1995 - fuzzybase - a fuzzy logic aid for relational database queries

8/7/2019 1995 - FuzzyBase - A Fuzzy Logic Aid For Relational Database Queries

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FuzzyBa se: a Fuzzy L ogic A id forR e l a t io n a l D a t a b a s e Q u e r ie s

D. G azz ot t i ~, L . P ianc as te l l i 2, C . Sar tor i 1, D . Be ne ve nta no 11 - Universit~ di Bologna, Dip. di Elettronica, Informatica e Sistemistica2 - U niversitA di Bologna, D IEMA b s t r a c tTh is pape r presents a similarity query generator fo r DBM Ss. A user query wh ich tur nsout to be too restrictive and returns an em pty set of row s is relaxed and transformed into asimilar one: the result ing set o f tuples will resemble, at some degree, th e set d efined b y theoriginal query. Th e relaxing activity is based on fu zzy logic and the system provides a use rinterface to express the query, to obtain suggestions o n possible search va lues and to va l-

idate, o n the basis o f semantic integrity rules, the ex pressed conditions.1 I n t r o d u c t i o n

Ex pe r t s ys te ms , ne u ra l ne t w orks a nd fu z z y s ys t e ms a r e d i f f e re n t w a y s o f i nc r e a si ngm a c h i n e in tel l igence, bu t , i n m os t c a s e s , t he e f fe c ti vene s s o f a s o l u t i on he a v i l y de -pe nds on the e f f e c t i ve ne s s o f da t a a c c e ss . F u z z y l og ic [1 , 2 , 6 , 7 , 8 ] i s u s e fu l bo t h i nA I a n d h u m a n r e a s o n i n g a s w e l l a s in d e c i s i o n m a k i n g a n d i s w e l l s u it e d i n s e ar c h in gprob l e ms w he n w e c a n de fi ne a s e t o f s e a r c h c ond i t i ons , bu t w e c a n a c c e p t a r e s u l tw h i c h resembles , a t s ome de g re e , t he e xp re s s e d c ond i t i ons .

A c o m m o n D B M S i s d e s ig n e d t o p r o c es s exac t quer ies , e . g . se lec t * f ro m Tw h e r e n a m e = " J o h n " . Y o u a r e o f t e n a ll o w e d t o se t u p q u e r ie s w i t h p a t te r n m a t c h in gs c he me s , bu t m ore t ha n o f t e n suc h s e a rc h i ng f e a tu r e s a r e r e s t r ic t e d t o t he s i mp l e s t se-lec t 9 f r o m T w h e r e n a m e l ike " J o " , m e a n i n g to r e t r ie ve a l l r e c o rds w i t h t he f ie ldn a m e b e g i n n i n g w i t h t h e s t ri n g " J o h n " , s u c h a s " J o n a t h a n " o r " J o h n n y " .M ore o ve r , i f a que ry " f a i l s " t o r e t r i e ve a ny da t a , s i nc e t he r e a r e no r e c o rds i n t heda t a ba s e w i t h the s pe c i f i e d a t tr i bu te s , t he r e i s n o w a y o f m a k i ng t he D B M S re t ri e vere c o rds w i t h a t t r i bu te s s i m i l a r t o t h e o n e s s p e c i f ie d b y t h e u s e r d e f i n e d q u e r y .T h e r e f o r e , u s i n g a " t r a d i t io n a l " D B M S , i t is i m p o s s i b l e to e x p r e s s s i m i l a r i t yquer ies . T h e p u r p o s e o f F u z z y B a s e i s t o o b t a i n r e s u l ts w h e n t h e t r a d it io n a l q u e r yfa il s: t he p rog ra m ma na ge s t he g r a dua l re lax ing o f t he s e l e c t i on p re d i c a t e s o f t he que rye x e c u t i n g a f u z z y al g o r it h m . T h e p r o c e s s is c a rr i e d o n u n t i l t h e n e w q u e r y r e t r ie v e s ano n-e m pt y s e t o f r e c o rds i n t he da t a ba se : t h i s s e t i s t he m o s t s i m i l a r t o t he oneo r i g i na l l y s e a r c he d by t he u s e r.O n s um m a ry , t he c onc e p t o f que ry i t s e l f i s f uz zif ie d: t he u s e r de f i ne d que ryma t c he s r e qu i r e d da t a w i t h g r a de one , w h i l e a fuz z y s imi l a r i t y que ry m a t c he s r e qu i r e dda t a w i t h g r a de l ow e r tha n one : t he c l o s e r t he s i m i l a r i ty g r a de is t o one , t he g r e a te rt he r e t r i e ve d da t a a r e l ike t he on e s s e a r c he d b y t he u s e r [ 9] .Th e c a pa b i l it y o f s i mi l a r i t y q ue r i e s i mpo s e s on e ma j o r l i mi t a t i on . Th e fi~7-A fica-t i on mu s t be d r i ve n by a s e t o f r u l e s w h i c h a r e s t r i c tl y r e l a t e d t o a s pe c if ic a pp l i c a t iondom a i n : i t w o u l d be i mp os s i b l e t o p e r fo rm a n e f f ec ti ve, non - t r i v i a l , r e l a x i ng a c t i v i t yfo r a ge ne r i c a pp l ic a t i on dom a i n . F o r t h i s r e a s on , F uz z yB a s e i s pa r a m e t r i z e d , a ndm us t be i n i t i a l i z e d fo r a s pe c i f i c a pp l i c a ti on dom a i n .Th e fuz z y - l og i c i n f e r e n ti a l e ng i ne o f F uz z y B a s e i s a b le t o fo rmul a t e p rope r s ugge s -t i ons a bou t pos s i b l e va l ue s o f s e a r c h ke ys . P os s i b l e s e a r c h va l ue s a r e ca l c u l a te d by aContact Address: Claudio Sartori, DE IS - Univ. Bologn a, Viale Risorgimen to, 2, 1-4013 6Bologna, Italy, Tel: +39 51 644.3554 (op. 3001, fax 3540), e-mail [email protected]


