Quo vadis aggregation?

Mesiar, Radko; Kolesárová, Anna; Stupňanová, Andrea

doi:10.1080/03081079.2017.1402893

Cited by 38 publications

(9 citation statements)

References 50 publications

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“…One of nowadays significant directions in aggregation theory emphasized in the recent overview article (Mesiar, Kolesárová, and Stupňanová 2018), namely the aggregation on (bounded) lattices. For general systems, where we cannot always expect real (or comparable) data, this extension of the underlying career together with its structure is significant.…”

Section: A Brief Review On Uninormsmentioning

confidence: 99%

New construction approaches of uninorms on bounded lattices

Çaylı

2021

International Journal of General Systems

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This article continuous to investigate the construction approaches for uninorms on bounded lattices. We introduce some new methods to obtain uninorms with an identity e ∈ L\{0, 1} by using closure (interior) operators on a bounded lattice L. As a by-product of these methods, we present two families of idempotent uninorms on bounded lattices. Furthermore, we provide some corresponding examples to illustrate that our methods can differ for different closure (interior) operators.

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Section: A Brief Review On Uninormsmentioning

confidence: 99%

New construction approaches of uninorms on bounded lattices

Çaylı

2021

International Journal of General Systems

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“…Although this motivation of aggregation function cannot be used in one dimension, analysing the case n = 1 sometimes proves to be helpful before going into higher dimensions. For completeness we note that there are different approaches to the very definition of an aggregation function; for example, in the survey [8] the domain is restricted to [0, 1] n . We say that an aggregation function as defined above is super-additive if A(x + y) ≥ A(x) + A(y), and sub-additive…”

Section: Preliminariesmentioning

confidence: 99%

Remarks on Super-Additive and Sub-Additive Transformations of Aggregation Functions

Hriňáková¹,

Šeliga

2018

Tatra Mountains Mathematical Publications

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In this contribution we modify the definitions of the super-additive and sub-additive transformations of aggregation functions. Firstly, we define k-bounded transformations that represent only finite decompositions with at most k elements. Secondly, we introduce two other transformations that preserve the super-additivity property in some sense. Also, a remark on continuity of the classical super-additive transformation of an aggregation function is presented for one-dimensional case.

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“…The relaxation of the monotonicity condition for aggregation functions is listed as a recent trend in Aggregation Theory [13]. One of the main advances of the introduction of directional monotonicity is the formation of the so called pre-aggregation functions [12], which have been successfully applied in fuzzy rulebased classification problems [11].…”

Section: Introductionmentioning

confidence: 99%

Strengthened ordered directionally monotone functions. Links between the different notions of monotonicity

Sesma‐Sara

Lafuente

Roldán

et al. 2019

Fuzzy Sets and Systems

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In this work, we propose a new notion of monotonicity: strengthened ordered directional monotonicity. This generalization of monotonicity is based on directional monotonicity and ordered directional monotonicity, two recent weaker forms of monotonicity. We discuss the relation between those different notions of monotonicity from a theoretical point of view. Additionally, along with the introduction of two families of functions and a study of their connection to the considered monotonicity notions, we define an operation between functions that generalizes the Choquet integral and the Lukasiewicz implication.

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Quo vadis aggregation?

Cited by 38 publications

References 50 publications

New construction approaches of uninorms on bounded lattices

New construction approaches of uninorms on bounded lattices

Remarks on Super-Additive and Sub-Additive Transformations of Aggregation Functions

Strengthened ordered directionally monotone functions. Links between the different notions of monotonicity

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