Abstract:

On the basis of the thought of interval sets and filter theory, noncommutative residual lattices and fuzzy filters on the interval sets were discussed, providing the algebraic structure of the 〈∈,∈∪Q〉fuzzy filters of noncommutative residual lattices on interval sets, and giving the representation theorem of several equivalent characterization.

Key words: non-commutative fuzzy logic, interval sets, noncommutative residual lattices on the interval sets, 〈∈,∈∪Q〉fuzzy filters, characterization