S-approximation Spaces: A Three-way Decision Approach

In this paper, we investigate properties of the lower and upper approximations of an S-approximation space under different assumptions for its S operator. These assumptions are partial monotonicity, complement compatibility and functional partial monotonicity. We also extend the theory of three way decisions to non-inclusion relations. Also in this work, a new representation for partial monotone S-approximation spaces, called inflections, is introduced. We will also discuss the computational complexity of representing an S-approximation space in terms of inflection sets. Finally, the usefulness of the introduced concepts is illustrated by an example.