Computing with words using the 2-tuple linguistic

0 downloads 0 Views 206KB Size Report
Computing with words using the 2-tuple linguistic representation model: Analysis of consistency ... at least the same or better results than the ordinal model as a ...
                                             ! 

 '   (!     (       ! ) *   

 (     +   (  ,     (      ,  ) (  - (. - (    -/!  ,( 0   (!  (  (!  . ! +    ( ( , 1 ( ) (( (2   ( ,     ) (!     ( (  ,    ! ) *          )  (!           ! ) *  !! !  (!       ,(

  

*   ,(  ( ! (!      (       (  1     (!            ! ) *  3*4    (2 (     . +  (!     ( ( 56 7 89:                   5; 79 '

(   .   (  / (!        (  , .  ,    22  ,  5;9  ,   (!    579

             "# $%  "#   &

          

569  /        (,(

!   ( 

    (!           589   

$ ( (!    (         / (!       58 9 )     $ (    ( (   .    (  )  !       (     (      ( (       (  (    () ,  (     ,  (    ( (   0      (  , , ,  ) ((   ) (   

(           ,   

   (():    $ ) ((  ,  )   > 22 ?!         ( ( ,   =. @  (

  (!  $ (   (    % ) ((    -=- -  , (  (  !  )  )    $    ; ) (( /           ( , , ,  >((   ( ( !   /    ( 

       ) (( /  ,  )   (    ( 

            

      (( ) ) /   1  ! )      .  ,      ( (  (( /  0(    &   ,     (  

































*       .  C !  !  !  !   ,           (!    !    !  (        : $$ %         $$ % &'    $$ %     $$ % &    

> ( !     (   !  )  

 (    !  (!         ,  ((): $# %    $# % ('          $# %   $# % )  *+,

>  ,!      .   )((  (!   ,( G     !        ) (!    '    0 .    ,(  (!  (  (!   +    ) +  !  (          (  !      3 (,(4 !  !     ' 36 (,(4  !

    $ 3 (,(4:















                       

    



                 

      



       

   

  

                 

'          (()!: %

   ! $ $ $ $

   

(#! !    

 !    

!









       

# # # #

!    

$ ! !        

!    

$ ! !        

!









!    

!    

$

!    

    !  ! 



# # # #

!









!    

  '&  (& 



'    22   . &    (   , !:  & C 3 4  53  % 4   3  % 49

!









(  # # # #

$

! ! !             =(   $  $





























$

$

# # # #

367$68$6874 37$6$$6;664 3$6%%$667$64 36;67;64 3$6%$66;$64 36%874 36;67;64 376%64

# # # #

376%864 3$66;64 3%676%64 3$$6;66764

$



%



*   & & C 3 $7 %%%$ 74 & C 3 7% $7 66$4 & C 3 ;8% %$8 74 & C 3 ;8 %76 7%$4

"#    $ '  .    /!  22   ,  569    ) ((   I  @ / 5$9  ! 5%9       /! (    22     

  !    .  A,!  (()!  : (  +"J  ! # ;6; 67 # %$ 6 # 6%$ 8; # 66 ; ',(  K/!   '   

 !   - +'    , (    (!    !  #   . - (/)0 )( 

 !  )    , (   #   .'   0   $ '         ! (!  $ ( )         59:

$

367$68$6874 3;67;664 3$6%4 3$6%4

3;6676664 3;%6776864 37$666874 3%867$6664



% ,   !  '  

  " ##$ %% &   ! $ $ $ $



  '%% !%

',( % % ,   !   # -    $ '  .  (  !! !       ,!  . H     *       !! !  . H     5;9 ?    ,  22   ( (       22  ,  ) C 3  4  3) ½  ) ¾   ) 4 ) C 3  4  3) ½  ) ¾   ) 4 )     !  22     !  (  #    $  %    !     )!    $  





Make Multi-Granular Uniform Linguistic Information

2-tuple 2-tuple Fuzzy Sets Transformation in the in the BLTS BLTS

Fusion Method

Backward Fusion result: Step

Fusion result:

2-tuple in S T

2-tuple in S i

>!  : >   (!  (  (!   