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f uz z y- log ic c on t r o l le r ba se d on a kn ow le dge t a b le m a de o f l ingu i s t i c r u l e s e xpr e s s ingr e la tions be tw e e n a t tr ibu te s . Th i s f uz z y e n g ine ope r a te s on ly on num e r ic a l a t t ribu te s ,f o l lowing the s t a nda r d s t ruc tu r e o f F u z z y Log ic C on t r o l l e r s ( F LC ) , a nd i s m a de o fth r e e m a in b loc ks [4 ]:1. F uzzyf icat ion : a crisp use r d e f ine d se a rc h va lue i s f uz zyf ie d by pa r t i t i on ing ther e l a te d c on t inuou s un ive r se o f d i sc our se , r e p r e sen te d by the in t e r va l o f poss ib leva lue s o f tha t a t t ribu te in the da ta ba se , u s ing th r e e f uz z y se ts , l a be le d Smal l , Me-dium a n d Large . T h e n , m e m b e r s h i p d e g r ee s o f a n y s e a r c h v al u e to t h e t h re e m e m -be r sh ip f unc t ions o f the f uz z y se ts a r e c a lc u la te d .2. Decision-ma~'ng: the ou tp u t f uz z y va lue fo r a sea r ch ke y i s s e t b y c onsu l t ing at a b le o f l ingu i s t i c r u l e s e .g . i f A i s Sm al l and B i s M edium , then C i s Larg e , andexecut ing fuzz y logic inferences on the av a i lable ru les . Th e ou tpu t fuzzy va lu e i sm a d e o f t h re e M e m b e r s h i p D e g r ee s ( M D ) t o a n y o f t h e m e m b e r s h i p f u n c t io n s o f

