This section covers general knowledge of fuzzy similarity measure, intuitionistic fuzzy similarity measure, linguistic similarity measure and linguistic vector similarity measure. Some of the most basic similarity measures are mentioned. In order to make it possible to compare new measurements with old measurements, based on the expression, we classify similarity measures as follows:
1.1. Fuzzy Similarity Measures and Intuitionistic Fuzzy Similarity Measures
The similarity measure is an important mathematical concept that is used to estimate the degree of similarity between objects and to be applicable in pattern recognition problems such as clustering, classification and information retrieval. In the case of inadequately defined and ambiguous objects, instead of the traditional similarity measure, fuzzy similarity or intuitionistic fuzzy similarity measures should be used.
1.1.2. Definition 2
An intuitionistic fuzzy set (IFS) A on a universe X is an object of the form 
, where 
and 
. For each 
, 
, 
are respectively called the degree of membership, degree of non-membership of x in A of x in A, and following condition is satisfied (Atanassov 1986):
,
(1)The set of all IFS on X is denoted by 
.
Consider the case where X contains n elements. For 
, we denote by 
and 
the degrees of membership and non-membership of the i-th element of X into A, respectively (
, …, n). Here are some of the most commonly used fuzzy and intuitionistic fuzzy similarity measures.
1.1.3. Definition 3
Consider A, 
(Baccour et al., 2014):
It is convention that if the denominator is 0, the fraction is equal to 1.
1.1.4. Definition 4
Consider A, 
(Baccour et al., 2016):
It is convention that if the denominator is 0, the fraction is equal to 1.
Some typical application of fuzzy similarities are: image processing (Bloch 1999; Weken et al., 2005; Weken et al., 2004), fuzzy reasoning (Wang et al., 2008), shape retrieval using the SQUID data set described with Fourier descriptor (Gadi et al., 1999), shape classification (Baccour et al., 2007), handwritten Arabic sentences recognition (Baccour & Alimi 2010; Baccour & Alimi 2013) and medical diagnosis (Son & Phong, 2016).