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Transcripción

1 !! "#$! "%&' "&# ( &$ )*!)!,!"-,.//0

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3 ! - "-! "#$! '&2& 3" 4 -.//5

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5 TO THE KING! " #$ % &! %

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7 ! RESUMEN &-&#-" '#3-6 7 " 3# 8 2 & &* *&6 9 - :' &6-&#-;%& "" *!&# & %&"6 & *&, &* *&, : & -2!6 7' &%&!&&*#'<$ *3- - 2& 76 & # "& 76 -&# # 7 #: &- ""!&# & &* *&6 -&# 7 7 " : "# "= "9 :"#!& &&7"6 "# "$% & 3-, &*# *&,)" &, >*, *&

8

9 ! NDICE GENERAL &&'() * *$ ) *$ & *,) * & * -"*& *. -"*&/& &) * ? @ @6? A AB 656)C "* *.2 66) /A @6)C "* * ) A 6.6 ) AB 646 ) /D 6@ )C AB -"*4 5 * ) @5 6.6) )> E) @ 6@6F @ 606)C D. -"*8&9,& *0.,)4, *0: / *0.:

10

11 3 NDICE DE TABLAS -63# #G -.6& & 2"0 -43# #G2"B B -@3# #' G2"/ # #H & & 2" B& & 2" / -A& & 2" D& & 2" B -/3# # 2"A @/ -3# # 2"A @/ -.& & 2"A @/ -43 *# / -@# *# *& @ -5 " *# @ -B *# )&* *& A& &*& D# D -./ *# #*& B/ -. *# )&* *& B -..& &*& B. -.4# B@ -.@ *# *& B5 -.0 *# )#&* *& BB -.5& &*& BB -.B# A/ -.A *# #*& A -.D *# )&* *& A. -4/& &*& A. -4# A0-4. *# #*& A5-44 *# )#&* A5-4@& &*& A5-40# D/ -45 *# #*& D.

12 3-4B *# )#&* D4-4A& &*& D4-4D# DB *# #*& DA *# )#&* DD &*& DD *# #*& /4 *# )#&* &*& *# #*& /A *# )#&* /D -0/& &*& /D -0# *# *& " *# )#&* & &*& # D -0B *# #*& / -0A *# )#&* / -0D& &*& /# *# #*& *# )#&* & &*& B -50 *# #*& / -55 *# )#&* B& &*& A#":& -5D *# #*& B/ *# )#&* B& &*& B.&" B4"= %&" "3IJ&* *& B. -B0- "= ":IJ BD -B5)"&* -& A0 -BB)"&* ) D.

13 3 NDICE DE FIGURAS '&#( '&.&* N A '&4&* N D " KLM3" "" N / '&0&* 7KLM3N,K-LM) N / '&5&* KL,K-L B5 '&B&* KL,K-L BA '&A&* KL,K-L O A '&D&* KL! "! # A4 '&/) *& $- &"- /6B / '&) *&%&- &"-/6B '&.) *&'-( &"-/6B '&4&* &"-/ '&@9"*&KL) )*,K-L)*),KL,K L&,,KL&&),:K*L ) '&09"*&KLPP46K-L3P4@P: D '&59"*&KLPP*6K-L3QQQ:, *&-3R: B@ '&B9"*&KLPP46K-L'&P: A '&A9"*&KL"P*6K-LPP0// A0 '&D9"*&KL) )*:K-L)*) D/ '&./9"*&KL) )&-:K-L..., * -/ DB

14 3 '&.9"*&KLPP4:K-L'&P: /4 '&..9"*&KL"P*:K-LPP0// /A '&.49"*&KL) )*,K-L)*),KL,K L&,,KL&&),,:K*L ) @ '&.@9"*&KL) )*:K-L)*) D '&.09"*&KL) )&-:K-L..., * -/ '&.59"*&KL) )*:K-L) / '&.B9"*&KL )-:K-L) )0$$ '&.A%&&) '&.D #&"I'%&" '&4/ #! I'%&" A '&4 #&"I! %&" B/ '&4. #&"I' "3IJ B4 '&44 #! I' "3IJ B5 '&4@ #&"I! "3IJ BA '&40 #&"I' ":IJ A/ '&45 #! I' ":IJ A. '&4B #! I&" ":IJ A@ '&4A #&"I')"&* -& A5 '&4D #! I')"&* -& AD '&@/ #&"I! )"&* -& D '&@ #&"I')"&* ) D4 '&@. #! I')"&* ) D5 '&@4 #&"I! )"&* ) DA

15 3 LISTA DE SMBOLOS ST SSTT ' ' ,6 ' { < >, =,,, }, - Ã ã 28-68: ; <6 6 8 # 6 - = Ã ( ã ) 6- ã,ã -. >?, (- ( ) ) AB6, -6-3@0@C 2?

16 3! Ö 2 29!DE Ö -, 2 - D- ( ã ) A ã ( ) A - ( ) A ( Ø ) A,23- Ø ( ) í 4,26 ñ?& ñ F8F ñ ñ >GH ñ ñ F8F ñ ñ, ñ., >G H I ñ - ( ), ( ) ( ) - 23 I $I = Ó GF& á á > ' (- ) 0 K EEE á#23- á# 23- J AB6 > = ' > 6 >

17 3!, 2 ( ), <66= > {,, } <66= &!&HU (- ) 3 >2 26, - E (- ) ( ) - í > = ( ) ( ) ( ) , - E 268 -= ( ) ( ) ( ) - í 2 -,.,, A, 2 - { } [/, ] E = { } ( ) ( Ø) 239!23- Ø - <6 [ /,] , -.,, A A

18 3! &&( Ø) 23- Ø ' '>? G > 4 G,.,, 4 G5 * I (- ( )) J, ( ) 23 I $C$0 > I * I (- ( )), 5- ( ) - 23 I 0ICE B65E 3 %B 4 G 4 G 5 -= 9 8L , >G5 B8 >G5 & &B >G55- <66=9 3 ( ñ, ñ. ) 9, ñ ñ. ( I ) 3,5I <66=5 3 ( ñ, ñ. ) 5, ñ ñ. ( I ) 3,5I 3 >G >

19 3! MH (-) ' MN >G=5B8 >G=5& AB6 MH = ' ' 3 M, N' ( I ) IE23 3 IE - ( I ) - IE , IE ( H) 6 H /D 63DHM 366 D 2-- DU 62-- D 6 D ( I, ) D D V D ( I ) D, D D D I, D 6 ( ) 6-- :DI ; 4 R 23 >G H / R, [,) H H 0 H K EEEH * H H6 6 H 2 8, H, H = H E = { }

20 3! H H H% 3 H > 6 M, <6H E 4 - ( Ö) ! D Ö ( ) 23-6-! D- ( I ) 0 K 23 I > H6 -:DI ; -:DI ; * -: D 0 K ; -: D 0 K,, D D- DK D* D#NN O' DE E 6D 6-9DL0NNK 9DL0NNN 9DL0NNN > 63 <6 & I <66= 3 (- ( )) J,9 6 - ( ) 23 I 0 C$$ > I

21 & I (- ( )) 9, ( ) I $ I = E AB69E ( Ø) 23- Ø 7 [ /,],&&" (/, ] I I I8 -- IU 6I -66 D ( I, ) I I 23,., I B >G 4

22

23 Captulo I. INTRODUCCIN &", ( ' *&( M&"(N *"#6,-&"" *# &%& "2!("73# '&2&:"&"6,,! &3-%&"&&3 %&"%&!& *W..XW.4XW@DXWB@X6 & 3#:"&# 9": '<$ &W.XW4DXW55XW5DX62"& %&"6 ; ".%<<$" = 7, - 5 3E P & -E 9 B,3E -6 :7& 8 J,6;,&E 2"3MN:MN* &&6"7 3 &&'* M N& "&: *&& &$-%& &!' ' & $ 6), $ 2& *& W/.X&:&" &,&"9"'<$6 3&'! %&" && & 3 * W..XWDXW0.XW04XWA0X6 & ' %&" %&!& &* W54XW.AX6 Y &

24 . &* '<$%& & 3# &* #'WD5XW/X6 &, 7 & &*# '<$ *3--2&7W54XWA@X,"%&9 2".:46 ; "6%<<$"=!">- 6 8, 309 8B B 9,6EJ 5 :Q29 & 5 8&, 36, R;E 2". # M 3,N& ' &63# '<$ M 5 N & - "%& * # M 3,N,, M 5 N & &* '<$6 &*# - 2& M - 8&,& N%&&2&76 &*, *&, " &*#!6, &* - ;" *%&*& #6 ; "0%<<$"=!">-, 3 0 -, :7 & 8-5 =, ;E 2" 4 & *" & &* '<$ - *&" &2&7W5XW54X6 * &*#!, # &*, " &*# (6 %& &*# -&""* M ("N *6

