New extensions of quasi-overlap functions and their generalized forms on bounded posets via ⋄-operators

Qiao, Junsheng

doi:10.1016/j.fss.2021.05.004

Cited by 5 publications

(2 citation statements)

References 52 publications

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Section: Preliminariesmentioning

confidence: 99%

“…A bounded poset (P, ≤ P ) is a poset with a greatest element and a smallest element (Gierz et al 2003;Qiao 2022a). From now on, symbols P, S always represent bounded posets (P, ≤ P , 0 P , 1 P ) and (S, ≤ S , 0 S , 1 S ) , respectively (Qiao 2022a(Qiao , 2023. For a nonempty set X, the mapping from X to P is called a P-fuzzy subset of X. P X denotes family of all P-fuzzy subsets of X (Qiao 2023).…”

Section: Preliminariesmentioning

confidence: 99%

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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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