University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 20 5 2023 10 01 Divisible associative aggregation operations on finite chains 1 8 7756 10.22111/ijfs.2023.44566.7845 EN Yan Su Suzhou University of Science and Technology Yong Su School of mathematics sciences，Suzhou University of Science and Technology，Suzhou, Jiangsu 215009，China Radko Mesiar Faculty of Civil Engineering, Department of Mathematics, Slovak University of Technology (STU), Bratislava, Slovakia Journal Article 2023 01 19 There exist several versions of discrete counterpart of continuity in the framework of finite chains, e.g., the smoothness, the divisibility, intermediate-value property and the 1-Lipschitz property. In this paper, we first discuss the relationships among the smoothness, divisibility, intermediate-value property and 1-Lipschitz property. Second, we present complete characterizations of divisible associative aggregation operations on finite chains. https://ijfs.usb.ac.ir/article_7756_3fd07989aa5b991cbabb5a2a33d7c881.pdf