25 4 Bases de Datos Clsicas y el Problema de Rigidez &",":$ "8 2 K8, '9 M- 8 '" :"NL - 8 WABX6 W4BX & " DB/6 "" - #,! $ 2&6 &! '&2 & - - 6'&2-&2& '- " F'-:R&3##' %&" " 7& W@XW4AXWABX6&79"8 7*8 %&&:'2 &-#'63,'&2 &"7-7 > KM&& >&: '&'NL W./XWABX6 '&2!& " ">.:>4W0.XW04XW5/X6 8 7 " 3 %&"' &, & &* -" ' ( WAXW4/XW4DXW@@XW@DXW0DX6) & -",!!7 2"6&"7,%&" -3 &" &"73" &':, & 3 *"#'& * &&6" %&" && 2": 32"@,& >6 ; "7%""?@-A 8 3 0=:7&,6; - 29 E -:7& $6 58 J9 SE,6;E 8 & J,6 8 D 5= 2?<HM%M?O%HT$> T

26 @ ' ( "7 &*& "WB@XWA0X )"",: #&';* &&6 2"@, :"& %& * : - Z " ' * &&, $, ( :& '!"7 & 62"0&-"6 ; "3% ""?? 0 66%M?E, = 2?<HM%M?O%HT$> T 5? K,8& G9 8E 9 &#".*!""!'&"; "3! U! 0 0 *$ A2 $ V$ A $ ' $ H E & WE *$? E0 * &#"6*""""; "3! U! A $ ' $ H E

27 0 " &!, 2" 0, # &%& 7 ' - 6 && - 2& & ":&*6":& -&M"2N&6 '& &-$',%&& - &M*N,&& "7 &,'; &&62"5"&-"6-: 2", $ &"7-%&9& &":%& *,& 9"2&6,& " $!$,&:& -&!-" &&6 ; "B%,""? 2 J, 66%M?? 0 3E 8? K & - &? - G? 0!E 9 - E E -" ' (&'& #'W@@X6 $ &" *# &' &*3-K%&!& 9""L6 Conjuntos Difusos y Consultas Flexibles [ W/.X &2$ 2&*&D506"!# &: *& " " 6 $, 7 ", "(# &( # ' " 36 & # - ", "7 7 8 "7, *#, " ):)" "7', '*," *"#,"(#,7,:" 6

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

29 B -2 7 &*3- " &*, &! &*#&2&7: #-2 &* *&6, *"MDI N, D&&* *&,I&2&7,:& # *&6 Contexto del trabajo: SQLf ) -2 * " & *&' WB4X6 & ",*&( '&6WXW.XW4X,6WDXW./XW4/XW4X,\(:J 6W5.X,W55X,J2"6WB.XW//X,) 6WBBX,"6W@BXWAAXWADX,: 6W5DXWB/XWB0X6-2-$* & *&6,& -2 &J6W45X:'W@0XW@5X6 # & " 3-26 & >*WDX,& 3# > *&Z%& &" 3#"7" >- 2& *&W./XWB4XWA0X6"",9 ;3# >%&"&*#!K" 2".L6 & &##&&*#( K" 2" 4L6)" &*# - %&&* *,&' *%&*&6Y -2 \:(:J 6W5XW5.X, : 6W@XW@.X6 ), 6WXWDXW.0XW.BX"-9 &*#6-2 -"!&& *&"- &*#!:(6 9 W54X "#%&,! 3 ' *# &*, "7 & ) "# ]'WD0XZ%& - MD I N & 3& &-2&7@ ;6-2 &" #6 9 W54X "-9 "#%& #& 3 "& ' &'WA.X66-2 "7 WDXW.4XW.0XW.5XW.BXW.AX:!&# WAXW0XW.@X & &* *&- *%&6

30 A El Problema de la Evaluacin de Consultas Difusas 3! #'*&,"&, 3&&&W4DX6(# %&'!&# & "& *&"&":%&&7WAX6 "&*&( "&!&# & 3 8 7W@/XW@AXW0AXW5BX6&& "" :&# &!"2 "= &6 "", "( &,! &&, $ " &6 & '$, -"!&# &7", '&*",-Z &&, ',& %&*"!&##"'WAX6"-',, '", - &"9 " & (-6Y*&# "( &6!&# & *& "7 "2%& & 76Y&%&7& ' *# *, " " ' & :*"# * 6,&& -& & ",:%& # - ' *# *&,!( - "! -&6 8 7 ;, "7 9" *& &&6, ',%& "- && ( WBX6# 9" *& * $ -! &&6 9" * - ' 9"7 "&:$*&! & - 6 ) >* & '& ""!&# & W5XWBXWAXW5XWAXW..XW.@XW.DXW4.X6 """7 " * 3 & " 8 2 7" & #'%& " & *&-& &&%&3 * - 6

31 D "" ""7 "%& & - & *& " ' '&WAXW..XW.@X6""&' *#- * #- &: &9&# * &&6 '! #!& &"2" -;%&, " && 6 & $ 2& *&, 3& 3# 2& *&:2&7,!9,>G:á# & 2& *&6 $, 3 3 : *&6) & Z ""!&# & *&- 3WAXWB@X6 "" $! ,, ", %& " & *& '&,"",&" & 76 $,!&# & $! '$ 3 * &76 & ' "2, - 3 *&:, "-2 3 & *&6 *& " ' ")!#WB@X6 Y -%& & & *& >*, -!& & 7 >%&,-&""*%&& *&K!#&L,, &&&2&"7-K!#9-L6 )%& &%&!&&*#'<$, " - )!#6 "7, " %& # & 3 " & *&W0XW@XWB@XW44XW00XW05X6 -, 7 - & &* *&,: $,! %& & '"-9 "&:3 "6

32 / &&* *&,&&"9 &$ " ;" * 7& ' *#W.@XW.AX6 "9 - ':" *&6" "2 ) & *& ' '&6 )! -2, -$ & ' %& - )!#6 Justificacin e Importancia del Tema &7&"' ' *"#, 7 :& &* 6), %&"&:!!&" *"# -,& ":"!"", "%&& -*"# &&"" & 6 &#"! -;%& """7* 6%&-&!' '$ - 6 "7,,"*&(M&"(N *"#6 -& " :"" *# &%&9"7-'&2&:, '&",*" &"6 '# & #"&: " #' *&,%& "3 6Y& - " %&" &&, - &( #Z "& "! G%& $! &&%&"" 2"6 8 7;,"&" &"!,!;-:! $ "2 &!- &# &8 %&' & *&6&,- 8 "?& ", ', :!&"W4DXW@0X6

33 "-', " & *& & "7 %& " & 76 '$ - * :"" "(#%& &,& &( " &# & *&6 &# & & #'*& '# 6), "&: " -"!"" * " & *&WBXWAX6 ) &%&!& &*# '<$, - %& ""!&#- )!#"-2 3 " & *&W@XWAX6),$ -"- *- *"" " & &* *&%& - # )!#,: "-9 & -*%& & W00XW05XWBDXWA/XWA@XWA5X6 ' " %& ' " -2 3 " & *&, 7 '& & "" & *&%&!& &* '<$ " 8 2 &"" -& "=WA@X6 Objetivos de la Investigacin 9%& '& -;%& "" *!&# & &* *&6-2 ' & >*%&!& &*# '<$ *3- - 2& 76!'# & -&# # " 76 "!#"-9->* &%&!& &*# '<$ *3- - 2&768 7;, "&#"-23 " '&2 *& "9!&#"7 & %&&6

34 . Metodologa )(-2!&,'&%&&# L & *" &&* *&>*:# &* *&6.L )#: &-*" # )!# &&* >*6 4L *# ""!&#& L )'"- ' '&6 -L )'"- ':8 *&6 L )'"- # )!#6 L & - )!#, 3 *&7& ' *# 7 "= """ $*"6 Conclusiones & -2 $&"&- " & *&%& '& ""!&# &' 6 "", & ' & *# & "( &6-2 & - " &!&# '& & *& "2%&&&*#,"!#*&6" ' -2&%&!&&* *& *" MD I N %&!, "7 - -"!&# *"MDI N, '& W/X6 - """ '$!'#&( %&$6 "-', 7, ",& # & &--, #!'6

35 4 Captulo II. CONTEXTO DE LA INVESTIGACIN &", 8 & " &( "& " & " : 6 " 8 2 &'$ "": &# 6 -, " &* -" ' (6'&%&" &&& & "" & 76 - $ %&",%& & 3 " '&2 &76 -" &*& " "&', #& & * &&6"& %&:& &&&& & *, 2& &,:%&,!' &, ' & *6 && 7 -' &: ' '&:& &"76 '& &', & & & -" & &6"" &$', --$' &6 &! - & *, %& #$',%&7-6&! 6,& %& :&K&!$L:,,& &;6 "! &&' "&"&# -"6""&&-;%& &# &6 "" "%& &&! - :%&,

