Fernández Fernández, Francisco JavierBustince Sola, HumbertoHoranská, LubomíraMesiar, RadkoStupñanová, Andrea2021-09-162021-09-162020J. Fernandez, H. Bustince, L. Horanská, R. Mesiar and A. Stupňanová, 'A Generalization of the Choquet Integral Defined in Terms of the Möbius Transform,' in IEEE Transactions on Fuzzy Systems, vol. 28, no. 10, pp. 2313-2319, Oct. 2020, doi: 10.1109/TFUZZ.2019.29338031063-670610.1109/TFUZZ.2019.2933803https://academica-e.unavarra.es/handle/2454/40510In this article, we propose a generalization of the Choquet integral, starting fromits definition in terms of the Mobius transform. We modify the product on R considered in the Lovasz extension form of the Choquet integral into a function F, and we discuss the properties of this new functional. For a fixed n, a complete description of all F yielding an n-ary aggregation function with a fixed diagonal section, independent of the considered fuzzy measure, is given, and several particular examples are presented. Finally, all functions F yielding an aggregation function, independent of the number n of inputs and of the considered fuzzy measure, are characterized, and related aggregation functions are shown to be just the Choquet integrals over the distorted inputs.7 p.application/pdfeng© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other work.Aggregation functionChoquet integralFuzzy measureMobius transforminfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess