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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.<\/jats:p>","DOI":"10.1007\/s10462-024-10753-y","type":"journal-article","created":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T15:04:16Z","timestamp":1716303856000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["n-Ary aggregation operators on function spaces: perspective of construction"],"prefix":"10.1007","volume":"57","author":[{"given":"Junsheng","family":"Qiao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,21]]},"reference":[{"key":"10753_CR1","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.fss.2017.12.014","volume":"346","author":"JJ Arias-Garc\u00eda","year":"2018","unstructured":"Arias-Garc\u00eda JJ, Mesiar R, Klement EP, Saminger-Platz S, De Baets B (2018) Extremal Lipschitz continuous aggregation functions with a given diagonal section. 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