36 @ "", * &, - " - 2& &#,:'&-2& &#6 &#"7' # - "!# &&, "-9!"" * * & %&"6 $, "& ( & " :&" * %&& 9&&6 " & W./XK>*L& *&("7!* &'&2&* & 7 > " 3# &%& # *&6 "" -2, >* ; & & *3-%&"$&*#'<$&&& ": "6",>*&:" -26-2! &-&#'*!7 '# 3-6 7, ", *, ": " *""!&# &%&!& &* *&6-2 " && & "- *" D I K &* L6-2*"&&# -& )!WB@X:9 W54X6 )!&'&2>*:)!#&"69 & #"7 &&* *& >*:&'!&#- ' &'6 $& - "*" -7: "!'#( 6# '&"3&!&","$""# -2( 6

37 0 II.. Bases de Datos Relacionales - ""& " *"#;- "! &''" " #6)&"&#: '&, " *H " " 8 2 K8,&''9-8 '":"L6" 3##! &&'" :! *$ "" 6 " " * # *"# & "& 6 &, " &8 6 '$ -," $&! -#"&:-2, &&"&:! ""*$6 W4BX,DB/,&8 -& # "" &&*$6 " -""7 #6&",":$ '& '&2 & - &# *"# - 6 *%&"7':*" F'- : 7& 6 7 '&2 & #,*&- &'&27>W5/X6'&2! 7 &-- 6 >, ",& '&2!6 "-', $ '&2 "! - "& & "&# 6 '&#":$ ""- " *& > = 9 $ '&2 "! WABX6 &,7 & >K ">IDD>4W0.XL& 3# "6 Y " *#:&(# *& *

38 5 &&: "" 6*&&! & &&%&&' "&-&6 &-,*"&:"6Y & &!' '$ 6&&*$" $,-"2" 68 -!" &&6), - "" "" "(# &6 ', & &, - " %& 7"$"" "6"(# &7&"%&: $&; DB/, W4BX&8,&- # $ 2&6Y! " & & #""76 2& * %&" #6 & %&" " 3# #6 &",9-:""*6 =!.%<C!"! I,, I 2&7,, * * H & * *& 8"&&& H ( I,, ) I %&" %&%&" # H I %&# 6 %&"

39 B ; "2%<"!C! 8-6 & E -6,6 & & 6 E -6,J 86= %M?= = R = R! 66%M? 3 - = X G GE 6? *E &#"0%!""!'& "; "2 0 0 *$ A2 $ V$? E0 * " " &* "&! "6 & $"&-& *6"", -& * &*&# #& "6 =!6%#"!C H ( I,, ) I &%&",, H

40 A I,, I,,,!" *&*&# H I %& (, ),., -& *&&"* #&," '&2 '"#&& %&!&& '6!.%!D E 76! -& KL, &*3# %&"#H = I EEE =I! ; "F%#"! 6%M?= = R = R! - 3 WE &5 6 E %M?? *! = EC! C :; X E C! C 0 X EC!C &7"-9&" -! * " &-& * &%&" #6Y#MN, * &#6!6%!DE K L " H = I EEE =I!

41 D ; ":% "! 6%M?= = R = R!- 3W 6 =!C X!C R X!CR 2& -& &#& & * 6Y ;I!6& 2& -&"" *&*, %& 2& -&*"&!6 =!0%"$"!C G"$ H ( I,, ) I &%&" {, &2& -& %&@& G#, H ( ) { ( E E ) H 2H %&@&, H ( ),,:# ( H@ ( H@ "3# &#&- & "- 7"", - &72& -&7!#6&%& %&" #& "7 &!,,!!,'&%&!"6!&*" *&%&"

42 ./ =!7%"$ H ( I,, ) I ( ), *""%&@, H ( ) ( ; ".%"$"! - 86%M? 3W :-; G -6 - &E 9, 6 :H % ;9 8= H % -== = R = R! , = H % Y-Z!XH % YZ! 9,6= H % Y-Z! 3 G#,! 9 = H % Y-Z!X H % Y Z!

43 . -9,-8 6 6? -, G#,E &#"7%!""!'" "; ". - (#SWVW0#< 0 (#SWWK#< 0 *$ (#S$NK#< A2 $ V$ (#S0*W#<? E0 * & & -&"&6,"!!*76 -&&#&!"&* #,"!!"6 =!3%"$,? H : H. ( =,, =,, && -& H. %& { } ( ( ) = ( )) H. H -H.,@,@, H { }( 2E = 2E ) H 2 2

44 .. ; "..%"$,? 6 8 8, & 6 :H % ; 3 0$E -6: [; 8= [ - = -. = = R! 9 6 8, -9 = - [ - -H %! - [ -. -H %!, [, -8-66H % E 6 -. E 6 [? -, -9 &#"3%!""! H -0 -K (#SWVW0#< (#SWWK#< (#SWVW0#< (#S0*W#< (#SWVW0#< (#S$NK#< 0 0 ) &%& #, # ", "-9 &*"#" 6 '&""7- -2 W4B,4AX*&%& &# $ *& '&2!6

45 .4 '&2 - &&*$ ""6 " " *'&26"&"&# " *&F'-W4AX6 & '& '&2 & -- 6 '&2 - & 2& '- " F'- :R 3# #' %&" " 7& 6 '&2 & -, "7-7 > '&2 & && 6 & *# ', '&2!& "& ">.:> '&2 &> >&'&2&& & 6Y - F'-: 7&6>"-9 &: "'&,"9:*& ''#,6# $ >,"!'#6 7 >, & * W5/X6 7 $ > " *",:%&&7"7 *&-*" *" &6 &&*& " & > -%&"&I6 # && - -7 F'- ):#,) &:#6 >,& &""#!&&, -&! "-'< 6 "-9, & "" "- -& 7 %&" &&,"- #& *2 -&6 " &" " "-'< -&: "- #&"7%&:# "- # -&

46 &&, 9 *6&#" & 3#"7 "7 &6 =!B%"" = H, H,., H %& H &%&" ( I, I,, I ) H,,,.,.,, %& H, H,., H - H &"- * { } 3{ }( H H 3 ) :, 3&"- { } 3{ } { } { }(, 3 -%&"> &7&&,&7&&8 :& 7&&` G,%&6"7 && & 7&& :#6 Y * -&%& 7 ' K - -&L6 * # '-%&-&&"&2&Z:"&!( -&6 && & *%& & 2& K& "&2&L6'& -! 6 7&&8 *-&!-&6 7&& ) & 6 & - & 6 7&& ` G # # 6 Y * %&&* -*' 6 #& 3# %& &!& &%& &&, &%&

47 .0 "#, &%& "9: &%& -& ;, & -%&7, #& &-& -%&36 ) ( ", *"" 3: "7 #' >6 &"%& 7*"( #' :3 #'&2 '"#6 >, 7&& ` G 6 " *#"7 '7&&` G: &9-%&7&&6 =!2%"< ""I H,, H %& H &%&" ( I,, I ) H,,,, & &,9 ',%& H,, "" * H & # &2& -& H,, H Ö 3# &> 2?, <HM H, H O%H,, Ö & 8 D&:& *" { 6 í } ( Ö ) =,, H H ( ) ; ".6%"< " H % 3 0$ 6 [ 3 00E, 8

48 .5 =29 & 8 9 0$6 &:; 8 8 \ DE 2, ] J, -3 E 2? <HM O%H %.6,%.6 H % %, [, H % % 6 = aa > % 6- = > [6 < / - > %. -. = %.6- = ( Ö) = 6%.6, 6%.6 % [ %. 6% 6 = aa 6% 6- = = 6%.6-6 [6 < / 8 66H %? 6 [? Ö? ^E &#"B%""""; ".6 %KE %KE A2 V$? * %&" && & 3 "%& "' #'&-* 6,&&7-' & 7&&` G3# >6

49 .B =!F%!"< "I Ö & -%&" 2? &&'$, <HM H, H O%H,, Ö 3# &> 2?,,, <HM H, H Ö &-%&"D,&:& * " ( Ö ) = ( & &&%&& -& &-%&, 'MVN& & 6!0%#DJE $"-V& & 7&&!( -& &!&, & '& :#6 )! & *#"& "2 - "; -& 7&& :"; 7&& 8, &"7 -& : 7&&6 &# " '& 9 ', - )# 6 &-'&, 7 &# &%&&>6!.%!#C"! " H H "" * & #

