Super- and sub-additive envelopes of aggregation functions: interplay between local and global properties, and approximation

Širáň, Jozef (2018). Super- and sub-additive envelopes of aggregation functions: interplay between local and global properties, and approximation. Iranian Journal of Fuzzy Systems, 15(7) pp. 13–21.

URL: http://ijfs.usb.ac.ir/article_4279.html

Abstract

Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and Sipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, Fuzzy Sets and Systems 291 (2016), 40{53]. In this article we give a survey of the recent development regarding the existence of aggregation functions with a preassigned super- and sub-additive transformation, and address approximation of these transformations. The underpinning feature of the presented results is dependence of global properties of super- and sub-additive transformations on local properties of aggregation functions. [brace not closed]

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