Opposite fuzzy sets with applications in image processing

Diverse forms of the concept of opposition are already existent in philosophy, linguistics, psychology and physics. The interplay between entities and opposite entities is apparently fundamental for balance maintenance in almost a universal manner. However, it seems that we have failed to incorporate oppositional thinking in engineering, mathematics and computer science. Especially, the set theory in general, and fuzzy set theory in particular, do not offer a formal framework to incorporate opposition in inference engines. Considering sets along with their opposites can establish a new computing scheme with a wide range of applications. In this work, preliminary definitions for opposite fuzzy sets will be established. The underlaying idea of opposition-based computing is the simultaneous consideration of guess and opposite guess, and estimate and opposite estimate, in order to accelerate learning, search and optimization. To demonstrate the applicability and usefulness of opposite fuzzy sets, a new image segmentation algorithm will be proposed as well.