'    0   (()!   :

   



                     )   ) 

    

                    )   )  

    







  

 4 C 3   4  





       )  C E 3 4   C E 3% 4       A,!  (()! ((  ( :         )   $ $ $ )    



G!       :    

% C E3 





                                      *   + 

              

# # # #



3   $4 3  64 3  4 3   74



3 ;74 3   %4 3  $4 3  %64



$

3   ;84 3   $4 3 4 3 %4 3  ;74 3  4 3  %;4 3  4

   " ##$ %% &   !



$ 3 %$4

$ 3 %;4

$ 3 %64

$ 3  $64

   '&  (&  +  

# # # #

# # # #

# # # #

# # # #

! 3  64 3 $%4 3 $%4 3  4

',( 8

! 3  4 3  4 3  64 3  64

',(  !

! 3   $$4 3  4 3 $%4 3  4

! 3  64 3 $%4 3 $%4 3  4 =(   $ 

! 3  %74 3  %4 3 4 3  %74 

! 3 $64 3 $%4 3  64 3   $$4

! ! 3 $%4 3 %74 3 $%4 3 %74 3  64 3 %74 3  64 3  %4 =(   $   !

!

!

3 $%4 3 $64 3 4 3 $%4 ',( 

3 $64 3 $%4 3 %74 3 $%4 3 $4 3  4 3 4 3  64 3 %74 3 4 3  64 3  %4 =(   $  

! 3  64 3  4 3  4 3  4

! 3   $$4 3  4 3  4 3  64



! ! 3  64 3 %74 3  64 3  %4 3  4 3 4 3 $%4 3 4 =(   $  

',( $ B) )    ,!  $ ( !       $ (: C E3     4 C 3   4   



 













'   . &    (  #  , )  (()! . :     & C E3  4  



  







)  C E 3   4   C E  3   4

'   ,  : & 



& ,

& '

& $

3   ;4 3   64 3   64 3    $4 3 ;$4 3   ;%4 3   ;%4 3   %4 3   ;4 3  4 3  4 3   $;4 3   ;64 3  84 3  84 3   $4 ',( 6 &   G?'  (  

# # # #

"#    $ '       $ (  0  (    ( '   )

     ( )         

 !    (    ./  , (    (!    !  #   . - (/)0

    '  ,(  L' (!    !  ( M  , ( !: 34 '  .   ( ,   .   (  34  ( ,  (!  $ (

A,!  (()!  (   !! !   : =. @  $ ( # & C 3 $7 %%%$ 74 3   ;4 # & C 3 7% $7 66$4 3  ;$4 # & C 3 ;8% %$8 74 3   ;4 # & C 3 ;8 %76 7%$4 3   ;64 ',( 7 K ( )  22  ,   $ ( *(   .(    )  ,   (()!   :    

', ! ./0 1&              

'

              ¿  

- % 2            ¾  

1             ¿   

',(  (    ( 

A ,&    (2   .   $ ( (!    ( (    (()!   ):  ?!    $      ( 1      >   )    (   ,(  )  ,    .  ( , (  ,   . !        (   (        ( .      ,  .  )(  $ ( ( .    ( )        (  '     ( , ,  $ ( (        ,  .  1        * ) (/ ,       ,     (         >( ()! ) )      +  (!    ( (:

 0    *    ,(    (        ,  +  (   !  

 22 /! (      ((      (  $    ' ( () ,    (    (  (   .      )    59   /!         

    $ (

!     "    ,      (          (!  $ (    ( (   ( ( (!     ( ( )  )   $ ( (          ( ,   =. @  (  (  )     (!   .   



"#  59 @@ G  I   /  ( !    ( (    ( :  =.     ' !+ @      (. : ? 22 - (     -/! -  ' (! '   ! (   G (! 566 #   #   2% 388;4 %%8 569 - (! "? O !  - O( A !! ! A   ?!  ? ,( 3  4  3   #   3 388%4 %6%

579 K !   G ( '  ,(  ?!   .   ( ( 

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

Suggest Documents