50 .A &2& -& H,, H & 2? <HM H H O%H %&! 2? <HM HO%H H = H H $ >3 %& *"#6 " & ''#6 & * *"',"'& =!:%,! I&"&I2&7-66 I&*&# = ( I ) >!*& ''# * 6 M&N6 Y& &"&2&Z*"(*#/6 *& ''# * &"M&"N,"73"M"3N,"$" MN:" M!'N6;"! >&&& *& *& ''#6

51 .D =!.%,!!DE I&"&I2&7-66 I = ( I ) ({,,., }) * *& ''#& & 7&&6& & *&# ''# '*%& & &7&* %& &" *"#6 "" &, & &";*& ''#, %&$;"&%&!&&*&# ''#,:%& 9 9-2%&!-6 =!..%"< ",!I Ö -%&"> 2? <HM H,, H O%H &*&# ''# Ö 3# &> 2? ( ) <HM H,, H O%H Ö & 8-66D & & *" ( Ö ) = { ( ( Ö)

52 4/ ; ".0%"< ",!! 6 8 H %? [? E & 8 9 0$ &:; \ D= 2?, (% 2E) <HM H % % [H % % 2 O%H % E = > % E- = -> -2 = % 2E- > [E < 0! 8 E \? W8-5= ( Ö) =, E% 2E % [ % 2 E% E = E% E- = E- E-2 = E% 2E- E [E < 0 &#"2%""""; ".0,%KE! WE "", #7&&` G&&'$,7&& & " 6

53 4 =!.6%!!"< "I,!! Ö -%&"*&# ''#> 2? ( ) <HM H,, H O%H &&'$ Ö 3# &> ( ) <HM H, H 2?, Ö & 8-66D,&:& ( Ö ) = ( > -&& & & # &6 " " -%& &6 Y & $"7 - >6-%&K-%& L "&-&6&-& "" && &Z ; * %& &-&& &-& &36 ) ( ", *"" &-&6 $ " "-9 "* -%& & >,! -3:"7 &, *# -%& &&*"'"-&:&-&6 & ">%&!-2 M N, M]N, MN: "# & &-%& %&&&!& &*&# ''#6

54 4. M N"%&& &&!$6 "&:": 6 M N& *"& 3 %&! " M N M]N6 "- '# #': M N,-3&%&%&!%& & M NMN6 =!.0% D/&E I Ö &&-I&> #> I'? Ö Ö & D &6D&:!! í ( ) = ( ( Ö) ; ".7%"" D/&E 6 8,8 =29 & 8 9 0$6 & :;E 8 D 8:I'?;\=

55 44 2? <HM O%H I'?! H % 2? <HM O%H! % 2 H % = > E < 0 > % E- = % [ -> % 2E- = -2 = ( Ö) = 66, 6 H % H % [ 6= aa 6- = 6-6- = < / 8 66H %? 6 6 [? \? ^E M]N &* 36 Y "!* &! " K * & -%& 3L *& "# '; " & &-&6 "7 *7,& :" "7 M N67'; 2" 6

56 =!.7% D8EI Ö&&-I&> & 7 "# #> >@ Ö Ö & D &6D&:!! ( ) ( )( ) í = Ö MN K&* &!L!* &! " K * & -%&3L*&"# " & -%& 6 =!.3% DEI Ö&&-I > & 7 "# #> Ö Ö & D &6D&:!! ( ) ( )( ) í = Ö

57 40 ; ".3%"" DE 6 8 6H % 30$E = M & E b D= 2? <HM H % O%H 2? <HM H %! :; = ( Ö) = H % { }}( ) E H % E 8 66H %? \? VE &#"F%""""; ".3 - (#SWWK#< 0 *$ "M N,M]N:MN"&:" -2,:%&9 && &* 7& >6 87, 7 3# " & &* '<$6

58 45 "# -%& &! " & K& &*&# ''#L,!& " &!"K *& -%&3L6 =!.B% C,!!I Ö&&-I >&*&# ''# & 7 "# #> Ö Ö & D &6D&:!! ( ) ( )( ) í = Ö ; ".B%!C,!!I 6 8 6H % 30$E,8 =M & 9 38E 8 D -6 6 bd= 2? <HM < H % 2?, O%H ( ) <HM H %! =

59 4B ( Ö) = H % E <, ({ }) E H % 8 66H %? \? NE &#":%""""; ".B * "?I\BB0.I 0 4/?I\40BI '&%&" &&*"#-'& *6 2" B6 >!& && &# &%&"3 %&"6'& 7&& M)]N:G 6Y " & 6 ; ".2%<<$"! 7,, - 5 3E J 5 :29 & -8&, $L R;,E 7&& M) ]N " - - & -&67&&MG N"& #-'&6 # & 3# %& &!& -& 7&& M) ]N: *& ''#- -&6)",3

60 4A :"7 ">&" %&-&#",!9 &-&6*73 ";:"; -& #! - && *#, "- " " " "& K" )# &# -&:#"L =!.2%"I H&#%&" H ( I,, ) I & #-*. & #-'& * {, }, &-& Ö 3# &> %& 2? <HM %4'>A HO%H Ö & D. HU&-2& # H%&!* # { H ( ) } H U í = 2&!& HU { HU( ) } = 6 = ( H ) # HU & { } ` ` ( H ) = H H = { H` E =! } & & Ö * " ` ( ) = ( H ) { } í 2

61 4D ; ".F%"<" 6 8 H % 8 = H % -== = R = R! -==! ==== R! 830W D 8 \= 2? <HM %E- H % (%E- = E- > E = E) %E-, E! %4'>A < 40 % O%H H` = { % ( E%E- = EE- EE = EE) } = { H` ( E%E- = ) } %E- %E- { } ` ` ( H ) = H H = { H` E%E- =! } %E- \ = ( Ö) = ` {,( { EE }) < 40 } % E- H H % 8J?? 0$? 00, b? 0K=

62 @/ &#".%!""! 0K* 2& 2> K ^WV2 > $ N$0K (H 7 * *^ ' 7S * WVN$ 7 0K*2 H ' <H *$ &#"..%!""! - (#S0*W#< 0K* (#SWWK#< ^WV2 (#S$NK#< N$0K (#S0*W#< *^ (#S$NK#< WVN$ (#SWWK#< 0K*2 &#".6%""""; ".F %E? -%& & & "-9-!'' - 2& ## *& ''#6 *#;" 7& & *&# ''#6 " ", 3# & ";*& ''# ' # "-! "*!6)",'6 =!.F%" "I H&#%&" H( I,, ) I & #-*. & #-'& *

63 @ {, }, {, } &-&, &-& &*&# ''# Ö 3# &> ( ) 2? <HM %4'>A Ö & D HO%H. HU&-2& # H%&!* # { H ( ) } H U í = 2&!& HU { HU( ) } = 6 = ( H ) # HU & { } ` ` ( H ) = H H = { H` E =! } & &Ö * " ( ) = U ( { 6 H }) ( U í H ). { } %&" &&"#'&-*'& *%&7,& "7&&M` GN:MG N6 =!.:%!!"I Ö& > 2? <HM %4'>A HO%H. --& ''# ( )

64 @. Ö 3# &> * '&' &&'$, Ö 2? <HM H %4'>A.. &&'$, Ö 2? <HM HO%H "- :. &'$, Ö 2? <HM H Ö & D&:& ( Ö ) = ( II.2. Conjuntos Difusos D50,[ &2 2& *& W/.X6 "!# *& " 2 *& " 6 7 ", $ "(# & # ' "36Y * " # * ""7, *#, ", " "7', ' *, " *"#, "(#*3-,7 :" 6 2&, & 7,* 3 &:- 7 " * 6) 2"' 2!,, ""&:- ' 6 2& *& " 3 6

65 2& *&, "7M2& NM2&7N2&, & $ 2& & *# #' 6 "7 #' ""-$ " 2&& " 6 # & & #'-!& 6 & & 2& 7 K L : # - &")","& 2&Z,!! M! N6'&,"& *& 2&Z &:,!! M*N6 ", & 2& *&, &', & * #' *&6 " *& ""-$ 2& *&!&!' /:,!! #' *& 7 ' W/,X6 / M*N,"%& M! N6#'*&:*!! M*N:M! N6 G: #'- # 2&*&6 #')-$, '! 7"&&" - :&" 6"-9- *&#' *&, "! &!"!W/,X6 #'#-2, ) 2& *&" '<$&""7 "&, 7 &#&"962& :& & ""- 2&:"&!%&7 6,2& *&' &#" ""-$: " 3&#6 & ' & " &!,"M2!N,M-' N,MN6

66 ) $' &, &*& ""-$, &: '! W/,X6 " &! &' %& & ""-$2& *&6' &&,&& &! & 2& *&6 * * - &!6 ' "&#2& *&,"%&' / 3&#6"' ""-$":/" %&7-2& *&K"& L6 =!6%; =C, #- I&2&7 *&23- -, I" &*&# I [/, ] " & 2& *&- I - ( I & '& *" *& ""-$%&"&:&& *# 2& *&6"&&"# " 2& *&&' ""-$6 =!6.%; = =! I &2&7 { } I,.,. [/, ] 3# = 2 2 *&2& *& -&! I *&# ""-$

