Intuitionistic Fuzzy Clustering Algorithms - Intuitionistic Fuzzy Aggregation and Clustering - page 229

Drawing support from the interval-valued intuitionistic fuzzy distance matrix, we
can extend Algorithm 2.10 to the interval-valued intuitionistic fuzzy environment
and raise the interval-valued intuitionistic fuzzy MST clustering algorithm:

Algorithm 2.11

Step 1 Construct the interval-valued intuitionistic fuzzy distance matrix and the
fuzzy graph:
In this step, we first calculate the distance d ij

y j by Eq. ( 2.105 )or
( 2.107 ) to get the interval-valued intuitionistic fuzzy distance matrix D

d y i ,

=

= d ij n × n ,

and then draw the fuzzy graph V D with n nodes associated to the samples y i

,

( which are expressed by IVIFSs and every edge between y i and

y j having the weight d ij , which is a real number coming from the interval-valued
intuitionistic fuzzy distance matrix D

i = 1 , 2 ,..., n )

= ( d ij ) n × n .

Step 2 Compute the minimum spanning tree (MST) of the fuzzy graph V D by

,

Kruskal method (Kruskal 1956) or Prim method (Prim 1957).
Step 3 Cluster through the minimum spanning tree (see to Step 3 of Algorithm
2.10).
Example 2.9 can also be used to illustrate Algorithm 2.11 when the evaluation
information is expressed in IVIFSs (here omitted for brevity).

2.7 Intuitionistic Fuzzy Clustering Algorithm Based on Boole
Matrix and Association Measure

2.7.1 Intuitionistic Fuzzy Association Measures

Since clustering is the grouping of similar objects, we usually need to find some sort
of measure that can determine the degree of the relationship between two objects.
Generally, there are three main types of measures which can estimate this relation:
distance measures, similarity measures and association measures. The choice of a
good measure will directly influence the clustering effect. Next we shall seek for
some association measures to be prepared for cluster analysis.
An association measure is an important tool for determining the degree of the rela-
tionship between two objects.Many scholars have given various associationmeasures
(see Xu and Chen 2008 for a review). For example, Xu et al. (2008) introduced the
associate measures ( 2.89 ) and ( 2.100 ). Gerstenkorn and Mafiko (1991) proposed a
method to calculate the association coefficient of IFSs, which was formulated in the
following way:

j = 1 μ A (

x j ) · μ B ( x j ) + v A ( x j ) · v B ( x j )

c 1 ( A , B ) = j = 1 μ (2.157)

x j ) · j = 1 μ x j )

2

v A (

2

v B (

A (

x j ) +

B (

x j ) +