f u z z y s et s " S m a l l " , " M e d i u m " , a n d " L a r g e " .3. Defuzzyf icat ion: t h e o u t p u t cr isp va lu e i s cum pu ted w i th the f ttzzy-centroidm e tho d . Th e c r i sp ( n on- f uz z y ) va lue ob ta ine d i s t he poss ib le va lue de s i r e d .T h e i m p l e m e n t e d F L C p e r m i t s g e n e r a ti o n o f f u z zy s u g g e s t i o n s a n d e x e c u t i o n o ff uz z y c ohe re nc e c on t r o l s o f u se r de s i r e d va lue s . Th i s e ng ine i s gu ide d by a t a b le o ffuz zy if . .. then . .. r u le s l i ngu i s t i c a l ly e xpr e s se d : the se r u le s sum m a r iz e the e xpe r tk n o w l e d g e . A n e x p e r t o f th e a p p l i ca t io n d o m a i n m u s t c o d e h i s p re c i o u s k n o w l e d g e i nthe se ru le s , a s the y a r e im p or ta n t gu ide l ine s f o r u se r s in c h oos ing se a rc h k e ys a ndse t t ing the i r s e a rc h va lue s , so tha t t he y c a n b e e a s i ly l e d to r e tr ie ve the da ta the yde s i r e d , o r , a t l e as t , m o s t s im i l a r to those de s i r e d .The m a in f e a tu r e s o f the sys t e m a r e the fo l lowing :9 C om ple te pa r a m e te r i z a t ion , i n o r de r to m a na g e a ny so rt o f da ta ba se : i t c a n be de-f i n e d a gener ic she l l t ha t c a n be t a i lo r e d to a w ide c l a s s o f a pp l ic a t ions .

9 I t ' s e a sy to ge ne r a te que r i e s by us ing a G UI , e ve n f o r ve r y l a r ge da ta ba se c o lle c-t ions w i th e ve n hund r e ds o f a t t ribu te s tha t o f t e n a re unc om f or t a b le to ha nd le bym e a n s o f co m m o n query by example f o r m s o r S Q L .9 Ge ne r a t ion o f similari ty queries: F uz z yB a se ge ne r a te s a que r y tha t l ooks l ike theuse r de f ine d que r y i f t he l a tt e r fa i l s t o r e t ri e ve da ta f r om the da taba se . The que r y i t-se l f i s f i tzzyf ied: i t i s s im i la r to the us er def ined que ry , w i th a com pu ted grade.S u c h u n c e r t ai n re t ri e v al m e t h o d i s a f u n d a m e n t a l b a s e f o r m a n y c o m m o n p r ac ti ca la pp l i c a t ions , suc h a s s imi l i tude des ign [5].9 G e n e r a t i o n o f u s e f u l sugges t ions f o r the use r w he n he i s c hoos ing se a r c h ke y s o r i sse t t ing search va lues . Poss ible search values are c a lc u la t e d by a f uz zy con t ro l l e rwh ose kno wle dge i s ba se d upo n a ta b le o f l i ngu i s ti c r u le s [ 4] . T h i s fuzzy inferen-t ial engine i s a lso responsib le of uz zy con t ro l s upo n se a r c h va lue s c o r r ec tne ss.9 N o n - f u z z y crisp controls upo n the c ongr ue nc e a nd c o rr e ctness o f s e ar c h va lue s de -f ine d by the use r d u r ing que r y spe c i f ic a t ion . The se c on t r o l s a r e s t ruc tu r e d in twosec t ions : absurd ru l e s a n d warning rules: the former a re unv iolab le s t ruc tura lr u le s a bou t in t e g r i ty o f the un ive r se r e p re se n te d by the da ta ba se , t he l a tt e r a rewa r n ings o f poss ib le e r ro r s in se a r c h va lue s .9 De la y o f que r y e xe c u t ion to the l a t e s t m om e nt , to inc re a se ef fi ci e ncy , e spe c ia l ly inthe c a se o f d i s t r ibu te d da ta ba se sys t e m s : on a ne tw or k c l i e n t F uz z y B a s e c a n ge n-e r a t e the p r ope r que r y r e ly ing on ly on i t s l oc a l f uz z y a nd s t a t i s t i c a l knowle dge ,the n a da ta ba se e n g ine ( e .g . a n S Q L se r ve r) p r oc e sse s the que r y a nd se nd s r e t ri e ve dda ta ba c k to the inqu i r ing c l i e n t,


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9 C o m ple te c on te x t inde pe nde nc e o f the c ode wi th r e spe c t to a spec i fi c a pp l i c a t iondom a in . F u z z y B a se r e lys on ly on a se r ie s o f t a b le s c on ta in ing s t r uc tu ra l in f o rm a -t ion a bou t the da ta ba se , t o be se t up a t i n i t i a l iz a t ion t im e by a n e xpe r t o f the a p-p l i c a t ion f i e ld . The in i t ia l i z a t ion p r oc e dur e i s " t r a nspa r e n t " f o r the e nd use r .The r e m a inde r o f the pa pe r i s o r ga n iz e d a s f o l lows : se c t ion 2 i l lu s t r a te s the m a inda ta s t r uc tu re s o f F uz z yB a se , w i th pa r t i c u lar a t t e n t ion to the r e p r e se n ta tion o f r u l e s .S e c t ion 3 de sc r ibe s the f unc t iona l a r c h it e c tu r e o f F uz z y B a se , wh i l e S e c t ion 4 de sc r ibe sthe f i rs t a pp l i c a tion do m a in f o r w h ic h the sys t e m ha s be e n t e s t e d .

