Fuzzy relation matrix and fuzzy Max-Min operation for biomedical signal classification

Abstract

Fuzzy Set Theory (FST) has been applied to many fields such as control, signal and image processing, medicine, the economy, etc. The results show that FST yields efficient solutions to various problems. In crisp set theory, a member of a set is represented by 0 or 1. So, in a crisp set, a member either belongs or doesn't belong to a class. However, in FST, a member of a set is represented by a degree between 0 and 1. The degree is called Membership Degree which shows belonging degree of the member to the class. The Membership Degree is computed using the Membership Function obtained by the experts on the subject or a priori knowledge. Fuzzy Relation Matrix is obtained using the Membership Function and the Membership Degree. The Max-Min operation in a fuzzy set, which refers to OR and AND operations in a crisp set, is applied using the Fuzzy Relation Matrix.