A theoretical development on the entropy of interval-valued intuitionistic fuzzy soft sets based on the distance measure

In this work, the axiomatical definition of similarity measure, distance measure and inclusion measure for interval-valued intuitionistic fuzzy soft set (IVIFSSs) are given. An axiomatical definition of entropy measure for IVIFSSs based on distance is firstly proposed, which is consistent with the axiomatical definition of fuzzy entropy of fuzzy sets introduced by De Luca and Termini. By different compositions of aggregation operators and a fuzzy negation operator, we obtain eight general formulae to calculate the distance measures of IVIFSSs based on fuzzy equivalences. Then we discuss the relationships among entropy measures, distance measures, similarity measures and inclusion measures of IVIFSSs. We prove that the presented entropy measures can be transformed into the similarity measures and the inclusion measures of IVIFSSs based on fuzzy equivalences.