scholarly journals Maximal directions of monotonicity of an aggregation function

2021 ◽  
Author(s):  
B. De Baets ◽  
H. De Meyer
Keyword(s):  
Aggregation Function

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.

A method of constructing fuzzy implications from the FIφ-construction

2021 ◽  
pp. 1-14
Author(s):  
Yifan Zhao ◽  
Kai Li
Keyword(s):  
Specific Property ◽  
New Method ◽  
Aggregation Function ◽  
Fuzzy Implications ◽  
Construction Methods ◽  
Fuzzy Implication ◽  
New Construction

In the recent years, several new construction methods of fuzzy implications have been proposed. However, these construction methods actually care about that the new implication could preserve more properties. In this paper, we introduce a new method for constructing fuzzy implications based on an aggregation function with F (1,  0) =1, a fuzzy implication I and a non-decreasing function φ, called FIφ-construction. Specifically, some logical properties of fuzzy implications preserved by this construction are studied. Moreover, it is studied how to use the FIφ-construction to produce a new implication satisfying a specific property. Furthermore, we produce two new subclasses of fuzzy implications such as UIφ-implications and GpIφ-implications by this method and discuss some additional properties. Finally, we provide a way to generate fuzzy subsethood measures by means of FIφ-implications.

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 Robustness regions for measures of risk aggregation

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Silvana M. Pesenti ◽  
Pietro Millossovich ◽  
Andreas Tsanakas
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Random Variables ◽  
Distribution Functions ◽  
Aggregation Function ◽  
Convex Risk Measures ◽  
Linear Growth Condition ◽  
Risk Aggregation ◽  
Definition Of

AbstractOne of risk measures’ key purposes is to consistently rank and distinguish between different risk profiles. From a practical perspective, a risk measure should also be robust, that is, insensitive to small perturbations in input assumptions. It is known in the literature [14, 39], that strong assumptions on the risk measure’s ability to distinguish between risks may lead to a lack of robustness. We address the trade-off between robustness and consistent risk ranking by specifying the regions in the space of distribution functions, where law-invariant convex risk measures are indeed robust. Examples include the set of random variables with bounded second moment and those that are less volatile (in convex order) than random variables in a given uniformly integrable set. Typically, a risk measure is evaluated on the output of an aggregation function defined on a set of random input vectors. Extending the definition of robustness to this setting, we find that law-invariant convex risk measures are robust for any aggregation function that satisfies a linear growth condition in the tail, provided that the set of possible marginals is uniformly integrable. Thus, we obtain that all law-invariant convex risk measures possess the aggregation-robustness property introduced by [26] and further studied by [40]. This is in contrast to the widely-used, non-convex, risk measure Value-at-Risk, whose robustness in a risk aggregation context requires restricting the possible dependence structures of the input vectors.

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