67 @0 - =, {,, } ( ) = / -, {,, 7%&3#H 6 2& *& "-9 7%&& !",2&,& &3# { } = 2 && *& ""-$, *"6 2& *& & "# &! &!6!- & *3# *&# ""-$6 =!66%; == & I &2&7,., I %&. 3# (,., ) = *&2& *&-I*&# ""-$ ( ) ( ) ( ) = ( 4 ) ( ) < < < > 4 2 7%&9H 6?B 2& *& "-9 7%&&23- -? - #'7*,&"%&9 '&

68 @5 0 x x2 x3 x4,.%!& K"; = $ 2& *& * %& - 3 9:76,-,cI:cI6 &2& *&2&7*" " &!%& 7 " 3& 2& *&6, "' ""-$ /6 =!60% ; = &2& *&-&!I 2&7 ( ) * " { } d ( ) I ( ) ; & 2& *& 2& 7 " &!%& 7 " & 2& *&6, " ""-$ ' 6

69 @B =!67%L"; = &2& *&-&! I G 2&7 ( ) * " { } d ( ) I ( ) "%&7; %&7-2& *&6 =!63%; = &2& *&-&!I 2&7 ( ) * " { } d ( ) I / < ( ) ce & 2& *& 2& 7%& "&:""-$":'&!"$" c6 =!6B%MN; = &2& *&-&!I á [ 0,] á# 2&7 á * " á { I ( ) á} ci'"' ""-$"":c6

70 @A =!62%MG; = &2& *&-&!I á [ 0,] á# 2&7 á * " { I ( ) á} á = 3&#! e &2& *&;:/I6 ci:ci "$ ;"6.% - á G O &2& *&-&! I á, [ 0 ] á 2, ( á á ) ( 2 á á 2 6% - á G P &2& *&-&! I á, á [ 0 ] 2, ( á á ) ( ) 2 á á ;& &2& *&,%&! ""-$ "7" 2&6 2

71 @D =!6F%"; = &2& *&-&!I ;" &&( ) * " && d& ( ) ( ) & " & #!& & 2& *&6' I!& &2& *& *"&&6 =!6:%G$; = &2& *&-&!I #, ;" ( ) * " ( ) = &&( ) & 7'- 2& *&, - 2& "", #:&# 3 $ 2& *&6 #''#,2&#: :&#- *& "",#:&#,!"6 "" 2& *& " && " "" & 3& 6 " - & 2& *& "-97 "" - 6

72 0/ =!0% "; = &2& *&-&!I 2& *&- I * ( ) = ( ), #-2& *& *" &"'& & -"&!,!:"#W/,X""&6 =!0.%&" >?& [/, ] [/, ] [/, ] "& (( ñ ) ) ñ = "&! ñ (( ñ ñ ) = ( ñ )) ñ... ñ ((( ñ ñ ) ñ ) = ( ñ ( ñ ))) ñ. ñ # ñ (( ñ ñ ) (( ñ ñ ) ( ñ ))) ñ. ñ4. 4. " '&, & * # 2& *&6 K"$"L & " '&6 &", & # # 2& *&,:, &,# 2&# *&6

73 0 =!06%!; = :2& *&-&! 6 : 2& *&-I, * ( ) = ( ) ( ), &"'& I" '& & " '&6 I" '&& --W/,X%&"&!,!:"#, &/"&6 =!00%G&" 2#>?& [/, ] [/, ] [/, ] "& "&!! 8 # (( ñ ) ) / ñ ñ (( ñ ñ ) = ( ñ )) ñ... ñ ((( ñ ñ ) ñ ) = ( ñ ( ñ ))) ñ. ñ4. 4. ñ4 ( ñ ñ ) (( ñ ñ ) ( ñ ))) ñ. ñ4. 4. ñ4 "'& &I"'&6 =!07%G&" &"'&,#,I"'&, * (( ñ ) ( )) ñ ñ. =.

74 0. &# 2& *& * "& "-# ' ""-$ " & I" '&6 & * &# - I" "'&& #6" # &&",&#&&" - " K"73"L%&I" 6 =!03%!; = :2& *&-&!I 6 :2& *&-I, * ( ) = ( ) ( ), &I"'& 3&#:"& &2&:&""! 2& *&6"&,"- 7 "-, 2& *&: & ""6 "7 I! 2&*&6 0%G$; = &2& *&-&! I,%& ( ) &" I"&

75 04 #:&# 2& *&"&&" -&!6 7% #$!C! ; =, : 2 2& *&-&! I &"' -&! ( 2) = ( ) ( ( 2) = ( ) ( 2) á I: á I -&!-#:&#6 3% #$" á GC" á G : 2& *&-&! I á [ 0,] &"' -&! ( ) á = á á ( ) á = á á ( ) á = á á ( ) = á á "- '<$ &", & & *#"&%& " 3# *&6, &!(, *&6&-'&,, 7&9" *& *&" '<$$"& # *&"26

76 '*& ' *& -&'WA.X6' *& * & ''#%& &- " MN: MN6 ' *&- *&, " 8 *&6 =!0B% = I&2&7 * ( I ) [/, ] %&&- I ( I ) @ 2 ( ) = / C ) ( ) ))) 2 2 &' *#&' *& &*&#--I&" *&I"-'& *# =!02%" = I&2&7 * ( I ) [/, ] [ 0 ] - = I &" *&-I

77 00 '- - (- ) = ( - ( ) { } & " I%& - ( ) - ( { } = & %& -9 WD,54X %&!! &#&* *&& -!9 &' *&6!7"7 6 II.3. Cuantificacin Difusa "7" #'*&3# &*#, & " & &* '<$, " 2& *&6 "-9*& & [ W/X6 &*# *& &!!', &'! W@4,B5,BA,DA,DD,/X6 9 W54X & & " &*# *&" & &* *& #';" &* 3:&!6 "-',& & - %& 7 3: &!6 "7,'&!&;3 " "%&* & # #'6 2&* 3 &* '<$ " M ":$ N, M N, M3" " " N, M3" " N, M "N6Y"*3-(3# #'6

78 05 &* '<$ '&2 & & & 2& *&6 &*, $ *, " *&" &* *&62& *&%&7 &* *& 2& %& "- *# &* 6 # &* '<$ &&6-, 3-27"&# 6 # &%& &* '<$ 7 & "7 &! '&2 &6),& &* '<$: & #!,&&", " ""6 & & *# " &* *& & &#K L6 ';&(,*&* -&:&* 6), & & "", & '& &*, : &" 6 * ': &%& "-#, " 6 &%& &* '<$ - &2& *&"&""& : ""3& 6 =!0F%= = - - & $"- '<$ > & & 2& - *& D ( R) %& ñ D ( ñ ) = 0: ( ñ ) = ñ D >--&): >-" &* -& %&-&&( "M3" "0N,M".N6Y" 2& *& '!6) &%& '!, &' ""-$ 2& *& ' &7 "-&* 6

79 0B =!0:%=#" D&&* *& %&D&2- & D &* ) 2& "6&* "M"" N,M":$N &* 6Y &-2& *&!& W/,X6 ) &%& # &' ""-$ 2& *& ' & # "- '* &* 6 &! &* *&" *&-!W/,X6 =!7%= " D&&* *& %&D&2-& D = [ &* %& %& " & 2& *& &*&# ""-$ 6) 2", '&. M "@N & &* -&, M":$ N & &* 6

80 0A =!7.%= D&&* *& %&D&-& ñ ñ 2 D D ( ñ ñ 2 ) ( ñ) ( ) D ñ &* &* '<$ 2& *&*&# ""-$" 6)2",'& 4 &* M &"@N & &* -&, &* M N&&* =%@AD"7EQ@#ADC-E =!76%= D&&* *& %&D&-& ñ ñ 2 D D ( ñ ñ 2 ) ( ñ) ( ) D ñ

81 0D = %@AD"7EQ@#AD-E &* &" %& %&&*&# ""-$%&,",:, &9 6)2",'&@M3" & &* -& &" : M3" " " N & &* &" 6 =!70%=" D&&* *& %&D&-& ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = > = < = ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ ñ D D D D D D D D D D D D D

82 5/ E*@#AD "E #'7:# &* 3K L:&!K L6 &!"& "7' &* *&, " "& '& 06 &* 3 M3N & &* -& Z"%& &* &! M) N & &* 6"- "7$' )&* *& G-&",&* & - "%& *' 6 & &* " M&*#!N6 3 &* '<$! & &* - *&"6& &* " M&*#(N,*&&WDX:W5X6

