Fuzzy SQL

!"#$%%%&'('INTRODUCTION....................................................................................................................................... 1 SOME NEW DATABASE CONCEPTS .............................................................................................................. 2 Conventional Database Joins................................................................................................................. 2 The Fuzzy WHERE statement ................................................................................................................. 4 UNDERSTANDING FUZZY SETS............................................................................................................ 5 FUZZY SEMANTICS VERSUS FUZZY DATA ................................................................................................... 8 TUNING FUZZY SETS TO QUERY SEMANTICS............................................................................................. 10 THE NATURE OF FUZZY SQL QUERIES........................................................................................... 12 !"#$%#!"&$$%%$%'%$!"("$%#! "")(&%'('(%*'(+(,(,(-&%../01&*'&(,(,2*'&&&%'%('(-3'&4-(../01&/&5/+(.(6&%( -&7/,'&&&''&,+-&../01,((&(&7,/&'&((8''(+'-/%/7/../01&&9(,:9: (,'%('(('(+-&;-&(&/(&/''9:& ,/-&&/&4+(+(.(,../01&/&&&%(( +COLUMNS ROWS RELATIONAL TABLES SPREAD SHEETS FUZZY SQL BASE RECORDS UNIFORM DATA ADAPTER FUZZY SELECTION AND RANKING RANKED RECORDS 4../01/&)(&%%*(%&&'((&%8+4&',''-&,'../01(&(%%((-/,9(,:(/''&&+-&&/& ! " )(#6&'(',(-&-+(+&&(%/,&((++7(&,(,(4-&'-(+-'8,(-&&4-5,*&,'(&(/(+(-,%&2'%('((&'('((&&(+(+&%&%&-&+(.(-&COLUMNS ROWS KEY (IDENTIFIER) COMMON DATA COMMON DATA <(:-&4-& &+&&'%(-&(7(,'8/ 4& '(-('(&=/&(&(&('(('&(&%*/,%-&(&8/4-&'/'(('%(&,'(((-(&('(((-&&((&'(&((%-&('(4&, &&-(+&&''('('('((-&&/&&>((#" $4-&'(('+'&&')(%&&'-&('((&,'(&%(+%8,2+(&:&(,'(+''&&(+(((+(-&&''0/1(++01)(01&&'%'(&/ %((&( %'-&((&( %-&&-3((%'%&,-&%'(7/-&',(&( 1 When a row is identified my multiple columns (such as Store Name and SKU for an in-store inventory system) then multiple records clustered on one of the key columns can also be rapidly retrieved. Thus all the stores that have a particular SKU in-stock could be found very quickly. 