2 D a t a S t r u c t u r e s in F u z z y B a s eThe c us tom iz a t ion pa r am e te r s o f F uz z yB a se a r e c on ta ine d in a se r ie s o f t a b le s.D om a in da ta c a n be e i the r in loc a l t a b le s o r on a r e m ote se r ve r. The F uz z yB a se t a b le sare grou ped as fo l lows:

a ) Da ta tha t c us tom iz e the ge ne r i c she l l a nd i t s u se r in t e rf a c e .b ) S ta t is t ic a l i n f o r m a t ion a bou t the da ta ba se .c ) Th e da ta base i tse l f .d ) Crisp r u le s , s t r uc tu r e d in a bsu r d a nd wa r n ing s , c o n ta in ing in t e g r i ty c ons t r a in ts o fthe va lue s o f da ta ba se a t t r ibu te s .e) Fuzzy r u le s , ne e d e d to "p r og r a m " the F L C be ha v io r so tha t i t c a n de l ive r sugge s -t ions a nd c on t r o ls o f s e a r c h va lue s .The s t a t is t i c a l i n f o r m a t ion t a b le p l a y s a p r e e m ine n t r o l e in pa r a m e t r iz ingF u z z y B a se ope r a tions . The s t a ti s ti c a l t a b le c on ta ins the c om ple te de sc r ip t ion o f e ve rya t t ribu te in the da ta ba se . Th e s t a ti s t ic a l i n f o r m a t ion ne e d to be b r ou gh t up to da tewhe n e ve r the da ta ba se i s sup pose d to ha ve be e n c ha nge d s ign i f ic a t ive ly : the i r c or -r e c t ly m i r r o r ing o f s to re d d a ta i s a v a lua b le p r e lude to the r e t r i e va l o f de s i r e d da ta .A se r ies o f con t ro ls abo ut search va lu es a re a r ranged to obta in quer ies re t r iev ingda ta the c lose s t t o us e r ' s w i l l . Tw o t a b les , c on ta in ing absurd rules a n d warningrules are ke p t : t he f o r m e r e s ta b l ishe s c ongr ue nc e r u le s on se a r c h va lue s p r ov id in g da tain te g r ity , the~ a t t e r is m a de o f sug ge s te d r e l a tions be tw e e n se a r c h va lue s tha t g ua r a n te ere t r ieved da ta s igni ficance . M oreove r , thos e tab les con ta in app ropr ia te co m m ents toe a c h r u le tha t a dv i se s the use r a bou t the m is t a ke s in the que r y se a r c h va lue s .Q uery cor rec tness i s a fund am enta l pre lude to avo id a use less da ta access . In fac t,que r y p r oc e ss ing c a n r e qu ir e a s ign i f ic a n t e xe c u t ion t im e , e spe c ia l ly f o r r e m oteDB M S s , the r e f o r e , i t i s wor th to e xp lo i t a ny a va i l a b le know le dge in o r de r to r educethe r i sk o f a qu e r y f a i lu r e a nd the e f f o r t ne c e ssa r y to m od i f y a f a i l ed que r y .