83 5 3 &*#! '& &* *&, & *" #6 "7 "" *": *".6 *" & 2& 7 " - &*#6,9"&&* *& - "&2&7%&*& # *&6 =!77%!= =,. I &2&7 & *&- I D &&* *& 3#'<$ MDI %&& )-!,*7MDI N3# ( I) *:5 36,, 6; & # *" Z : 5; & &* *&,&*#-2&7 : ;, : *&-2 &*# 2&# *& #" : ;,:36, ;::,6;6 &* *& *".& 2& *& " &!-&*#6# *". - " & 2& *&%& *& *&6 2& *& - "-9" & *&-&2&76

84 5. =!73%!=,6 I &2&7 & *&- I & *&- I D &&* *& 3#'<$ MDI %&& K )-!,*7MDI N3# D ( I )2",*:5 36,, 6; & # *".Z %&$: 5; & &* *&,2&- &*#2& *& : 36, ;,: *&-2&*#2&# *&#": ;::,6;6 "-9 & '& &* *& 3 &*# ( *" "7 3 9" *" :.,!"6 *"4&&* *& - *&%&&"* & =!7B%!=",0 I &2&7 2 *&- I D &&* *& &!-- I

85 54 3#'<$ M D 0 K %&& * *7MD 0 K ;3# D ( ) '&&# *"4M5 = 3,,6N6 M 5N&&* *&%& - %& M N,M3,N:M,6N,*" MN,%&""- 2&7M" N6 G:&#3"7&* *& *" 4: *"6' *# &# *"4 * " *"# *"#& *" I&2&7.%?",0 2 *&-I D&&* *& &!--I #&* *"4 M D 0 K ; "7"%&! {,,. =, *&-@: -&; = ( ) ( { }

86 *& - *& " &,%& * & "6 " *& "' 6 =!72%!= ==7 I &2&7 2 *&- I ;"[,],, / D &&* *& &!-- I 3#'<$ M3>,. J ' ",, %&& *7MD 0 K D,, ( ) 2 2 2" M 5 = 3,,6 0 $EW $E N6 M 5N & &* *&%& - %&M N!,M3,N! /6B: M, 6N!/6@,%& * "MN,%&""- 2&7M" N6

87 50 6%? = ==7 I&2&7 2 *&-I ;"[,],, / D&&* *& &!--I #&* *"@ M D 0 K,, ; "7"%&! ( {,,. =, *&-@: -&; = ( ) ( { } ) *&-@: ; = ( ) { } 3",%& *" *"4:.," %&, & & & & # &*# *&, &* ;"*":.6

88 # &* *&!' & # &*# *& W@4,0B,54,BA,DA,DD,/X6 ]' WD/IDDX!'#! " &* '<$, WDA,DDX 9!& & '& & 6 -[ W/X,) WB5X:]'WB5X6 9 W54X& "7 &&* *&6Y " %&, & & --, # &* *& - * 6 - & %&!"7>*6 & &#6 ".%"=!,.$" "* I&2&7 & *&-I D&&* *& ( D( I ) ) [ 0 "6% -"=!,.=! I&2&7 D&&* *& 0 : K *&-I%& ( ( ) ( )) I. D ( D ( I )) ( D( I 2 )) D ( D ( I )) ( D( I

89 5B "0%"=!,. =" I&2&7 D&&* *& & *&-I%& ( ( ) =/ ) I D D ( D( I ) ) = ( D( I ) ) "7%!"$",."-= I&2&7 & *&-I - ( ( I) ) I "3%!"",." I&2&7 & *&-I ( ( I) ) I

90 5A "B%"=!,6$" " I&2&7 & *&-I & *&- I D&&* *& ( D ( I ) [ 0 "2%"Q,6<$",. I&2&7 & -I & *&-I D&&* *& ( D ( I ) D (@) = @ { I ( )} = "F%$-CI",6=" I&2&7 & *&-I & *&-I D&&* I ( ( ) =/ ) ( D ( I ) = 0 ( ) I ( ) / ( D ( I )

91 5D ":%$-CIQ",6$ I&2&7 & *&-I & *&-I D&&* I ( ( ) =/ ) ( D ( I ) = ( ) I ( ) / ( D ( I ".%I#"Q,6<$",. I&2&7 & *&-I & *&-I D&&* -& ( D ( I ) D ( I ) = ( "..%!"",6" I&2&7 & *&-I & *&-I ( ( I ) = (!! ) I (

92 B/ ".6%!"=DLE" "" I&2&7 & *&-I & *&-I &* M>GN ( ( I) ) =! I "" ",:!' *# &* *&6 9 W54X - %& # "# ]' WD0X, ;%& * %& &" " "%& & && &&* *&- K)& )& 0:)&.L6 9 W54X"-9& # *"." "& &#'#-,&: %&'& & 6) -2" ]'WD0X&&#- 2&-6Y " # "#6 '" '# &*,&'*&3 &* 6Y- *" :.6 %&$ # *" &* -& 6 # 6@6 *"& *"%& " #&%& &* *&6 # MD I N, D& &* -&,! :&&-2&7@ I%&* ã K]L MG:D"@N:ã. K]LM

93 B =!7F%!! I &2&7 & *&- I D &-&&* *& ' *# MDI N ( D ( I ) ) = ã (@ I ( ãk@l#:@ -ã *# &"'&6 ( ã (@ )) = ( ã (@ )), ã. (@ ) ( ã = D ( (@ )) (@ ) ( ) ( ã. (@ )) = &"'& "& -!,' "'& :. *&7!! #&* *&MDI N6' "'& :. 2""*&2& #' 2&# *&6&", & MN6 '"'&,-'&!6%!! I &2&7 & *&- I

94 B. D &&* -& "'&. "'& ' *# MDI N, D = { } D I ( ( I) ) ( ) ( & " %& I. ( ) ( ) ( I &-'&, -2 &"7%& 2&# #' " MN6 ; ".:%!! I = {,,, } 39 = {,6B0,60,6 } #"#: I ;,= I ( ( ))) = = & = /60 { I } & ( ( ( ), ( ) ( 6.0,, ) ( 60,6B0), ( 6B0,60) (,6.0), (,6/ ) -&# 9 W54X # &"' # &* *&- '

95 B4!0%!!" = I &2&7 * & *&- I D &&* -& ( D( I ) ) = (- = ( I ) [ 0 ] %& ) (@ ) D - = I [ 0 ] %& - ( ) ( ) "! #"#"& '*& &' %& 9 & 6 WD,/,.@,.0,.5,.B,.AX & ""!&# & &* *&6-7 "" " @6 *" &* *& )-!! &* %& -& & & *"%& &( %&!,& &* -&6W.@X&-!" '& %&!,]'"-9 "WA,DDX6"-', * *""*"6 " *"# "!& # & &* -& & # & &* 6 "7 M*"#-&N6 *"'&

96 =!7:%&=!#" D&&* I&2&7 & *&-I *? -6 #DKIL" D D *"#-& DI, * ( ) = D D I ( ( ) ( )) {/ I } ( ) ( ) V V D D > I B%&=!#"$"$=#"C$" #% D&&* *& I&2&7 & *&-&!I D KIL*"#-& DKI,L DD &&* *&-& D D &&* *& -& D" D &&* *&" -&!,"":%&%&%&,';,&" $ &* *# D

97 B0 0%<$" &=!#" D&&* I&2&7 &) *&-I ( D I! ) ( D I! ) D KIL*"#-& DKIL ; "6%&=!#" < ^! I = {,, } 3 9 = {,6B0,60,6 }. - I=? I! I! <^!E

98 B Q@#A G:&*"#%&"!&#&&* &#&&* :!!6 &* & " #" '6), "7*"#M*"##"N6 =!3%&=!! D&&* I&2&7 &) *&-I *? -66 # D( I) ( I) " '# I ( ) = ( D 6D, * ñ D` ( ñ ) = ( ñ )

99 BB 2%&=!!$"$= " #% D&&* *& I&2&7 & *&-&!I ( I) D *"##" DI! D D & &* *& ) D D & &* *& )!,"":%&%&%&,';,&" $ &* *# D 7%<$" &=!! D&&* I&2&7 &) *&-I ( D I! ) = D ( I) ( ) D ( I) *"##" D( I) ; "6.%&=!! I = {,, } 3 9 = { 6.0,60,6 }. 4 - I - <WE? I! I! = {,6B0,60,6 }

100 BA 0 0 0,25 0,5 0, ,25 "7M*"#)N*"#%&"!& #&&* &#&&* -&6!7*"#-!! &* -& 6 D&&* -& I&2&7 & *&-I =!3.%&=! " **"#) #DKIL" O O ( I, ) O O I &3# I&&!"@ I O @ = ( I ) = /, $" &*, * "

