Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets

Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In order to handle these types of problem parameters, some fuzzy (or intuitionistic fuzzy, interval-valued fuzzy) extensions of soft set theory are presented, yielding fuzzy (or intuitionistic fuzzy, interval-valued fuzzy) soft set theory. In this paper, we define the distance measures between intuitionistic fuzzy soft sets and give an axiom definition of intuitionistic entropy for an intuitionistic fuzzy soft set and a theorem which characterizes it. Furthermore, we discuss the relationship between intuitionistic fuzzy soft sets and interval-valued fuzzy soft sets and transform the structure of entropy for intuitionistic fuzzy soft sets to the interval-valued fuzzy soft sets. (C) 2013 Elsevier Inc. All rights reserved.