A bsu r d a nd w a r n ing r u le s r e p r e se n t a f l e x ib le too l to a s s i s t t he use r in the f or m ula-t i o n o f a q u e r y w h i c h d o e s n o t v i o l a te t h e s e m a n t i c s o f t h e a p p l ic a t io n d o m a i n : t h e yrepresent the crisp k n o w l e d g e b a s e o f t h e p ro g r a m a b o u t t h e d o m a i n .The r u le s m us t be c ha r a c te r s t r ings c on ta in ing a bo o le a n e xpr e ss ion wh ic h c a n bee va lua te d by the F oxP r o in t e rp r e te r , t he r e f o r e the y m us t be bo th syn ta c t i c a l ly a nd se-m a n t i c a l ly c o r re c t.The f uz z y know le dge ba se i s m a de o f a t a b le c on ta in ing lingu i s t ic ru l e s , suc h a s:

i f f i e l d I N l = < l a b e l > [ f u z z y c o n d . ]A N D f i e l d I N 2 = < l a b e l > [ f u z z y c o n d . ]A N D f i e l d I N 3 = < v a l u e > , [ c r i s p c o n d . ]T H E N f i e l d O U T = < l a b e l > [ f u z z y o u t p u t ]whe r e fi e ld lN1 , fi e ld I N2 a nd f i e ldOU T ar e two poss ib le f uz z y inpu t s a nd the f uzz yo u t p u t o f t h e i m p l e m e n t e d F L C , a n d f i el d lN 3 i s a crisp i npu t . The se m a n t i c o f the


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c r isp inpu t i s s t r i c t ly boo le a n ( non f uz z y) : i f t he c o n d i t i o n f i e l d lN 3 = < v a l ue > is true( f uz z yf y ing i ts boo le a n va lue , it ha s m e m be r sh ip de g r e e 1 ), t he n the r u le i s c om pute dby the F L C ; i f i t i s f a l se ( m e m be r sh ip de g r e e 0) , t he n the r u le i s no t c om pute d . Th i sbe ha v io r is the c ohe r e n t r e duc t ion o f f uz z y log ic to b ina r y ( cri sp ) log ic: i f the M D a s-s igne d to the c r isp r u le is 0 , f uz z y AN D ope r ato r, im p le m e n te d by the m in im umsqua re s ru le , w i l l a s s ign to f i e ldOU T a f uz z y va lue M e d ium w i th nu l l M D, tha tw o u l d n o t i n f l u e n c e th e p o s s i b l e v a l u e c o m p u t a t io n f o r f i e ld O U T .The im ple m e n te d F L C i s a two f u z z y inpu t s , w i th c r i sp inpu t , a nd one f uz z y ou t -pu t sys t e m . It i s , i nde e d , r e duc ib le to a one o r non e f uz z y inpu t a nd none c r isp inpu ts im p ly by in se r t ing va lue 0 in to the f i e lds c on ta in ing a t t r ibu te s num be r s .3 F u z z y B a s e A r c h i te c t u r e

Th e so f twa r e i s s tr uc tu r e d in som e f unda m e n ta l m o du le s :9 S ea r ch key s i n s e rt io n mo d u l e w hich con ta ins the num er ica l search va lues fuzzyf ica-t ion pha se .9 Fu z z y lo g i c i n fe r en ce mo d u l e , whic h ge ne r a te s poss ib le va lue s a nd c on t r o l s o fnum er ica l search va lues9 Cr i sp con tro l s mo du les , s t r uc tu r e d in a bsu r d a nd wa r n ings .9 Fu z z y co n t r o l mo d u l e .9 Qu er y g en er a t i o n mo d u l e , w h i c h p r o v i d es a S Q L q u e r y .9 S i m i l a r i ty q u er i e s mo d u l e , b a s e d o n f u z z y l o gi c.9 A d d - o n s m o d u l e s, f o r the upd a te o f s ta t is t ic s , de pe nd e n t va lue s c om puta t ion , p r in t ,

s e s s ion sa ve a n d r e s to re , pa r a m e te r s tun ing .3 .1 S ea rch Key s Ins er t io n

