Abstract:

Based on the extended residuated lattice of extended Rough set, the concept of topological extended residuated lattice is introduced and its filter is studied. Also, the N-filter of the extended residuated lattice and the v-filter of well topological residuated lattice are also studied, and the quotient algebraic structures are constructed corresponding these filters.

Key words: extended residuated lattice; Rough set; topological extended residuated lattice; filter