2 The concept of shared domains is central to the philosophy and mechanics of a relational database. A domain essential defines the permissible values for a column. Thus two columns share a domain when they are restricted to the same set of permissible values.?'(&%'0/1(++&&-/*((+&)(&(&:-&4(/-'((&(,(-''(/4)('-'((&/-//(,(-((,(('&,'(/5 (&*(&(,4)('-&%/(,&5'(/((/+&''/&&&-&NAME YEAR_FOUNDED LOCATION EMPLOYEES SIC CLASS NAME YEAR PRETAX AFTERTAX PROFIT INVESTMENT DATABASE 4)(&(&:-&&%%(,('(&%-%(@#(@#((*('&/-%&&(##/&4&&'017/%&(+8,%(+ ! 4,&(,where&(&7/,'/'(('%&-&('(/(%(,7/('&%'%&&-&'+$&&%&'&&%8&3((+%-&('(+(%-%'&/ $ NAME YEAR_FOUNDED LOCATION EMPLOYEES SIC CLASS NAME YEAR PRETAX AFTERTAX PROFIT INVESTMENT DATABASE NAME PRETAX EMPLOYEES JOIN 40/>(A'&& ((''&',(7/(++&,&4& (&&,7/&(%-(&/''(,%&9&(+01%'('(('(/(-,-&-&'&%-&'(('(%'%&&'&(-/'+'(&(+'&(& ,((%&(&'-'&('*&, '&&'-/%&(-'&(-&(*'(/%@((*-%#/&%(-&'( +&*/'&((,7/?%8&&&((*&'( % & ' ( ../01('&(%%/,(+(,(,(-&9&(+&7/,'//'%/%(-&('('&( (-&(*&(+&4&'('&&&+(,('&&( */'(8,&'&((&6&-&&(+7/8"#$?../01&8*''((((&' ,&',/(+(+,*('&&'&5 4&8(,'('-&7/&&'&&%&',-''+(((/-&&&(*7/&'&,%(+%& &'%& (&-(&%(:&(%4BC24-,B+(.((27( &,,(+&'(((+-/&'&&,,(+ (//(&&( ((-,'8&(((, &%4-(../01'&&&&/5/'%/%(( &(&(+/4&&',(&('&,7/('('&,7//*&&(+/+&+&('& ('(('&(&/'(,((,((&((,/7/)(%%%&%/&(%%/,7,/(+'& ,-&&((/(-&'%,('(&,&%%8,../&&-(+-'8&,../01(&%/%8(%/&(-&'7/'&&) *D&,&,%'(((+'4&&,('(+',E+((('(/''('(%,.&&, +'4',-((,../+'&,&&&''(, (+&-(+(/4-+,,('-%(%&&/&5(( +'(+&-,&&(-,&)(,../+'(+& '(-&(&&%%&&/-&&,'(+'(&&/%/&,,('-%((&&%'%,('"&& (,../&&&-/*((+'(',4)('(((&-&%&&',/-(/(5(&%+&--(/ 4&-%-(/(4! &%&'!,&-(/4(&&,(&} 6 { ³ = height TALL m 4+%%&E8m ('&-& +&%&%&&8&('&,4.0 4.5 5.0 5.5 6.0 6.5 7 10 Member of Set Height (In Feet) 4&411:,(( ?'(&&-&''&',(&&&-(/ -%(&,&((&(&-&,&4&&(,(,,(+&(4%&(&*,(('&&-, 44-(/&/'&F((,,((7&('&& (4%&&-(/&('&&,''&&,'('(&(&(+'&&&4&'(&(&&(('(%'(& %-(&-%(&&,&'((&)('&,4& (&&(,,((&(+&('&&(4--/(+(+,(('&-&/&,&(4&-&&'(%('(&&+(,'(-&(&/' 6&&-&+!&''/&&%&-&+-+(.NAME HEIGHT WEIGHT SEX AGE RESIDENCE NAME DATE ITEM/SKU QUANTITY PRICE STORE DATABASE ITEM/SKU VENDOR QTY ON-HAND BACKORDERED !4:-&48(+(&&(+(,(,(&'&,&,&'&4/%(,(+%(*,(%-+*(&&& (&,%(&4-&%&,&-(&-&"#4&4-Name Height Weight Age >'8&( 6G # (& !6G D6G &&/ !6G $# B6D/ 6G !$( 6#G #$$ ),%&(,((,4(/(&&*,(+&'4'&((+017/%8&(+8&5 ##&(!B(/%(&&',&4-4-&%&&%(&"#4&& Name Height Weight Age Tall >'8&( 6G # (& !6G D6G &&/ !6G $# B6D/ 6G !