An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of S we have f#92;preceq 1#92;circf#92;circ 1#92;circf (resp. f#92;preceqf#92;circ 1#92;circf#92;circ 1) and it is semisimple if and only if, for any fuzzy subset f of S we have f#92;preceq 1#92;circf#92;circ 1#92;circf#92;circ 1.
Source: wiktionary