A Novel Ambiguous Set Theory to Represent Uncertainty and its Application to Brain MR Image Segmentation

This article presented a new set theory to deal with ambiguousness, which was entitled as an "Ambiguous Set Theory". The proposed ambiguous set theory can represent any feature into four degrees of memberships, viz., true, false, ambiguous-true and ambiguous-false. This kind of representation provides granular visualization of features, and helps to model uncertainties very effectively. In this article, initially we discussed the motivation to introduce the theory of ambiguous set. Then, we proposed methodology of ambiguous set by: 1) defining it in a precise way, 2) presenting a mathematical representation for the set, and 3) giving various mathematical definitions for the set. Applications of the proposed ambiguous set were demonstrated in human brain MRI segmentation. Various comparison results demonstrated the effectiveness of the theory over existing well-known approaches of the image segmentation.