The se a r c h ke ys in se r t ion m od u le l e ts t he use r se t t he se a rc h va lue s tha t w i l l p r o -duc e the se l e c t ion p r e d ic ate o f the q ue r y to be ge ne r a te d .The in se r t ion m od u le c he c ks i f it i s poss ib le to use the c hose n a t t ribu te a s sea rc hk e y . A p r e l i m i n a r y c h e c k is m a d e w h e n t h e p o p - u p m e n u i s b u i l t u p . T h e v a l id a t i o nc ond i t ion is s to r e d a s a boo le a n e xpr e ss ion in the s ta t is t ics table .Af te rwa r ds , t he m o du le p r e se n t s a n in se r tion f o r m t a y lo r e d to the a t t ribu te typ e(num ber , charac te r s s t r ing , enum era te , . .. ). The use r can spec i fy search v a lue or searchin te r va l i n tha t in se r t ion f o r m . The use r c a n a l so a sk f o r a sugge s t ion a bou t a poss ib leva lue f o r a num e r ic a l s ea r ch ke y . The se poss ib le va lue s de pe nd o n the p r e v ious lyspe c i f i ed se a r c h va lue s . W he n the spe c i f i c a t ion is m a de , the in se r t ion m o du le e xe c u te sgener ic cons is tence checks fo r num er ica l fie lds: sea rch va lue or search in te rva l m us t beinc lud e d in to a t t r ibu te ' s va lue s in t e r va l i n the da ta ba se .Th e f t tzzyf ica t ion of search va lues par t i t ions the unive rse of d iscourse in to threef u z z y s et s l a be l ed " S M A L L " , " M E D I U M " a n d " L A R G E " , a s s h o w n in F i g u r e 1a.The n , f o r e a c h num e r ic a l se a r c h va lue , t he th r e e m e m be r sh ip de g r ee s to the p r ope rm e m b e r sh ip f unc t ions o f the f uz z y se t s a r e c om pute d . Tha t is a w a y o f e xpr e s s ing them a gn i tude g r a de o f a ny se a rc h va lue w i th f uz z y l ingu i s t i c va r ia b le s r e l a te d to a ttr ib -u te ' s va lue s in the da ta ba se .I f the va lu e to be f uzz yf ie d i s a search in te rva l , then the f t tzzyf ica t ion phase ass ignsto f uz z y se t "S m a l l " the m e m b e r sh ip de g r e e o f the sm a l l e r va lue in the in t e r va l , t of u z z y se t " M e d i u m " t h e M D o f th e a v e ra g e p o in t , a n d to f u z z y s et " L a r g e " t h e M D o fthe la rger va lue .


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Le t us suppo se tha t the s tored va lues of the search k ey y e a r a r e be tween 1980 and1995. Th e interval 1990-1993 is be ing searched. Th e fuzzyflcation of the searchinterval com pu tes the mem bersh ip degree values as the heights o f the intersectionsbe tw een the projec t ion o f the search va lue and the mem bership func t ion cons idered , asin F igure lb , g iv ing: M D(SmaI1) = 0, M D(M edium ) = 0 .5 , M D(L arge) = 0 .78.

MEDIUM

minimumvalue

LARGE

in the db maximumalue n the dba /

1,0.780.5

0

SMALL MEDIUM LARGE

~ 9 9 51990 1993b)

FIGUR E | - P ARTIT IONIN G ANF FUZZYFYING A SEARCH INTERVAL

Be for e finishing, the insertion m odu le visual izes tw o w indo w s containing the fol-low ing information:a) fields us ed as search ke ysb) f ie lds ye t to be spec i fy as search keys in the query .The m anda tory search keys , spec i f ied by the sys tem ins ta ller into the s t a t i s t i c s t a -ble , are sup po sed to be fundamental k ey s for re trieving the d esired data into the database. Fo r instance, i t is useful to force the use as search key s of f ie lds that p erm it agreat select ivi ty or that im ply an important categorizat ion o f s tored data.3 .2 Sug g es t io ns M o dule

Sugges t ions m odu le is a s imple but e f f ic ient im plementa t ion of a two-inputs one-outp ut Fu zzy L ogic Co ntrol ler [4]. A s a m atter of fact, i t is a fuzzy inferent ia l enginewith a crisp input adde d. The crisp c ond it ion val idates the com putat ion o f the rule ,for instance:I F a t t r i b u t e n u m . 1 2 I S s m a l l

