Rectangles-based discrete universal fuzzy integrals

0559712 - ÚTIA 2023 RIV US eng J - Journal Article
Mesiar, Radko - Kolesárová, A.
Rectangles-based discrete universal fuzzy integrals.
International Journal of Approximate Reasoning. Roč. 148, č. 1 (2022), s. 162-173. ISSN 0888-613X. E-ISSN 1873-4731
Institutional support: RVO:67985556
Keywords : Aggregation function * Choquet integral * Discrete fuzzy integral * Hypergraph of survival function * Rectangle mapping
OECD category: Pure mathematics
Impact factor: 3.9, year: 2022
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2022/E/mesiar-0559712.pdf https://www.sciencedirect.com/science/article/pii/S0888613X22000925?via%3Dihub

Using hypergraphs of survival functions, we propose a rather general method for the construction of discrete fuzzy integrals. Our method is based on various rectangle decompositions of hypergraphs and on rectangle mappings suitably evaluating the rectangles of the considered decompositions. By means of appropriate binary aggregation functions we define two types of rectangle mappings and four types of discrete fuzzy integral constructions, and we also investigate the properties of the introduced integrals and the relationships between them. All the introduced methods based on non-overlapping rectangles coincide in the case of the product aggregation function, and then the related integral is the Choquet integral. Several examples are given.
Permanent Link: https://hdl.handle.net/11104/0333423