$( 6#G #$$ 7'8%,+'(&%&(""&&&,&'&&&'&D((/'&-(+'+.&4&&(/ %/,&(+'&+'(&'('/%''(+,(( ,4-/%(+-(/-%(4((4)('&%%(/,%'&&(-* &+-(''-'-&+(&(%(%8(+(+-(/(&(7/'(+&((+,7/(('&('&%&(&-(7/&(8(%(?%(&-%/,*&&(+'(',44& -(+&&,,../&#,../&&(&(,../&&/,('(+(&8(%+&('/,(-(&D(/,((%('(//,(&'&&4&(*B'('&&'&/+%,&&%,/(/,%+(8,(&&'%-&",(-(&,../&&(&+, -&(&,",((&4&&6&8,../&%'+,(,4+&%&&,../&,((4.0 4.5 5.0 5.5 6.0 6.5 7 10 Degree of membership Height (in Feet) $4../4:,((%'/,,(8(,&((,44((+ +(/('&&+&&-&,('(,,../&)&&'&+%+,-&+&%&%,,,&-&,H#$I(,../&44.0 4.5 5.0 5.5 6.0 6.5 7 10 Degree of membership Height (in Feet) [0.43]%../D-&& ?&(-8H#$I(J)(&+,,,&-,,../&4?'(8-&&&&,'-/ &,&((4/(&%7&(&8%'-,,,%'('4J %',,,&(,'('4J 4&,../&8&'('84(*&&&+(+,-&,('(&4+(,(-,'&%%('&&('&((+,,../&9&(+&(%%'((%,(4'&& %&+'(+(7/&(&5 ##&)! 2','&+&'(,../&4(&+, -&&(4&8(,7/&&+%'''&6& +&-,4,../&4&+,-&'0/ -/)(*0)K&&(8&''&''(+%%/ +%7&4-&%&&&,&7/# "#4&& Name Height Weight Age m(Tall) (& !6G &'&&/ !6G $# &'( D6G &%$ ( 6#G #$ &%B6D/ 6G !$&!>'8&( 6G # & 4&(+-&&(&'((+-/'-/(*%'(& '&&&-&(4,../&'&,((,4'&(&&-(,(&+&(&(&+( ''%-+''(+&-&*;'(,((,((,4-/'(+(+-&(+,&&,-&,('(+&&&&-+(.(,&&(+(" '(('4(/(+('&&%((-'8+( 4.0 4.5 5.0 5.5 6.0 6.5 7 10 Degree of membership Height (in Feet) '<,((+4../)(&&(,4%'+('(+(("&8(%(&E%' D-&&,,,/-%L(,*(G (4-$&%&&&,&,../017/&(+(%,../&''(+(-&&"#4&& Name Height Weight Age m(Tall) (& !6G &'( &&/ !6G $# &%% D6G &$' ( 6#G #$ &!$ B6D/ 6G !$&>'8&( 6G # &(( 4&(%&,-&,('(&-(+&&((,'-,../&&4/)(&&'&4/(((/((/%(&&&-3'3+(-%/'('&*&&(4&,,../&,'&((+,'('4&&((((,../&& '&('&,/7&''('&,7&")- #)<(+((+&,%&F(&"& &'(',(,((+, %&A((+'((+,%&HEsemantikoV&+(,'(I&'(&7('%-&7&(,((+&(+-&(',&%'%%(-/&'& &44&((+&*&&(&,,../&-&,('(&(+(+ -&,('('(+&%%(%(%&&7/+# &&&-/&%(+,,,(-&-&(&,4,../&4.0 4.5 5.0 5.5 6.0 6.5 7 10 Degree of membership Height (in Feet) 4.0 4.5 5.0 5.5 6.0 6.5 7 10 Degree of membership Height (in Feet) 4.0 4.5 5.0 5.5 6.0 6.5 7 10 Height (in Feet) 4.0 4.5 5.0 5.5 6.0 6.5 7 10 Height (in Feet) (:,,(&,4../?(/&+(,../&(../01&/&/&&8/&,%&(-&& /&(''('%& (.&(+((-*/*'&-&,('(&(+#&+(&,'&&,,'(8'(('(;/(/(L(G/,('(,&'(+(*((+ &&,% +4(,,../7&-'(%(%,(,../&7&'-((/,../&&?,../&&%%(,('(&( &+''&'&,'-('('&16&87/,4(/()('&7/%(&-&-(/(,,((,/&%&'(&4(017/&##&( #&*! 4&,&7/&,'(4-B(/&(+'&&-4(/"# 4(/&&& Name Height Weight Age Tall and Heavy >'8&( 6G # (& !6G D6G &&/ !6G $# B6D/ 6G !