Intuitionistic Fuzzy Clustering Algorithms - Intuitionistic Fuzzy Aggregation and Clustering - page 185

Step 2 Calculate

C 2

= C ◦ C

⎛ ⎞

1 . 000 0 . 696 0 . 709 0 . 709 0 . 709 0 . 919 0 . 709 0 . 709 0 . 709 0 . 709

⎝ ⎠

0 . 696 1 . 000 0 . 913 0 . 768 0 . 740 0 . 667 0 . 913 0 . 889 0 . 771 0 . 811

0 . 709 0 . 913 1 . 000 0 . 771 0 . 764 0 . 665 0 . 937 0 . 889 0 . 771 0 . 811

0 . 709 0 . 768 0 . 771 1 . 000 0 . 764 0 . 709 0 . 768 0 . 768 0 . 968 0 . 755

0 . 709 0 . 740 0 . 764 0 . 764 1 . 000 0 . 665 0 . 740 0 . 811 0 . 764 0 . 861

=

0 . 919 0 . 667 0 . 665 0 . 709 0 . 665 1 . 000 0 . 696 0 . 665 0 . 666 0 . 640

0 . 709 0 . 913 0 . 937 0 . 768 0 . 740 0 . 696 1 . 000 0 . 889 0 . 771 0 . 811

0 . 709 0 . 889 0 . 889 0 . 768 0 . 811 0 . 665 0 . 889 1 . 000 0 . 771 0 . 811

0 . 709 0 . 771 0 . 771 0 . 968 0 . 764 0 . 666 0 . 771 0 . 771 1 . 000 0 . 740

0 . 709 0 . 811 0 . 811 0 . 755 0 . 861 0 . 640 0 . 811 0 . 811 0 . 740 1 . 000

then C 2

C does not hold, i.e., the association matrix C is not an equivalent
association matrix. Thus, by Eq. ( 2.86 ), we further calculate

⊆

C 4 C 2 C 2

= ◦

⎛
⎝

⎞
⎠

1 . 000 0 . 709 0 . 709 0 . 709 0 . 709 0 . 919 0 . 709 0 . 709 0 . 709 0 . 709

0 . 709 1 . 000 0 . 913 0 . 771 0 . 811 0 . 709 0 . 913 0 . 889 0 . 771 0 . 811

0 . 709 0 . 913 1 . 000 0 . 771 0 . 811 0 . 709 0 . 937 0 . 889 0 . 771 0 . 811

0 . 709 0 . 771 0 . 771 1 . 000 0 . 768 0 . 709 0 . 771 0 . 771 0 . 968 0 . 771

0 . 709 0 . 811 0 . 811 0 . 768 1 . 000 0 . 709 0 . 811 0 . 811 0 . 771 0 . 861

=

0 . 919 0 . 709 0 . 709 0 . 709 0 . 709 1 . 000 0 . 709 0 . 709 0 . 709 0 . 709

0 . 709 0 . 913 0 . 937 0 . 771 0 . 811 0 . 709 1 . 000 0 . 889 0 . 771 0 . 811

0 . 709 0 . 889 0 . 889 0 . 771 0 . 811 0 . 709 0 . 889 1 . 000 0 . 771 0 . 811

0 . 709 0 . 771 0 . 771 0 . 968 0 . 771 0 . 709 0 . 771 0 . 771 1 . 000 0 . 771

. . . . . . . . . .

0 709 0 811 0 811 0 771 0 861 0 709 0 811 0 811 0 771 1 000

C 8 C 4 C 4 = ◦

⎛ ⎞

1 . 000 0 . 709 0 . 709 0 . 709 0 . 709 0 . 919 0 . 709 0 . 709 0 . 709 0 . 709

⎝ ⎠

0 . 709 1 . 000 0 . 913 0 . 771 0 . 811 0 . 709 0 . 913 0 . 771 0 . 771 0 . 811

0 . 709 0 . 913 1 . 000 0 . 771 0 . 811 0 . 709 0 . 937 0 . 889 0 . 771 0 . 811

0 . 709 0 . 771 0 . 771 1 . 000 0 . 771 0 . 709 0 . 771 0 . 771 0 . 968 0 . 771

0 . 709 0 . 811 0 . 811 0 . 771 1 . 000 0 . 709 0 . 811 0 . 811 0 . 771 0 . 861

=

0 . 919 0 . 709 0 . 709 0 . 709 0 . 709 1 . 000 0 . 709 0 . 709 0 . 709 0 . 709

0 . 709 0 . 913 0 . 937 0 . 771 0 . 811 0 . 709 1 . 000 0 . 889 0 . 771 0 . 811

0 . 709 0 . 771 0 . 889 0 . 771 0 . 811 0 . 709 0 . 889 1 . 000 0 . 771 0 . 811

0 . 709 0 . 771 0 . 771 0 . 968 0 . 771 0 . 709 0 . 771 0 . 771 1 . 000 0 . 771

0 . 709 0 . 811 0 . 811 0 . 771 0 . 861 0 . 709 0 . 811 0 . 811 0 . 771 1 . 000