Floyd Mayweather apparently concedes T.I. had a solid reason for attacking him in Vegas in May ... because the boxer now proudly claims he had sex with Tiny.
Mayweather was promoting his upcoming fight Friday against Marcos Maidana, when someone yelled, "What about T.I.?" -- referring to the now famous Fat Burger fight.
Listen closely, as Floyd says, "What about the bitch? I was f***ing his bitch."
As we previously reported ... the photos Tiny posted of Floyd and his daughter on Instagram set T.I. off right before the melee ... so he clearly suspected something was up.
Floyd tried to talking to Tiny on the red carpet at the BET Awards ... but she flatly denied him.
1:00 PM -- Floyd tells us the audio wasn't clear ... and claims that's not exactly what he said.