Maximal directions of monotonicity of an aggregation function

Baets, Bernard De; Meyer, H. De

doi:10.1016/j.fss.2021.02.009

Cited by 9 publications

(3 citation statements)

References 27 publications

(49 reference statements)

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“…It is know that K δ is a copula whenever δ is a diagonal functions [22]. For other constructions of copulas given diagonal functions, see for example, [17,8,9,34,26,43].…”

Section: E On Range ⃗mentioning

confidence: 99%

Aggregation Function Constructed from Copula

BOONYASRI¹,

Tasena²

2022

CJM

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"In this work, we show that a slight change in the Sklar's formula tremendously affects the class of aggregation functions it represents. While the original formula can only be used to construct $d$-increasing aggregation functions, this new formula can be used to construct any continuous aggregation function excepted possibly those belong to the boundary of this set. In particular, all continuous aggregation functions can be approximated by aggregation functions in this form. This shows that it is sufficient to only consider aggregation functions in this form for most cases. Construction examples via this method are also given."

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“…It is know that K δ is a copula whenever δ is a diagonal functions [22]. For other constructions of copulas given diagonal functions, see for example, [17,8,9,34,26,43].…”

Section: E On Range ⃗mentioning

confidence: 99%

Aggregation Function Constructed from Copula

BOONYASRI¹,

Tasena²

2022

CJM

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“…, López et al (2021 presented a new way to construct AOs by means of affine operators. In 2022, De Baets and De Meyer (2022) studied maximal directions for monotonicity of AOs.…”

Section: Introductionmentioning

confidence: 99%

n-Ary aggregation operators on function spaces: perspective of construction

Qiao

2024

Artif Intell Rev

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For disposing numerous practical application problems involving expert systems, decision-making, image processing, classifications and etc, the investigations on the constructions and basic properties of n-ary aggregation operators (nAAOs) have always been a hot research topic with important research value and significance at theoretical investigations on aggregation operators (AOs). Herein, first, we propose a method for constructing nAAOs on function spaces via a family of known ones defined on a bounded poset, where those function spaces are composed by all fuzzy sets with that bounded poset as the truth values set. This method is different from the existing construction methods of nAAOs on bounded posets and provides a unified way of constructing usual nAAOs (like t-norms, uninorms, overlap functions, etc.) on function spaces via a family of known ones. Second, we present notion of representable nAAOs on function spaces and afford their equivalent characterization. Third, we discuss some vital properties of representable nAAOs on function spaces. Fourth, it is worth noticing that the obtained results cover the cases of nAAOs on function spaces composed of all interval-valued fuzzy sets and type-2 fuzzy sets when underlying bounded poset is taken as the corresponding truth values set, respectively. As a consequence, the theoretical results obtained herein have certain promotion and basic theoretical value for the mining of new potential applications of nAAOs in real problems, especially in expert systems, decision-making, image processing and etc.

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“…Fortunately, fuzzy measure, defined by Sugeno in 1974, can be utilized to depict the correlations of attribute indexes [7][8][9][10]. Meanwhile, aggregation functions and aggregation operators are investigated by many researchers recently [11][12][13][14]. Because of the fuzziness and uncertainty of actual decision issues, the evaluation values involved in the decision process are not always expressed as crisp numbers.…”

Section: Introductionmentioning

confidence: 99%