New results on the modularity condition for overlap and grouping functions

Zhu, Kuanyun; Wang, Jingru; Yang, Yongwei

doi:10.1016/j.fss.2019.10.014

Cited by 17 publications

(4 citation statements)

References 38 publications

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“…This enables us to obtain more sufficient output from the one-to-one and one-to-more pattern subsequent clustering of the basic classifier. On the other hand, overlap and grouping functions are also developing rapidly in theory and many profound results have been obtained, such as the construction of the corresponding fuzzy implications [10,13,16,17,40], the properties of migrativity, homogeneity, idempotency and limiting [4,7,14,50,51], the modularity equation between overlap (grouping) functions and other aggregation functions [42,48,49], the additive and multiplicative generator pairs [15,32], the n-dimensional extension concepts of overlap functions [22] and general overlap functions [12], the notions of interval overlap [36] and grouping functions, and the notion of interval-valued ordered weight averaging (OWA) operators with interval weights derived from interval-valued overlap functions [5].…”

Section: Brief Overview On Overlap and Grouping Functionsmentioning

confidence: 99%

Distributivity of ordinal sum implications over overlap and grouping functions

Pan¹,

Zhou²

2021

Kybernetika

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In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given.

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Section: Brief Overview On Overlap and Grouping Functionsmentioning

confidence: 99%

Distributivity of ordinal sum implications over overlap and grouping functions

Pan¹,

Zhou²

2021

Kybernetika

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“…The nice properties that the class of overlap functions presents, such as the closeness with respect to the convex sum and the aggregation by internal generalized composition [6], [7], allow its higher applicability, in comparison with other classes of conjunctive aggregation functions (e.g., t-norms [8]). Besides that, overlap functions were shown to satisfy several interesting properties, some of them necessary for different applications, as properly studied by, for example, Bustince et al [9], Bedregal et al [10], Dimuro et al [11], [12], [13], Qiao et al [14], [15], [16], [17], [18], Wang and Hu [19], Zhou and Yan [20] and Zhu et al [21].…”

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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“…Since the appearance of the concept of overlap functions, many authors have dedicated time to the theoretical research on their properties and related concepts, such as Qiao [10], Qiao and Hu [11], Dimuro et al [5], [8], [12], [13], Zhou and Yan [14], Zhu et al [15], Zhang et al [16] and Cao et al [17]. Moreover, the application of overlap function is getting attention mainly because the associativity is not required during the information aggregation process, like in image processing [18], decision making [19], [20], wavelet-fuzzy power quality diagnosis system [21], forest fire detection [22] and classification by generalizations of the Choquet integral [23], [24], [25], [26], [27].…”

Section: Introductionmentioning

confidence: 99%