A N D a t t r i b u t e n u m . 1 5 I S l a r g e [ f u z zy c o nd . ]A N D a t t r i b u t e n u m . 1 0 I S g r e a t e r t h a n 2 [ cr i s p c o nd . ]T H E N a t t r i b u t e n u m . l l I S m e d i u m [ f u z zy o u t pu t ]If the crisp cond it ion is t rue, then the rule is com pu ted by the inferential engine,o therwise the ru le i s ignored by the process . The boolean semant ic ass igned to thecrisp input is the coherent reduct ion o f fuzzy logic to binary logic , in fact i t can beprov ed that the fuzzyficat ion of the crisp rule and i ts evaluat ion us ing fuzzy logicwo uld produ ce the same resul t obta ined by the boolean implementa tion: ass igning amembership degree 0 to the non-true crisp condit ion, the fuzzy AND operator, im-

p lemen ted by the min imum squares m e thod , w ou ld a s s ign a nu ll M D to t he ou tpu tfuzzy set , the reby it w ould be not inf luent on the com puta t ion of the d es i red poss ib leva lue ; the sam e way, ass igning a M D 1 to the t rue c ri sp condi t ion , the fuzzy AN Dopera tor be tw een fuzzy inputs and c ri sp input w ou ld ass ign to the outpu t the M D re-sult ing from fuzzy inference betw een the fuzzy inputs , so this adding o f a crisp inpu tresul ts coherent again with the fuzzy logic inference o f the sugg est ions m odu le . I t


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s h o u l d b e o b s e r v e d t h a t th e c o h e r e n c e o f th e i m p l e m e n t e d c r is p s e m a n t i c is n o t m i n e db y t h e f u z z y o p e ra t o r b e t w e e n f u z z y in p u ts , th a t c a n b e b o t h A N D o r O R .I f t he use r a sks F uz z yB a se f o r a va lue o f a g ive n se a rc h ke y , t he F L C c onsu l t s t hepa r t ia l v i e w o f the f uz z y r u le s ta b le inc lud ing on ly the r u le s w i th tha t ke y a s fuzz y

ou tpu t . The r u le s a r e r e a d in b loc ks w i th sa m e f uz z y inpu t s . I n f a ct , a c om ple x r u lei n v o l v i n g t w o i n p u t s a n d o n e o u t p u t c a n b e m a d e e x p l i c it in s u m o f p r o d u c ts , t h e ne x p r e ss e d a s s i m p l e A N D r u le s i m p l i c it l y c o n n e c t e d w i t h O R o p e ra to r .F o r e a c h r u le in the b loc k wi th the c r i sp c ond i t ion t r ue , t he log ic e va lua t ion o f ther u le i s c o m p u t e d : a m e m b e r s h i p d e g r ee o b t a in e d b y t h e m i n i m u m o p e ra to r (A N Dr u le ) o r b y t h e m a x i m u m o p e r a t o r ( O R r u le ) b e t w e e n t h e t w o m e m b e r s h i p d e g r ee s o fthe f uz z y inpu t s i s a s s igne d to the f u z z y ou tpu t .F u z z y ou tpu t s o f e a c h r u le b loc k a re supe r im pose d a c c or d ing to the c om pos i t iona lmax-min rule [ 4] : t he po in tw ise sum o f the o b ta ine d f uz z y se ts . F r o m tha t t he de fuz-z y f i c a t ion pha se c o m p ute s the d e s i r e d c r isp ou tpu t . The de f uz zyf ic a t ion m e tho d im -p le m e n te d i s t he g r a v i t a tiona l f uz z y-c e n t ro id m e thod , wh ic h i s c ons ide r e d to be themost genera l in cont ro l appl ica t ions [3 , 4 , 2] .Th e f uz z y c e n t r o ids c om pute d f r om e a c h b loc k a r e c om b ine d , i f t he y a r e no t toofar e a c h o the r. The p r ogr a m c o m p ute s a n a ve r a ge s um o f f uz zy c e n tr o ids i f t he i r re la -t ive d i f f e r e nc e i s sm a l l e r tha n 30% o f the a t t ribu te ' s va lue s in t e rva l o f the s to r e d da ta .Th a t ' s a de s ign e r ' s c ho ic e wh ic h c a n be t a y lo r e d to the spe c i f ic a pp l ic a t ion .Al l de s ig ne r ' s c ho ic e s , suc h a s ov e r l a pp ing g r a de o f fuz z y se ts pa r t i t i on ing theuniverses o f d iscourse , or the fuzzy opera tors na ture , or the def t tzzyf icat ion m eth od a reeas i ly chan geable by the sof tware ins ta l le r or by the use r i t se lf . The ac tua l choice ofpa r t i t i on ing the un ive r se o f d i sc our se by the f uz z y se t s ove r l a pp ing f o r 25% of the i ra r e a is c ons ide r e d a g ood t r a de of f f o r m a n y c on t r o l a pp l ic a t ions [ 2 , 4 ].3 .3 C r i s p C o n t r o l s M o d u l e