101 BD = D D D ( ) ( ) = = 0 ( ) = 0 < ( ) D = D D D O O 3# - I ( ) ( ) - I = O / - I O O D -6D I, * ( ) O [/, ] ( ñ ) ( ñv I ) O ñ = F%&=! "$"$= "C$" D&&* *&-& I&2&7 & *&-&!I D O O O ( I, ) *"#) DKIL D ) O D & &* *& D ) O D & &* *& D " ) O D & &* *& " #%!,"":%&%&%&,';,&" $ &* *# a D

102 A/ 3%<$" &=! " >&&* -& I&2&7 &) *&-I ( ) D O O O ( ( I, ) ) D ( I, ) D O O O ( I, ) *"# DKIL ; "66%&=! " - 6 < V! I = {,,, } = {,6B0,60,6 } I=? -6 I! 6 a a a - - ( I ) O 4 = I = {,,,,, } 6I &L 6 - X O = {,6B0,60,6.0 }. -. O I L - O I X a <V!E O I

103 A R & "# &* *&, - ' *# & *" &* &", & *"#%& "- & 2&# *" &* "#,& : 6 *"# "M*"#8 #N6 =!36%&=!! D&&* &" I&2&7 & *&-I *? -66 #DKIL" D " KILD # KIL D " D, * ( ñ ) - ñ ñ ( ñ ) = D D - ñ > ñ ñ;""7-2%& ( ñ ) = D # D, * - ( ñ ) = D ( ñ ) - D ñ ñ ñ > @...A D ñ ;""7%& ( ñ ) =

104 A. :%&=!!$"$=C= Q $""K "=" #% D&&* *&&" I&2&7 & *&-&!I D " KILD # KIL*"#8# DKI,L D " &&* *&""&( D D # &&* *&""&( D!,"":%&%&%&,';,&" $ &* *# D " :D # B%<$" &=!! D&&* &" I&2&7 & *&-I ( DKI, L) ( D KI, L D KI, L) D " KILD # KIL*"#"# DKIL

105 A4 ; "60%&=!! I = {,, } 3 9 = {,6B0,60,6 } I- <NE? ( ) - I! ( I) ( I) ' #$& ( II.4. Lenguajes de Consultas Difusas & '& *%& * 3:! & *3-6)!WB@X& " &*3-6Y ' &# %&, *%& & &*3-, *%& - 2& *& "7 & 6 '& & & -& 3 :"# 6-2 &J": "W@BX,) :"WBBX:["J!:\ *&# -" #:"&# "6 ", '&2: " "- 2& *&: -&)--$6 8,): W5D,B0X &&" #:"&# *&& 2& *&,-&)--$:"6

106 88 " 88&*&(&"%& *&6*& &-$ *& &# *& *"#6 &',& -$ " ;, #& >*&%&;"&*(& *& ", " *& 2-26 " " & ;" *&, %& *& K L, & *&," * '<$: "9 - ;" *&6! & &* *&6 %&& " & " & & *& %&"7)R> " -$ "2 & *&6 " "&"(! >6; " -$ " & *&6",*",&"# & %&'&& & 7:-$ *&6 6@6.6 >] >]&*&(!*& &%&=" "2 W5,5.X " 3 "& 6 $ " " &: 3 >, #, * &&:* 6 >] " 3 *& 2&#: :&#6-7 " *&!: *&6 " & &* *& # * * *6 " & " &# & * >6 '&( &!"$" *#!&&6

107 A0 >* >*&>3 # $ 2&*& 3&K *&L* >&%&,&",9"7 ",%&" &!" *& & '&2>6 >* ; & "*3- &%& " &*# '<$ - 2& * &,!9 3# > && ": " &* *&6 "-9 " & &* * -;%& **6 )!&# &, &!""6 "7 " %& -!# W@,AX%&! &7%& &, &,I& & *&, " %& " & & '&2 *& 6 "" 7 %&!# - & >*Z&", & -&- && &* *&6 " )* )! WB@X -2 # $ 2& *& " 6Y&3#"- 8 " &I," *"&# "- 76"(&*3- %& &3 & " 6 )!& *"2 *3- %& " &# *"#6 Y & * *%& &*3- " 6Y- %& *%&

108 A5-2& *&""",",$, %&9*%&"7'6 Y && 3# *& >, " 3# "6 3#, " >*, &" '! " 6 & -&*& & %&! &>*,- %&9"!%&!&&6 Y &"9!&#3, &, 3 & " # &! *&6 "9 -&I & # *&"& & 6*%&",'&,-I&;2& 96Y &,*", "= "9 " &* "6 " ) 9 W54X& '# "#3&* "3# 9"&* "&- 6Y & 7:'&2 & >* " 9" &* "6 *# & 9 &* '<$ K &* *&L & &( " : " 3 '<$ KM3" " " N, M3" "4NL6&-2&!& " *3>*&&* *&- 6 '& * & " # # &* *&6 # &* *& - #! & K),]',: [ L,9 - %&&*%&""-& 3-6 Y - %& *%&!7 &*3- &

109 AB ' &;" #, ' *&6-2! *& &"7# &* *&Z &* & " * %& "- &*3-Z: "!&# &* *&"7"26 *!#, #%& & & &*#&!6 Y & # & 3# 3 >*!# *&:!2 &&* &!!( &'<$6Y &3>*!# *&6 &- ""# -"," *# '"!&#&%&!&&* '<$6 II.5. Consultas Cuantificadas Difusas *#: "7 >* -2 #! -2!W..XW.0XW54XWB@X69-2&& >* %& * "7,!'""!&# & &%&!&&* *"6&-'&7 &!# 3:"7 &, & -2! %&" && &*& " >* -%&"&6 # &&--7 F'- :#, & : #,: # 2& *&6& & >*&2& *& *,, &# *&&' &#76

110 AA ""'""-'< >>*6), &"7%& & & : # * 6 &# " &3#"7"7 &6 -%&">* & 7&&,& 7&&8 : & 7&& ` G,%& 6 "7 && & 7&& :#6Y*-& K3 -&L%&7 6-&&2& *& : '; ' *#6) ( 7, # "7 &&"7,9 ',& -&7&&6 7&& "-9 *& -#%& ' 2& *- 6G: -#&!:&!6 -# &! && * ;" & - 6 & -*":' ""-$;" & %& 6 -# &! && *&!"$" *#%& -&%&*- 6 7&& 8 ) & 6 & - & %&*7&&6)(7, # "7 &&"7,&#7&&6 7&& ` G 3# *& # 6 Y * # & &7 ' *#6 *%&*' ( 6 #& *&%& &!& &%& -& #6) ( 7, %&$*"" 3: "7 *& " >*67*-2 )!WB@X6 -%& & " & && &* *& 7&& ` G "- *&6, # &* *" 4,, *# *" 4 K*#@5LZ

111 AD &"""- *"6*# 04 * "7*" &6 2".@ & &%&" &&&6 =!30%"<" "I=!=0 H &# &-& H ] 0 [ D&&* *& *& 3# &>* 2? <HM HO%H D (- - ) 2 - && %&"D-&:& * " ( ) = E = ( D( - ( ) - ( ) - ( ) )) H 2 ; "67%"< 85 =: ; :, 6; :,, ; $WE D- 5=

112 D/ 2? 0E7 <HM M-! = [ ) =, &) = = && O%H &* '<$"-9& & "- *&,& &' "6, # &* & # 2".0 & &,"%&*#0@&"7*"6 =!37%"<" "I=!=7 H &# &-& H ] 0 [ D&&* *& *&K *&L [ 0] 2 3# &>* 2? <HM HO%H D ( )(- - ) && %&"D-&:& * " ( ) = E = ( D( - ( ) - ( ) - ( ) )) H 2 2 ; "63%"< 8 * = : ;: 3,;:, 6;:,,

113 D ; $EV $EN $EW $E^,X $EE D- 5= 2? 0E5 <HM 3 ( 0E80E90E 70E6 ) = [ ) =, = && &) =! O%H ) *#,*"4"7"%&!*"K3"L,: *"@%&!*".K3".L6), & )& B:)& /,*".& & *" &* -& # 6), '& & & *"4'&,"& >-&:, '&,& ' "!9K/#L6!7%!",7",0"< "=#" H &# &-& H ] 0 [ D&&* -& *&K *&L [ 0] 2 2? <HM HO%H D %&! 2? <HM HO%H D ( )(- - ) (- > - > - > ) 2 2 & *&&:!

