneous and sub-additive aggregation functions is given and a full characterization of shift-invariant, positively homogeneous and idempotent aggregation functions on [0,∞[n is presented. Lastly, some concluding remarks are added.

LOCALLY INTERNAL AGGREGATION FUNCTIONS

1999 ◽  
Vol 07 (03) ◽  
pp. 235-241 ◽  
Author(s):  
G. MAYOR ◽  
J. MARTIN
Keyword(s):  
Aggregation Function ◽  
Aggregation Functions

We introduce the concept of locally internal aggregation function with domain ℝn and values in ℝ, and demonstrate some results which lead to the characterization of such functions.

Analysis on Aggregation Function Spaces

2014 ◽  
Vol 22 (05) ◽  
pp. 737-747 ◽  
Author(s):  
Zhao Zhang ◽  
Zeshui Xu
Keyword(s):  
Decision Making ◽  
Function Spaces ◽  
Aggregation Function ◽  
View Point ◽  
Decision Matrix ◽  
Aggregation Functions ◽  
Structures And Properties ◽  
New View

In many decision-making problems, different methods usually yield different results. In this paper, we study all possible rankings of alternatives produced by applying a set of aggregation functions on a decision matrix. Those possible rankings depend on the aggregation functions that we use and the structures of the decision matrix. The aim of this paper is to investigate structures and properties of decision matrices and aggregation function spaces and give a new view point to understand aggregation spaces and decision matrices.

scholarly journals Remarks on Super-Additive and Sub-Additive Transformations of Aggregation Functions

2018 ◽  
Vol 72 (1) ◽  
pp. 55-66 ◽  
Author(s):  
Katarína Hriňáková ◽  
Adam Šeliga
Keyword(s):  
Aggregation Function ◽  
Dimensional Case ◽  
One Dimensional ◽  
Aggregation Functions

Abstract In this contribution we modify the definitions of the super-additive and sub-additive transformations of aggregation functions. Firstly, we define k-bounded transformations that represent only finite decompositions with at most k elements. Secondly, we introduce two other transformations that preserve the super-additivity property in some sense. Also, a remark on continuity of the classical super-additive transformation of an aggregation function is presented for one-dimensional case.

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