0600441 20260407132214.220241107235959.9 85208193348 001354223900001 10.1016/j.fss.2024.109178 9 s. P cav_un_epca*02566420165-0114499Elsevier Monotone measures (M)-property Weak (M)-property Pan-integral Choquet integral cav_un_auth*0475908 Kang T. CN 25 cav_un_auth*0101163 Mesiar Radko UTIA-B Ekonometrie Department of Econometrics E E Department of Econometrics 25 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0258953 Ouyang Y. CN 25 K cav_un_auth*0348640 Li J. CN https://library.utia.cas.cz/separaty/2024/E/mesiar-0600441.pdf https://www.sciencedirect.com/science/article/pii/S0165011424003245?via%3Dihub In this note, we provide an example to show the weak (M)-property is really weaker than the (M)-property for some finite monotone measure defined on infinite space, and hence answer an open problem which was proposed in the paper (Li et al. (2023) [9]). We prove that if a monotone measure μ is autocontinuous, then the weak (M)-property and the (M)-property of μ are equivalent. We propose the concept of (C-P)-property of monotone measures and show a set of sufficient and necessary conditions that the Choquet integral coincides with the pan-integral. We further study the relationships between the Choquet integral and the pan-integral in the setting of the ordered pairs of monotone measures, and obtain some interesting properties. WOS BA 10000 10100 10101 2026 4 RVO:67985556 https://hdl.handle.net/11104/0357783 S 109178 C MATHEMATICS.APPLIED|STATISTICS&PROBABILITY|COMPUTERSCIENCE.THEORY&METHODS 2.6 0.9 19.7 0.0062 0.613 14846 191 0.754 37.34 2.7 2335 Q1 2.200 229 Q1 82 1.43 Q1 91.4 2025 85208193348 SCOPUS PUBMED 001354223900001 WOS cav_un_epca*0256642 Fuzzy Sets and Systems 499 1 2025 0165-0114 1872-6801 Elsevier