Orness For Idempotent Aggregation Functions

Legarreta, Leire; Lizasoain, Inmaculada; Mardones-Pérez, I.

doi:10.3390/axioms6030025

Cited by 3 publications

(3 citation statements)

References 15 publications

(18 reference statements)

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“…providing different examples of functions fulfilling the newly presented axiomatic definition. This line of research is similar to that in Reference [28], where a new orness measure for aggregation functions generalizing Yager's proposal for OWA functions is presented. We pay particular attention to orness measures for the (discrete) Choquet integral and uninorms.…”

Section: Introductionmentioning

confidence: 58%

Axiomatization and construction of orness measures for aggregation functions

et al. 2021

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The notion of an orness measure for aggregation functions has been a relevant study subject whose history can be traced back to the early works of Dujmović in 1973. Intuitively, an orness measure quantifies the similarity of an aggregation function to the “or” function and results in an essential tool for decision engineering, field in which the choice of aggregation function is sometimes restricted to a desired value of orness (orness‐directed aggregation). In 1988, Yager presented a particular example of orness measure for ordered weighted averaging (OWA) functions and initiated a series of contributions aiming at proposing an axiomatic definition of orness measure for OWA functions. In this paper, we go much further and present an axiomatic definition of orness measure for the whole family of aggregation functions. We end by proposing two natural construction methods for an orness measure for aggregation functions. The particular examples of the (discrete) Choquet integral and uninorms are studied in detail.

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Section: Introductionmentioning

confidence: 58%

Axiomatization and construction of orness measures for aggregation functions

et al. 2021

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“…The formula also implies that the logarithms of these two OWA means are not affected by zero-gap fraction values, which is currently the major limitation of LX. Based on these considerations, we proposed a new clumping index as follows Ω although the large number of weighting vectors that can define an OWA can make it difficult to select the appropriate set for a particular situation (Beliakov et al 2007;Legarreta et al, 2017). This is particularly true in forestry research, as no previous studies exist related to this topic.…”

Section: Basic Theorymentioning

confidence: 99%

A new method to estimate clumping index integrating gap fraction averaging with the analysis of gap size distribution

et al. 2019

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Estimates of clumping index (Ω) are required to improve the indirect estimation of leaf area index (L) from optical field-based instruments such as digital hemispherical photography (DHP). A widely used method allows estimation of Ω from DHP using simple gap fraction averaging formulas (LX). This method is simple and effective but has the disadvantage of being sensitive to the spatial scale (i.e., the azimuth segment size in DHP) used for averaging and canopy density. In this study, we propose a new method to estimate Ω (LXG) based on ordered weighted gap fraction averaging (OWA) formulas, which addresses the disadvantages of LX and also accounts for gap size distribution. The new method was tested in 11 broadleaved forest stands in Italy; Ω estimated from LXG was compared with other commonly used clumping correction methods (LX, CC, and CLX). Results showed that LXG yielded more accurate Ω estimates, which were also more correlated with the values obtained from the gap size distribution methods (CC and CLX) than Ω obtained from LX. Leaf area index estimates, adjusted by LXG, are only 5%–6% lower than direct measurements obtained from litter traps, while other commonly used clumping correction methods yielded more underestimation.

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“…In recent time, some properties of this measure of orness have been discussed . Legarreta et al extended the concept of orness to the framework of idempotent aggregation functions defined on the real unit interval and on a complete lattice with a local finiteness condition. Based on Dujmovic's studies, Fodor et al proposed the orness index of any mean operator.…”

Section: Introductionmentioning

confidence: 99%

On the orness of Bonferroni mean and its variants

Figueira

Das

2019

Int J Intell Syst

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This article addresses orness measures to reflect the orlike degree of the Bonferroni mean (BM) and its variants. Some properties of these operators associated with their orness measures are portrayed analytically. However, the general orness measure involves the multiple integrals with the integral fold number being the number of the aggregated elements and as a result, the computation becomes complicated when the number of the aggregated elements is large. Furthermore, the analytical formula of the orness measure often cannot be obtained. For this reason, this study concentrates on Monte Carlo simulation to validate the result. We estimate the two parameters of the BM for a predefined orness value and a fixed length of the input vector. Besides the theoretical study of orness measure related to BM and its variants, the article also explores the simulation-based results. To support this, we provide four numerical examples. K E Y W O R D S aggregation operator, Bonferroni mean, decision-making, Monte Carlo simulation, orness measure

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Orness For Idempotent Aggregation Functions

Cited by 3 publications

References 15 publications

Axiomatization and construction of orness measures for aggregation functions

Axiomatization and construction of orness measures for aggregation functions

A new method to estimate clumping index integrating gap fraction averaging with the analysis of gap size distribution

On the orness of Bonferroni mean and its variants

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