Definability and textures

This paper aims to give a new perspective for definability in rough set theory. First, a counterpart of definability is introduced in textural approximation spaces. Then a complete field of sets for texture spaces is defined and using textural arguments, some new results are obtained for rough sets. It is shown that definability can be also discussed in terms of a complete field of fuzzy sets on a fuzzy lattice for the various fuzzy approximation spaces. It is also given a partial affirmative answer to an open problem posed by Wei-Zhi Wu in On some mathematical structures of T-fuzzy rough set algebras in infinite universes of discourse in Fundamenta Informaticae 108 (3–4) 2011 337–369.