On the coincidence of measure-based decomposition and superdecomposition integrals

0576150 - ÚTIA 2024 RIV NL eng J - Journal Article
Li, J. - Mesiar, Radko - Ouyang, Y.
On the coincidence of measure-based decomposition and superdecomposition integrals.
Fuzzy Sets and Systems. Roč. 457, č. 1 (2023), s. 125-141. ISSN 0165-0114. E-ISSN 1872-6801
Institutional support: RVO:67985556
Keywords : monotone measure * decomposition integral * Choquet integral * concave integral * Pan integral
OECD category: Pure mathematics
Impact factor: 3.9, year: 2022
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2023/E/mesiar-0576150.pdf https://www.sciencedirect.com/science/article/pii/S0165011422003736?via%3Dihub

This paper introduces two types of preorders on the system of all non-empty sets of collections (i.e., the set of all decomposition systems) based on a fixed monotone measure mu. Each of them refines the previous two kinds of preorders of decomposition systems. By means of these two new preorders of decomposition systems we investigate the coincidences of decomposition integrals and that of superdecomposition integrals, respectively. The generalized integral equivalence theorem is shown in the general framework involving an ordered pair of decomposition systems. This generalized theorem includes as special cases all the previous results related to the coincidences among the Choquet integral, the concave (or convex) integral and the pan-integrals. Thus, a unified approach to the coincidences of several well-known decomposition and superdecomposition integrals is presented.
Permanent Link: https://hdl.handle.net/11104/0346456