<i>N</i>-Dimensional Admissibly Ordered Interval-Valued Overlap Functions and Its Influence in Interval-Valued Fuzzy-Rule-Based Classification Systems

Asmus, Tiago da Cruz; Sanz, José Antonio; Dimuro, Graçaliz Pereira; Bedregal, Benjamín R. C.; Fernández, Javier; Bustince, Humberto

doi:10.1109/tfuzz.2021.3052342

Cited by 32 publications

(13 citation statements)

References 64 publications

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“…Many researchers started to develop the theory of overlap functions to explore their potentialities at different scenarios such as problems involving classification or decision-making (Lucca et al 2017;Asmus et al 2021;Nolasco et al 2019). The development of this theory can be found for example in Bedregal et al (2013Bedregal et al ( , 2017, Paiva et al (2018Paiva et al ( , 2021a, Bunstince et al (2021).…”

Section: Overlap Functions According To Alexandroff's Topologymentioning

confidence: 99%

L-valued quasi-overlap functions, L-valued overlap index, and Alexandroff’s topology

Paiva

Bedregal

2021

Comp. Appl. Math.

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In one recent work, Paiva et al. generalized the notion of overlap functions to the context of lattices and introduced a weaker definition, called a quasi-overlap, that arises from the removal of the continuity condition. In this article, quasi-overlap functions on lattices are equipped with a topological space structure, namely, Alexandroff's spaces. Some examples are presented and theorems related to the migrativity and neutral element properties are provided. It is shown that, in these spaces, the concepts of overlap and quasi-overlap functions coincide. Also, the notion of overlap index is extended to the context of L-fuzzy sets. L-valued overlap indices are obtained by adding degrees of quasi-overlap functions on bounded lattice L, as well as quasi-overlap functions are obtained via L-valued overlap indices and some examples are presented. Finally, the concepts of migrativity and convex sum are extended to the context of L-valued overlap index.

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Section: Overlap Functions According To Alexandroff's Topologymentioning

confidence: 99%

L-valued quasi-overlap functions, L-valued overlap index, and Alexandroff’s topology

Paiva

Bedregal

2021

Comp. Appl. Math.

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“…Overlap functions measure the degree of certainty to which an object belongs simultaneously to two classes while grouping functions quantify the degree to which the same object belongs to any of the considered classes. These functions have found applications in tasks involving a maximal lack of information and fuzzy preference modeling and have been extensively studied in multi-attribute decision-making [7], rule-based classification [8], and image processing [9].…”

Section: Introductionmentioning

confidence: 99%

Some Construction Methods for Pseudo-Overlaps and Pseudo-Groupings and Their Application in Group Decision Making

García-Zamora

Paiva

Cruz

et al. 2023

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In many real-world scenarios, the importance of different factors may vary, making commutativity an unreasonable assumption for aggregation functions, such as overlaps or groupings. To address this issue, researchers have introduced pseudo-overlaps and pseudo-groupings as their corresponding non-commutative generalizations. In this paper, we explore various construction methods for obtaining pseudo-overlaps and pseudo-groupings using overlaps, groupings, fuzzy negations, convex sums, and Riemannian integration. We then show the applicability of these construction methods in a multi-criteria group decision-making problem, where the importance of both the considered criteria and the experts vary. Our results highlight the usefulness of pseudo-overlaps and pseudo-groupings as a non-commutative alternative to overlaps and groupings.

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“…One solution to model that uncertainty is to represent each data as an interval, where its width represents the uncertainty associated to each observation [29], [30]. The use of intervals has shown to be a suitable solution to tackle classification problems [31], [32], [33]. For this reason, large efforts have been devoted to the development of mechanisms to fuse information in the interval-valued setting [34], [35], [36], [37].…”

Section: Introductionmentioning

confidence: 99%

Interval-Valued Aggregation Functions Based on Moderate Deviations Applied to Motor-Imagery-Based Brain–Computer Interface

Fumanal-Idocin

Takáč

Fernández

et al. 2022

IEEE Trans. Fuzzy Syst.

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In this work we develop moderate deviation functions to measure similarity and dissimilarity among a set of given interval-valued data to construct interval-valued aggregation functions, and we apply these functions in two Motor-Imagery Brain Computer Interface (MI-BCI) systems to classify electroencephalography signals. To do so, we introduce the notion of interval-valued moderate deviation function and, in particular, we study those interval-valued moderate deviation functions which preserve the width of the input intervals. In order to apply them in a MI-BCI system, we first use fuzzy implication operators to measure the uncertainty linked to the output of each classifier in the ensemble of the system, and then we perform the decision making phase using the new interval-valued aggregation functions. We have tested the goodness of our proposal in two MI-BCI frameworks, obtaining better results than those obtained using other numerical aggregation and interval-valued OWA operators, and obtaining competitive results versus some non aggregation-based frameworks.

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N-Dimensional Admissibly Ordered Interval-Valued Overlap Functions and Its Influence in Interval-Valued Fuzzy-Rule-Based Classification Systems

Cited by 32 publications

References 64 publications

L-valued quasi-overlap functions, L-valued overlap index, and Alexandroff’s topology

L-valued quasi-overlap functions, L-valued overlap index, and Alexandroff’s topology

Some Construction Methods for Pseudo-Overlaps and Pseudo-Groupings and Their Application in Group Decision Making

Interval-Valued Aggregation Functions Based on Moderate Deviations Applied to Motor-Imagery-Based Brain–Computer Interface

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