Techniques for Approximate Reasoning Based on Intuitionistic Fuzzy S-Rough Logic

Intuitionistic fuzzy S-rough sets (IFS-RS) is a new concept that is a combination of intuitionistic fuzzy sets (IFS) theories and S-rough sets (S-RS) theories. Based on the concept of IFS-RS, to the questions of propositional calculus on intuitionistic fuzzy S-rough logic (IFS-RL), a synthetic method for finding the truth of IFS-RL propositions using membership and hesitancy degree is proposed. The fundamental operation rules on IFS-RL propositions are exposed in this paper. The emphasized investigation is the techniques for approximate reasoning on IFS-RL, including the implications, the conditions, the multiplications, and the multi-dimensions on IFS-RL, etc. The related sets of mathematical formulas of inference compositional operations are derived. Finally, the correctness and validity of the developed methods are verified and the detailed steps of verification are shown with a particular instance.