$( 6#G #$ ,%+('%(-&&,'&&+-('(&4/*'&/-'&,&-(/(&&-/'&017/?'(--/'(+7/%&'&((+,../ &(5 ##&)#&+'! 4((,&7/&-&5%%('&&-4(/)( &7/%('%'(&&/&(+&%&(&&-%/&(&'('180 185 190 195 200 205 210 215 220 10 Degree of membership Weight (In Pouinds) 4/../%%(%,'&%+'(%'(,(& -&(/,../&4-!&%&-&&,',%+&(-(8-/-&& "#!4(/&& Name Height Weight Age m(Heavy) m(Tall) (& !6G &' &'( 6#G #$ & &%&&/ !6G $# & &'( D6G &(( &%$ B6D/ 6G !$&(( &!>'8&( 6G # &(( & ?../01(,'&&F(&((&&/F -&&(-4(/,../&&?(%(&%/'-(-&,('(&&,,',7/'(-*&&((84%&,'-((+&&5D-&D((D-&+2'&&%(&4-&&%(, -&&%8&"#$D(,4(/&& Name Height Weight Age m(Heavy) m(Tall) Min(Heavy,Tall) (& !6G &' &'&'( 6#G #$ & &%& &&/ !6G $# & &'( & D6G &(( &%$ &(( B6D/ 6G !$&(( &!&(( >'8&( 6G # &(( & &(( &/'(&(,-&&'(&(&&(%8&((4&(&%&(*'((&&$ -&+, -,(01&(&4+D-&''&(,(-&&&4&&,'(4-"#%+,4(/&& Name Height Weight Age m(Heavy) m(Tall) Avg(Heavy,Tall) (& !6G &' &'&'( ( 6#G #$ & &%&!'( &&/ !6G $# & &'( & $ D6G &(( &%$ & B6D/ 6G !$&(( &!&( >'8&( 6G # &(( & &! 4+(+-('&-&,('(&'&&',%&('&&'&&(+%(+-&%'%&&%&(4-!&+'(,('&+(,'(&(%((,&'('& .-&9(&((+/('&,../01&,/&/('/&%7/ (&&,('(+-&&16&'*-/ *((+../01('+)(&'&8(++&8(+,4/(D+'&&B(''(((01&(7&& ,(%%(-/+&%&/-%(($D+4017/&(##&( #&* #&*#&,*! %&4-('&&'&('(+'&,-&&('%(/(,&' 4&(/(&&4(/(D+"#'4/(D+&& Name Height Weight Age Tall, Heavy, And MiddleAged >'8&( 6G # (& !6G D6G &&/ !6G $# B6D/ 6G !$( 6#G #$ B('*((+-%'(&'&&%+-'(&,%'(*'&-(&(7/?'(--/'(+ 7/%&'&((+,../&(5 ##&)#&+'#&"-&! 4((,&7/&&-&5%%('&&4/(D+)(&7/%('%'(&&D+&(9(84(/,../&&D+&(&,../ (-&& & +&%&(&&-%/&(&'('25 30 35 40 45 50 55 10 Degree of membership Age (In Years) D+../! %%(%,'&+'(%'(,(&-&( D+,../&4-#&%&-&&,',%+&( -(8-/-&& "#(4(/(D+D && Name Height Weight Age m(MA) m(Heavy) m(Tall) &&/ !6G $# &( & &'( >'8&( 6G # &'$ &(( & ( 6#G #$ &'( & &%B6D/ 6G !$&$( &(( &!(& !6G &&' &'D6G &( &(( &%$ ?&*(&(../01%,('&&&&+,-&(D+,../&+%,&(&(D/&+&,-&?('(&,(&'+-&4- (&&,&&(%-,&"#4(/(D+&& Name Height Weight Age m(MA) m(Heavy) m(Tall) Min Avg ( 6#G #$ &'( & &%& &$!( &&/ !6G $# &( & &'( & &$! (& !6G &&' &'&&!!( >'8&( 6G # &'$ &(( & &(( & (( B6D/ 6G !$&$( &(( &!&(( &( D6G &( &(( &%$ &(( &4&&(+../01'(&,'(((017/%,('&'(&(&,()(../01&''&&'((,7/(&'+-'&,7/&%'( &&(-,'(-&('&&-(&&,'(((017& &/('&&4../01'&8&-('('&&-/('(+ '&&+((,7/'(+(+&(/&&(%&&'&'&&(',&'( '( &"('7/+ (,(&'&((' !"#$&%%%&'('M##$'()(+('11"49"##