A note on information entropy measures for vague sets and its applications

A new nonprobabilistic entropy of a vague set is proposed by means of the intersection and union of the membership degree and nonmembership degree of the vague set. The concept called vague cross-entropy of vague sets will also be discussed and its definition is given by analogy with the cross-entropy of probability distributions. Finally, two numeric examples are presented to illustrate the applications of vague cross-entropy to pattern recognition and medical diagnosis.