114 D.!3%!",7",0"< "!" H &# &-& H ] 0 [ D&&* *& *&K *&L { 0} 2 2? <HM HO%H D %&! 2? <HM HO%H D ( )(- - ) (- - ) 2-2 &-$ ' "%& = - %&!,-"!&& &-%&" &* *& "- &! &, 2? <HM HO%H D (- - ) %& >* -& & # & # &6" " -%& &6Y& "7 - '&2 & -- 6 &-& ""&& &,'& * &-&& &-&!& &3Z: 7&& -%& -*&-#6 & >*3#' *& >6" >, >* : %&! &"&: '& && 6)!WB@X& %&!6

115 D4 M N " - ' ""-$ &! " K * & -%& 3L & 2& *& K& & L6 M N"7"'# M N6 M N"-' && &&!$6!9 & M N, & *"& 3 %&! M NM]N6"- '##': M N, - 3 &%& %&! & M NMNWX6 M]N&* 36Y"-' &&! " K * & -%& 3L *& "# *& '; " & &-&6 MN K&* &!L"&' &&!"K *& -%& 3L *& "# *& " & -%& 6 -%& &! " & K*&# ''#L, 9 & " &!"K* -%&3&L63# *& "" " "6 >* M N,M]N:MN& "( &* '<$, &'&*# *&6 '&7 & "&* *&,93IJ::IJ6 "3IJ&& &- & " & &&* *&&' >6&& &!&& # &* *& *" 6 *"(# *# 006 && &, & &*, """%& &* &!!# 76 2".5 & &: "7 &! && &6

116 H &# &-& H ] 0 [ D&&* -& &# &-& -& # *&K *&L 3# &>* 2? <HM HO%H D ( 2? <HM O%H -) &?: ;D- 6-0!&:& * " { } ( ) E H = ( D( -( ) )) ; "6B%GS@!=.A M 6 0$ -6 8$EWE 8 D- 6= 2? 0E7 <HM O%H 0 2? <HM O%H b = Eb > =! & M]N:MN>& "( & &* *&6 &*# - * & %& *&"#"& -%&36

117 D0 "#& - & & "# *& K" *&L6 &*# && & *".6&& & " ":IJ6 *"' &: "7*" *# 056 2".B"&&%&" &&%&$& &6 =!3B%GS@!=6A H &# &-& H &-& H ] 0 [ - & "# *& D&&* *& &# &-& -& # *&K *&L 3# &>* ( <HM O%H -) 2? <HM HO%H - D 2? &?:; D- 6 -K!&:& * " = { E H = ( D( E - ) } - ( ) ( ) ; &85-6 $EW D- 5=

118 D5 2? 0E7 <HM >>>! 2? M- <HM O%H O%H b = Eb G: -&&& &%&!& & # &* *& *" 6)", & &* -&:,'&,& #*6!B%!",.",6=#" H &# &-& H &-& H ] 0 [ - & "# *& D&&* -& &# &-& -& # *&K *&L ( <HM O%H -) 2? <HM HO%H - D 2? %&! 2? <HM HO%H D 2? ( <HM O%H( - > ( ) '&,& &* : #-,:%&! "3IJ6), - & ""!&#6 $,-"!&-%& & *&"-, & -

119 DB,& D&&* -& 2?<HMHO%HDK2?<HMO%H*L.,& D&&* :-& #6 ( 2? <HM O%H -) 2? <HM HO%H - D %&) >* "-9 * & & 7&& M) ]N:MG N6"", # 7&&G & - &*&# ''#6 3# %& >* %& &* '<$& & MG N, &' &&* *&6 2".A"&& "*" & &* & >*6&-*"67&&` G - & #6&&&':"7 *#0B6 =!32%"I=!=. H &# &-& H ] 0 [ D&&* *& -& # *&K *&L 3# &>* 2? <HM %4'>AD H - &2 D- 6-0&: & * "

120 DA ( ) H ( E = ) ( D( H -)) = { H ( E ) } H = ; "6F%,.I= 5 36, -6 $EWE 8 D- 5= 2? 0E7 b <HM b %4'>A M- H ( = MH = [ ) ) & &* " "& 2".D6 &-*".6*"(# && &7 *#0A6 =!3F%"I=!=6 H &# &-& H ] 0 [ D&&* *& -, -2 *&K *&L 3# &>* 2? <HM %4'>A D - H - 2

121 DD &2 D- 6-0&: & * " ( E = ) H ( ) = = - 2 { H ( E ) } H = = ( D( H - ) ; 5 36, -6 $EWE 8 D- 5= 2? 0E7 b <HM b %4'>A M- = H O%H = [ ) & *".& & && *"& >-& -& #6& &* -&& &%&! )#B6!2%!,6,."=#" H &# &-& H ] 0 [ D&&* -& -, -2 *&K *&L 2? <HM %4'>A D - H - 2 %&! 2? <HM %4'>AD H (- > ) - 2

122 // )," # )#A& &* # -& #,& *"&&%&&"6!F%!,6,."!" H &# &-& H ] 0 [ D&&* *& & # -& # *&K *&L 2? <HM %4'>A D H - %&! 2? <HM HO%H %4'>AD H - - %&!, -"!& & -%& &* *&"- && *" 2? <HM %4'>A D H -

123 / II.6. Balance del Captulo ":$ 8-8 :! & >6&& &-%&", ":"6" >& *& ''#6%&$ &*"(# &6 &!' '$-, "-"2" &%&& Z,!$7-&'"!'#76 '& %&" & & " " & &6 - $ %&",%& & 3" '&2 &- #'6 &#' -" -!"" * * && %&"6 %& " & " :&" *%&& 9 &&6,! &3-6 "-2" &- 2&*&,& %&" "7': & &3-- 6 : $ 2&*&%&!-2Z á I:&,"&:;!&# &Z: '*& &',"&:""7 :!&# &&* 6 &* '<$ '&2 & & & #" =& 2& *& * & "76 Y &* "*3- # 6

124 /. &* *& *, & &(, -& : Z:,&"",, :&" 6 G:& &* *& *"MD I N, *".MDI N, *"4M D 0 K EEE NZ: *"@M D 0 K EEE,,,N6 *"4& *" *" 6 & *" *".6 # &* *& -2 #!!' 6!' -[,) :]'6 ]' & #- & "# 2&-6 # MD I N! & 3& &-2&7@ I%&*'& 2&# " MN6 # ]', "#,! & ' *&6 &" & ",. " I %& ( ) ( ) ( ) I. I,, # "#! D = { } D I ( ( I) ) ( ) ( ) 9 W54X & # "7 & &* *&6 Y " %&,* & &--,& # &* *& -* 6 # "# ]' &" "& & & -- 6)&"#&>*6

125 /4 9 " %& '& * *"."" & &- 6),'-2&- *"6 &* *& *"%&& &%& &* *& " & *" *" %& & 3&!" &* -& 6 %&!%& & *" &'!"&,","-', '&#&#*" ""6)(#(#-2 *#:*"(# *"6 *"# -&'& # &* -& &#&* D ( I, ) D V ( I, ) V D ( ñ ) = D ñ ( ) D I ( ) - - / ñ I ñ > I *"# #"'& # &* &&* D ( I, ) D U( I, ) ñ ( ) = ( ñ ) DU D E *"# ) ' & # &* &&* -& ( I ) 3# I ñ = O D O ( ) ( ñv I ) D O O O D, D ( I, ) O I & *"# 8 # "-& # & &* &" & 2&# &* "# ( ) D ( I, ) D ( I, ) D ( I, )

126 ñ = D ( ) ( ñ ) D ñ ñ ñ > ñ ñ ;""7-2%& ( ) = ñ D ñ D ( ) = ( ñ ) D ñ < ñ ñ ñ ñ ;""7%& ( ) = ñ D '&2 &*3-- " *&, "7 ">*6Y;%&" &%&& -26 && & >* %&!& &* *& -%& ", ": "6-2 *"(# "7 &6 -%&"& &&&* *&7&&` G, "- *&6#&* 4 (-, -, ) 2?,,, <HM H,, H O%H D. - -%& ", &* "-9 & & "- *&,& 7 &' " 6 2? <HM HO%H D ( )(- - ) & &* -& ' " 9, #&* %&!*"46 ",&%&&* *&-& -& &' M N6& &* *" 2? <HM HO%H D ( 2? <HM O%H -) "&%&&* *&& & &' M]N:MN ( <HM O%H -) 2? <HM H O%H - D 2?

127 /0 & &* -& #*,&*# "-*"6 ", &* & & - "'&,%&*& #6&-*" 2? <HM HO%H %4'>A D H - ", &* "-9 & & - "&&-2& *& '&%&*& # 2? <HM HO%H %4'>A D - H - 2 & &* &( -& # %& - &-2& '&,&%&!*"6 -"!&-%&" &"- & 2? <HM HO%H D ( ) 6 -"!&-%& &"- &,& D&&* -& 2? <HM HO%H D ( 2? <HM O%H -).,& D&&* :-& # ( <HM O%H -) 2? <HM H O%H - D 2? -"!&-%& "- & 2? <HM HO%H %4'>A D H -