Rough sets and textural neighbourhoods

Abstract

In this work, we discuss the neighbourhoods and approximation operators using p-sets and q-sets of a texture. Here, we show that the presections of a direlation correspond to lower and upper approximations in terms of successor neighbourhood operators while the sections of a direlation correspond to lower and upper approximations in terms of predecessor neighbourhood operators. For discrete textures, we observe that the weak forms of definabilities are preserved under the relation preserving bijective functions where the inverses are also relation preserving.