Deviation-based aggregation functions

Decký, Marián; Mesiar, Radko; Stupňanová, Andrea

doi:10.1016/j.fss.2017.03.016

Cited by 23 publications

(22 citation statements)

References 11 publications

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“…The main goal of this aggregation is to obtain such an output value that characterizes the whole set of inputs as concisely as possible. However, mentioned Daróczy's means do not always maintain monotonicity, i.e., they are not, in general, aggregation functions, [5,6,10]. Therefore, the authors in [5,6] introduced a so-called moderate deviation function, which ensures that the aggregation functions based on the moderate deviation functions meet all the properties of aggregation functions.…”

Section: Introductionmentioning

confidence: 99%

“…However, mentioned Daróczy's means do not always maintain monotonicity, i.e., they are not, in general, aggregation functions, [5,6,10]. Therefore, the authors in [5,6] introduced a so-called moderate deviation function, which ensures that the aggregation functions based on the moderate deviation functions meet all the properties of aggregation functions. At present, researches offer various constructions of aggregation functions, which are based on the use of the mentioned moderate deviation functions, [1,5,6,11].…”

Section: Introductionmentioning

confidence: 99%

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New Classes of the Moderate Deviation Functions

Špirková

Bustince

Fernández³

et al. 2021

Atlantis Studies in Uncertainty Modelling

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At present, in the field of aggregation of various input values, attention is focused on the construction of aggregation functions using other functions that can affect the resulting aggregated value. This resulting value should characterize the properties of the individual input values as accurately as possible. Attention is also paid to aggregation using the so-called moderate deviation function. Using this function in aggregation ensures that all properties of aggregation functions are preserved. This work offers constructions of the moderate deviation functions using negations and automorphisms on the symmetric interval [−1, 1] and a general closed interval [a, b] ⊂ [−∞, ∞].

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Classes of the Moderate Deviation Functions

Špirková

Bustince

Fernández³

et al. 2021

Atlantis Studies in Uncertainty Modelling

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“…All of these means are not monotone, in general. To avoid this problem and thus to contribute to the aggregation theory we have recently proposed the concept of moderate deviation functions [8,9].…”

Section: Introductionmentioning

confidence: 99%

Generalized deviation functions and construction of aggregation functions

Stupňanová¹,

Smrek²

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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“…There exist a great number of works that study aggregation functions, both from the theoretical [1,7,10] and the practical [9,16,21] perspectives.…”

Section: Introductionmentioning

confidence: 99%

Local Properties of Strengthened Ordered Directional and Other Forms of Monotonicity

Sesma‐Sara

Miguel

Mesiar

et al. 2019

Advances in Intelligent Systems and Computing

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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.

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Deviation-based aggregation functions

Cited by 23 publications

References 11 publications

New Classes of the Moderate Deviation Functions

New Classes of the Moderate Deviation Functions

Generalized deviation functions and construction of aggregation functions

Local Properties of Strengthened Ordered Directional and Other Forms of Monotonicity

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