Chi & Liu  extended TOPSIS to IVNS environment in which the attribute weights are unknown and the attribute values are presented in terms of IVNS.
The IVNS that consists of Intervals [mathematical expression not reproducible] for convenience.
For similarity and practical application, Wang proposed the SVNS and IVNS
which are the subclasses of NS and preserve all the operations on NS.
An interval valued neutrosophic set (for short IVNS
A) A in X is characterized by truth-membership function [T.
For two IVNS
, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
However, there is a little investigation on the similarity measure of IVNS
, although some method on measure of similarity between intervals valued neutrosophic sets have been presented in  recently.
When the universal set X is discrete, an IVNS
A can be written as
is characterized by an interval membership degree, interval indeterminacy degree and interval non-membership degree.
iii) Their intersection, denoted by (f, A) [intersection] (g, B) = (h, C) (say), is an interval valued neutrosophic soft set of overU, where C = A [intersection] B and for e [member of] C, h: C [right arrow] IVNS
(U) is defined by
As an important extension of NS, SVNS and IVNS
has many applications in real life [13, 14, 15, 16, 17, 25, 32, 33, 34, 35, 36, 37, 38, 39]
In this paper the Hamming and Euclidean distances between two interval valued neutrosophic soft sets(IVNS
sets) are defined and similarity measures between two IVNS
sets based on distances are proposed.
In the present paper we extend the concept of Lower and upper soft interval valued intuitionstic fuzzy rough approximations of an IVIFSS-relation to the case IVNSS and investigated some of their properties.