Entropy, similarity measure and distance measure of vague soft sets and their relations

Soft set theory offers a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. A vague soft set is a combination of a vague set and a soft set. In this paper, we introduce axiomatic definitions of entropy, similarity measure and distance measure for vague soft sets, and some formulas have also been put forward to calculate them. Furthermore, 13 theorems are proposed showing how the entropy, the similarity measure and the distance measure for vague soft sets can be deduced from each other. Some formulas have also been put forward to calculate the entropy, the similarity measure and the distance measure of vague soft sets by these relations. (C) 2013 Elsevier Inc. All rights reserved.