The state-of-art of the generalizations of the Choquet integral: From aggregation and pre-aggregation to ordered directionally monotone functions

Dimuro, Graçaliz Pereira; Fernández, Javier; Bedregal, Benjamín R. C.; Mesiar, Radko; Sanz, José Antonio; Lucca, Giancarlo; Bustince, Humberto

doi:10.1016/j.inffus.2019.10.005

Cited by 140 publications

(34 citation statements)

References 103 publications

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“…called marginal utility functions and ψ is an aggregation function (Dimuro at al., 2020). Note that the scale [0 1] is used for utility functions, although in the general case they are defined on R. The u ′ i s allow the expert to express the acceptable or not acceptable values; utility functions are used to ensure the following:…”

Section: Multiattribute Utility Theorymentioning

confidence: 99%

“…Nevertheless, it cannot be used to model wide spectrum of decision maker preferences since it has intrinsic limitation ( Grabish and Labreuche, 2010 ). On the other hand, CI operator is far less known but has given very good result in several domains and also from a theoretical point of view given raise to several extension ( Dimuro at al., 2020 ). Furthermore, contrary to many aggregation operators, CI is able to handle interactions between criteria and is the only one, in its basic form, to handle homogeneous and heterogeneous interrelationships ( Sun et al, 2018 ).…”

Section: Description Of the Ranking Processmentioning

confidence: 99%

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Control Sequence Ranking for Critical System Based on Health of Equipment Thanks to Choquet Integral

Bouaziz

Marangé

Voisin

et al. 2021

Front. Artif. Intell.

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This paper presents a ranking method of operating sequences based on the actual condition of complex systems. This objective is achieved using the health checkup concept and the multiattribute utility theory. Our contribution is the proposal of sequences ranking process using data and experts’ judgments. The ranking results in a decision-making element; it allows experts to have an objective and concise overall ranking to be used for decision making. A case study is presented based on an experimental platform; it allows us to compare two aggregation operators: the weighted mean and the Choquet integral.

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Section: Multiattribute Utility Theorymentioning

confidence: 99%

Section: Description Of the Ranking Processmentioning

confidence: 99%

Control Sequence Ranking for Critical System Based on Health of Equipment Thanks to Choquet Integral

Bouaziz

Marangé

Voisin

et al. 2021

Front. Artif. Intell.

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show abstract

“…However, this review does not consider many other applications, e.g. classification and patter recognition [36], [37], bioinformatics [38], fuzzy rule-based systems [39]- [41], preference learning [42], remote sensing [43], or ensemble reduction [44] and ensemble construction [45], [46], as it is the case of this paper. The usage of the Choquet integral as an information fusion tool necessarily requires the construction of a fuzzy measure.…”

Section: Related Work On Ensemble Aggregation By the Choquet Intementioning

confidence: 99%

Unsupervised Fuzzy Measure Learning for Classifier Ensembles From Coalitions Performance

et al. 2020

Self Cite

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In Machine Learning an ensemble refers to the combination of several classifiers with the objective of improving the performance of every one of its counterparts. To design an ensemble two main aspects must be considered: how to create a diverse set of classifiers and how to combine their outputs. This work focuses on the latter task. More specifically, we focus on the usage of aggregation functions based on fuzzy measures, such as the Sugeno and Choquet integrals, since they allow to model the coalitions and interactions among the members of the ensemble. In this scenario the challenge is how to construct a fuzzy measure that models the relations among the members of the ensemble. We focus on unsupervised methods for fuzzy measure construction, review existing alternatives and categorize them depending on their features. Furthermore, we intend to address the weaknesses of previous alternatives by proposing a new construction method that obtains the fuzzy measure directly evaluating the performance of each possible subset of classifiers, which can be efficiently computed. To test the usefulness of the proposed fuzzy measure, we focus on the application of ensembles for imbalanced datasets. We consider a set of 66 imbalanced datasets and develop a complete experimental study comparing the reviewed methods and our proposal.

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“…These aggregation functions or operators are described in detail in many monographs [ 29 , 30 , 31 , 32 , 33 , 34 ] and papers [ 35 , 36 , 37 ]. In particular, typical classes of aggregation operators are means, triangular norms [ 38 , 39 ], ordinary weighted averaging operators [ 35 , 40 ], Choquet integral, and its generalizations [ 41 , 42 , 43 , 44 , 45 , 46 , 47 ] called pre-aggregation functions, etc. Comprehensive experimental studies, in particular, on an applications of aggregation operators and generalizations of Choquet integral to the face recognition problems were presented in [ 44 , 46 , 48 ], respectively.…”

Section: Introductionmentioning

confidence: 99%

On the Improvement of Eye Tracking-Based Cognitive Workload Estimation Using Aggregation Functions

Kaczorowska

Karczmarek

Plechawska–Wójcik

et al. 2021

Sensors

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Cognitive workload, being a quantitative measure of mental effort, draws significant interest of researchers, as it allows to monitor the state of mental fatigue. Estimation of cognitive workload becomes especially important for job positions requiring outstanding engagement and responsibility, e.g., air-traffic dispatchers, pilots, car or train drivers. Cognitive workload estimation finds its applications also in the field of education material preparation. It allows to monitor the difficulty degree for specific tasks enabling to adjust the level of education materials to typical abilities of students. In this study, we present the results of research conducted with the goal of examining the influence of various fuzzy or non-fuzzy aggregation functions upon the quality of cognitive workload estimation. Various classic machine learning models were successfully applied to the problem. The results of extensive in-depth experiments with over 2000 aggregation operators shows the applicability of the approach based on the aggregation functions. Moreover, the approach based on aggregation process allows for further improvement of classification results. A wide range of aggregation functions is considered and the results suggest that the combination of classical machine learning models and aggregation methods allows to achieve high quality of cognitive workload level recognition preserving low computational cost.

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The state-of-art of the generalizations of the Choquet integral: From aggregation and pre-aggregation to ordered directionally monotone functions

Cited by 140 publications

References 103 publications

Control Sequence Ranking for Critical System Based on Health of Equipment Thanks to Choquet Integral

Control Sequence Ranking for Critical System Based on Health of Equipment Thanks to Choquet Integral

Unsupervised Fuzzy Measure Learning for Classifier Ensembles From Coalitions Performance

On the Improvement of Eye Tracking-Based Cognitive Workload Estimation Using Aggregation Functions

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