Fuzzy Community detection based on grouping and overlapping functions

Gómez, Daniel; Rodríguez, J. Tinguaro; Montero, Javier; Yáñez, Javier

doi:10.2991/ifsa-eusflat-15.2015.215

Cited by 6 publications

(4 citation statements)

References 31 publications

(45 reference statements)

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“…Then, since their introduction, overlap functions have been successfully applied in many fields like: image processing [22], [23], decision making [24], [25], computational brain interfaces [26], forest fire detection [27], wavelet-fuzzy power quality diagnosis system [28], fuzzy community detection [29], social networks [30] and classification [31], [32], [33], [34], [35], [36].…”

Section: Introductionmentioning

confidence: 99%

Type-$(2,k)$ Overlap Indices

Hierro

Roldán

Tiscar³

et al. 2023

IEEE Trans. Fuzzy Syst.

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Automatic image detection is one of the most important areas in computing due to its potential application in numerous real-world scenarios. One important tool to deal with that is called overlap indices. They were introduced as a procedure to provide the maximum lack of knowledge when comparing two fuzzy objects. They have been successfully applied in the following fields: image processing, fuzzy rule-based systems, decision making and computational brain interfaces.This notion of overlap indices is also necessary for applications in which type-2 fuzzy sets are required. In this paper we introduce the notion of type-(2, k) overlap index (k ∈ {0, 1, 2}) in the setting of type-2 fuzzy sets. We describe both the reasons that have led to this notion and the relationships that naturally arise among the algebraic underlying structures. Finally, we illustrate how type-(2, k) overlap indices can be employed in the setting of fuzzy rule-based systems when the involved objects are type-2 fuzzy sets.

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Section: Introductionmentioning

confidence: 99%

Type-$(2,k)$ Overlap Indices

Hierro

Roldán

Tiscar³

et al. 2023

IEEE Trans. Fuzzy Syst.

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“…Additionally, those functions were applied in decomposition strategies [12]. Gómez et al [13] also presented the idea of n-dimensional grouping functions, applying them as an alternative method to quantify the quality of a fuzzy community detection output based on n-dimensional operators.…”

Section: Introductionmentioning

confidence: 99%

Constructing Interval-Valued Fuzzy Material Implication Functions derived from General Interval-Valued Grouping Functions

Dimuro

Santos

Asmus

et al. 2022

2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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Grouping functions and their dual counterpart, overlap functions, have drawn the attention of many authors, mainly because they constitute a richer class of operators compared to other types of aggregation functions. Grouping functions are a useful theoretical tool to be applied in various problems, like decision making based on fuzzy preference relations. In pairwise comparisons, for instance, those functions allow one to convey the measure of the amount of evidence in favor of either of two given alternatives. Recently, some generalizations of grouping functions were proposed, such as (i) the n-dimensional grouping functions and the more flexible general grouping functions, which allowed their application in n-dimensional problems, and (ii) n-dimensional and general interval-valued grouping functions, in order to handle uncertainty on the definition of the membership functions in real-life problems. Taking into account the importance of interval-valued fuzzy implication functions in several application problems under uncertainty, such as fuzzy inference mechanisms, this paper aims at introducing a new class of interval-valued fuzzy material implication functions. We study their properties, characterizations, construction methods and provide examples.

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“…Those functions were also applied in decomposition strategies [18]. Gómez et al [20] also introduced the concept of ndimensional grouping functions, with an application to quantify the quality of a fuzzy community detection output based on n-dimensional operators.…”

Section: Introductionmentioning

confidence: 99%

On Construction Methods of (Interval-Valued) General Grouping Functions

Dimuro,

Asmus,

Pinheiro

et al. 2022

Information Processing and Management of Uncertainty in Knowledge-Based Systems

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Fuzzy Community detection based on grouping and overlapping functions

Cited by 6 publications

References 31 publications

Type-$(2,k)$ Overlap Indices

Type-$(2,k)$ Overlap Indices

Constructing Interval-Valued Fuzzy Material Implication Functions derived from General Interval-Valued Grouping Functions

On Construction Methods of (Interval-Valued) General Grouping Functions

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