Textures and fuzzy unit operations in rough set theory: An approach to fuzzy rough set models

In this paper, an approach for the fuzzy rough set models is presented using textures and a fuzzy version of the unit operations of Wybraniec-Skardowska. First, a fuzzy unit operation and fuzzy unit co-operation on fuzzy lattices are defined. It is proved that the well-known fuzzy rough set upper approximations as the approximation of Dubois and Prade are fuzzy unit operation. Using fuzzy direlations, an axiomatic system for fuzzy unit operations is studied and it is shown that fuzzy rough set systems obtained by different fuzzy logical connectives as Kleene-Dienes and Gödel implicators can be generated by the same textural fuzzy direlation. Finally, it is observed that the approximations of two different fuzzy rough set models together constitute two different Galois connections.