2Faculty of Computer Science and Information Systems, University Technology of Malaysia, Malaysia .... crisp clustering of points, but when m > 1 the degree of.
! (
#
!
"
& ! "
$
"'
"
) *
.!
" ! " ! 1 2
'
" +5&&, " "
'
"(
-
1
"
"
"
"
' "&
3
"
6
) ) *# '
! #+ #
# ! # #
#*# '
# # ! '
# !
'
'
! # '
' # + # # #
#
#
#
#
! #
# ,(" - # # #
# ' #,#-
# # # # ## ' # # ( # # # #) 3 # 3# 4 ) * * ! * ) ) * 5 7/+ ( # # # # # # # *# ' # # # #+
# # # # ' # . /+ ( # ! 0 # ! 1 # # # # # ! # + # # ) % ' ' # # # . 2/+ # ! 4 # # # # # # .6 8 # ! 0 + # ) 9* ) # # #
(
'
"&
7
#
#
#
#
#
# :;
#
# ) *9 #
# ! # . 2/+ # ! # ' + ! #
!< '
# #
' )
&
*
-
/ ## " "
!! # # !)
+
0 ! "
#
#
# # ,
'
$ %
-
##
%.
# ##
'
"
!"
# # # # +
" 3444 5 "
1
" (
' " )
" "
" ""
"
# "
"
! 1
!
& ' # !
" ! " +& () , "
" ## *
" # $ % # & ' #
!
0 + ##
! #
# ! 0
# ##
#
# # *
0
5 #
# # ) *+ # # ) #
#
# # # .?/+ # ! 0 # )#+ ( # ) *#+ ( # # 8 # # # ! ! # +( # ) 00 9 #+ ( # 2 ) # #! 1 + ( # 1 # # #+ # # ) * # ## # #+ #
) ) # # ? ) #
6
#"
$ % # ) *# % *# # #
#
# !
0 # # #
# # #
!
. #
/+
#
!# # 8 #
!
G
G6
G?
# # #
G7
) # ! ) *#+ #
#
G
G
! ) ! 0 # ! * ) # # * ) # # *# ' ' # # # . /+ ' # # # ! 8 # * # ! # # . 7/+ # ' # # # ' # # @ A ' # ' # ' . ?/+ # 8 # ! ## # ## #+ #) # ## # # # ## # # ' ## . /+ # ! # # ## #+ # # ## # ) 1 +
("
&"
'
$ ! #
,$
- # # '
1
#
##
# #
# # .B/+
# $ !
#
# #
'
# # #+ (
!
## # # ! # +C' ' # # # # , ! # # #
) # ) ! # # -
!
+> # '
1 # #
! '
!
.2/+
! # # # ' * ) ! # ' # # 1 # #+ 9 ! # # 8 # 1 ! ## # # ' ## * ) ! # ' # 1 # # + ! # # 1 ' ! # # ) 1 # ,) ## # #% ! #-+ ## # # * ) ! + H % # ! ! # ! 0 # #, ## ! # . B/+ = ( I ,& # # ) & # 9 # % #, ' # -+ # 9 # ## 89 + #
! # +
' (
# ) ## # 0
%*
' ()
J > '
7
F # F #
7 2
F # 2 ?
##
! #
G
+"
#
G2
# # !
"
)
' #
(
# ) '
# 4+
# #
'
#
# #
" #
# #
)
8 '
+
&L )
K:
#+
# # ##
&,>-
- # )#< 95)
;
K
K
+ &5>
# # * !
#
D
&, ) -
# + (
7 :
' D
' # ## . 6/+ * C+ * E+ .2/ # ' ! ' ## ) # ! # # # 3" # F #4 ! ' # 3" # # G2 G? G G6 # # ' ! ' # # G G7 # # # # ! #+ E G # # ' G # # ! ' + ) ) ) ' # # * G G ' +
J
) !+ # ! " #4 # 76 * #+ ( ### 1 # # ) # ' ' # ) ) * ! ! # # # * + # *# T"" # # 1 + *# # ) ) 1 # +!+ C! *# ) # *# ' # #+ ( ! # *# # # & $ $D ' +& D, *#D # # ! ! # *# # # # # ! ## # . /+ # # # # ## + * # ) # *! + # #0 # ## + # ' # ' # , ! #-+ ! # # # # # 1 G ) # )# I #, #-+ "I6 # 9' # I 77 #' #+ # # ! # ) 6 ? # ## ) ! 2+
01 #
#
##
+ +
)
!
#
# # # # ! $H P
)
) 7+
#
! # . /+ # ! 00
# ) # +( + 7+ +> 2+ (
'
#
# # ! 0 # # 0 #
+ #
!
9
1 (R ## )# G> )
/"!" ( A# =
"
# #
'
+ +
!
*
'
##
/"#"
+
# #
# # ) E ""$ $ = ES+ 2
1 #
#
* # . :/+ # # ! ) ) * ' * ' 8 #+ #
#
*#
# #
'
+ ) #
! !
"
#
#
# . #
' ! !
#
#
!
# #
+
#+
# # . /+
("
!
+"
' # #
# ) #
! /+
## #
# ## +
# #
# #
! !' #
# #
# " $> # # ) ' ## # #
+
# #
+2 C 0 !
!
! 9 00
# #
' #
+$
'
#
+
#
#
& $
$ =
+
= + ( '
!
) ! #*# . /
$
(
#+
2 )
## ! U
BBB T""
#
# >
"
"
+
# 6
! # #+ ! # * ! # ! + # # , # ! ! # ! ## ' C " C " C C " C C 'C C" C 'C " C C C C C C C C H # # # 0 7 # # 2 ## #+ # 8 :+2+ ( # # 1 # # # " + ## ) 7 * # ! # ::; & D * ) # 6 +:2;+ # # # 00 9 # # ! ! # # #! + ! ! # # ) # ## # # 0 ' ) ## ! +
%
?
, #
# ) ### # 1
7+ P1
? ?6B
::;
'
+
+
7?+
#8
, '
#
+66
7#
'
*
7 +?
2
# !
>& ) ! ' ! # # # )# # % # #+ ## # % . /+
45
6
) )
## # ) ) # # # #
#
8 # # # #+
# #
# ) *+
' #
! #
1 ) ) # 0 # !' # # # # N # A#
#
# ! ' # ! ! +
##+
# )
#) # #
# # #
# # # # # # +
#
# # 00 9
## #
# # #
2
#* # #
! #
#
!
#
'
'
! )
#
1
#
#
# # ## )
!
# # #
##
# #
! #
. /
# ! #
'
+
# !
00 # !
# , '
! 00
!
9
#
#
.?/
+ #
+ )#
' ) )# #-+ ( # # ) # (" # # ! '
#
.6/ ! # -+
# #
5
*#
# #
) (
!
# 1#
# #
# .B/
# #'
# # ! # #
# +
# #
# # #
# # ) # ) *+
# 8 #+ H # #+
! 8 #
) !
. :/
#
% # ) *
# $ % & ' # E !* * , ) F * B6 + * C+ * E+ 3 C ! $ P1 = ! " 4 EEE : : F
.7/
. / .2/
/
+
:: + F+ 3 # "
. 2/
#4
D
' + 9
"
+: FD G , E # + 629B: :: + + + # + + + >+ 3 R ( # " 4: "0 ( ' +7 + ? 9 ?7 ::2+ + + + + + + + + 3( ! ! C ! # 00 9 # " 4 ) " EEE " % : ( + 2 292 B ::2+ + + + + + + + + 3 ( ! ( # " E # 00 # ! $ = ! ( *# ## # 4 : D " ! 1 D + :D D, ' + 2 + + 6 966 ::2+ # + X+ 3$ ! 9 T ) $ 1 ! 0 4 ' + 2 +B + 6 796 7 :: + 1 P+ / ## F " "H & F " EP# ' ::2+ " # + = + 3 ## 4 & ' + + 7 + 7 9 2? BB + " ! "+ P+ 3 ( # 9" 4 EEE D ! E ' + 7 + + 9 7 B6 + C C+ $ + " =+ 3 # ## # ( # " ) *# 4 ) ( I ' + + + B29 6:7 ::7+ C Y 0 + "+ $+ 3 $ P ' ( # " 4 ) " "' 2 " 2 : + 2 :G , 1 + 967 :: + C C+ ! >+ " ! "+ = + * E+ $ F & : ! ! C ! ( # ! ::2+ C+ ! N+ + T+ ' R+ C+ =+ ! F+ 3= ! ) ! ! # ( # " 4 D " D ! ' +? + + :B9 ::7+ (! T+ 3& < $ 9 ( # " # & (G 4 ) " 344 EEE D D " ) ' H * & + ?9 6 BB7+ N # $+ X+ 3 00 9$ ! " $ ) H 0 4 / ## D "D ' + B + 29 : ::2+ &
##
#
9
D #+ #
#
! #
# # ! #
#
# #4 ::7+ / ## > ##
. ?/
.
/
$ ! 9 . 6/
27
(
. B/ N # $+ X+ 3$ ! 00 # " # $ 4 ) " 3 95 2 1 : &T + ?B9 :: + " . :/ T"" 5 ! " & ' " & F : +5&&: G3444, & ' # ' < + $ * T+ Z + [ T+ $+ 3R # 0 " ! > # ' 4 ) " D C( + B 9 :6 ::2+ . / "+ N+ : & " ! 1F 8 D ! ! R ! )F * & :: + . 7/ ** + ! + + 3 ( # " ! ) *# R #4 ( ; " " ' + + 6 + 779 7B ::7+ . / H + (0DE ( F " ( ) ! & ' # ! ) :::+ . 2/ ! "+ >+ 3 *# # 9E # ( # " # #4 ) " 4 :F : : " : D # ! " & + 229 ? :: + . ?/ ! X+ ! * R+ 3 # ! ! ( # " 4 ) " D) E : & F & " & ! 1 D >(P H & + 7 976 ::2+ . / \ ! + F N+ 3 $ ! # E # 4 ) " " : / )D E + 7 9 7B :: + $ E
' ! >
! BBB+
BB " # $ %
& ' # ##
$ % BB
#
# & ' # #
# ( # " ' # , (" # ) * ! # & ' # + # > " # ( # # ! # + # # # # #
$/ ## >
"
!
:
00
#
&
!+
#
(PPP
+ ' # E #
& ' # #> " !
# # & ' # BB2+ (
# &
! # +
#
#
& ' # ##
#
!
T ! #
! '# !#1> "#
##
, > "
6 !
,
'
## *
! ) * ) *+
' #
#
' #+
& ' # T ! BB + # ## ## " # = ," = E( * ! # + # # #+ # # # & H P+ N ! + ' BB6A# P1 ) # , -+ # + # # ## # ' ' # # # &
& ' # 2% # ! ( ( * )
! !
' E T *
! BB? # #
# # :: + # #
# # #
#
+
' # !
!
( # ) * ! # & ' # + # ( # + ) !
! ' '
#
# ! !
" ' , (" ::: # # " # $ % > "
& ' # ## !+
! !
2
'
' !
#
P ! ! & ' # BBB+ #' H $ # # ( ! & ' # + # > " ! ! * ! E !* * + # ## ) * # # #+ !*
" # $ % # & ' # # # #
'