The use r c a n e xe c u te con t r o ls o f c ongr ue nc e a nd c ohe re nc e o f se a rc h va lue s a t a nyt im e o f se a rc h ke y s in se r t ion pha se . The se c on t r o l s a re a u se fu l he lp to a vo id que r yfa i lure , then to save prec ious t im e . T he y a re a lso con s iderable he lpful guide l ines tothe spec i f ica t ion of a proper que ry tha t prec ise ly re t r ieves d es i red da ta .The c r isp c on t r o l s a re s t r uc tu r e d on two l e ve l s to e nha nc e c on t r o l s f l e x ib i l i ty : ab-surd rules and warning rules:1. I f an absu rd ru le i s v io la ted , the use r rece ives an e rror m essag e and is forced to

m od i f y the se a r ch va lue s invo lv e d in the r u le , a s r e c o rds w i th suc h a t t r ibu tes dono t e x i s t i n the da ta ba se .2 . I f a wa r n ing r u le is v io la t e d , t he use r r e c e ive s a wa r n ing m e ssa ge , a s r e c o r ds w i thsuc h a t tr ibu te s a r e no t suppose d to e x i s t i n the d a ta ba se , bu t the use r i s a nyw a ya l low e d to p r oduc e suc h a que r y .The r u le s a nd c om m e n ts tha t f e e d the se c on t ro l s r e p r e sen t the kno wle d ge o f a n e x-pe r t i n the w or k a r e a to wh ic h the da ta s to r e d be long . The y a r e a f im da m e n ta l s t a rt ingpo in t f o r op t im iz ing se a r c h ke ys ' c ho ic e a nd se a r c h va lue s ' s e t t ing .

' Th e a r c h i t ec tu r e o f the c r i sp c on t r o ls p r oc e dur e s i s ba se d on a s im ple loop p r oc e ss -ing one r u le a t a tim e : f o r e a c h ru le the va l ida t ion c ond i t ion i s e va lua te d ; i f i t i s t r ue ,the use r i s a dv i se d o f the e r r o r a nd , e ve n tua l ly , is f o r c e d to m od i f y se a r c h va lue s.3 . 4 F u z z y C o n t r o ls M o d u l e

The use r ca n e xe c u te , be ne a th c r isp c on t r o l s s t a t e d a bove , f uz z y c on t r o l s a bou tsearch va lues coherence .


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Th e f low o f th i s m od u le i s a s f o l lows : fo r e a c h num e r ic a l s ea r ch ke y , a po ss ib leva lue is a ske d the sugg e s t ions m o du le ; t ha t m o du le , de sc r ibe d in 3 .2 , i s m a de o f afuzzy infe rent ia l engine de l ive r ing a c r i sp ou tpu t as p oss ib le va lu e for a g iven searchke y : i f t he poss ib le va lue i s t oo f a r f r om the se a r c h va lue c hose n b y the use r , t h e n awa r n ing i s ge ne r a te d .The fuz z y- ge ne r a te d wa m ing d o no t fo rc e the u se r to c ha nge a n y se a r c h va lue , a ssuc h r e co r ds m a y s t il l e x i s t i n the da ta ba se . T he m a x im um d i s t a nc e be twe e n these a r c h va lue a nd the poss ib le va lue i s a de s ig ne r ' s c ho ic e .3 .5 Qu ery Genera t io n M o dule

The q ue r y g e ne r a t ion is e xe c u te d w he n the f o l lowin g c ond i t ions ar e t rue :1 . A l l m a n da to r y sea r c h ke ys ha ve be e n spe c if ie d .2 . The e s t im a te d se le c t iv i ty f a c to r o f the que r y is sm a l l enough .

I f t he que r y doe s no t r e tr ie ve a n y da ta , t he query generat ion module star ts thes imi lar i ty query generat ion m odule t o o b t a i n a n e w q u e r y w i t h r e l a x e d c o n d i t i o n s ,a nd r e pe a ts the ge ne r a t ion a nd da ta ba se se a r ch pha se .3 .6 S imi la r i ty Qu ery Genera t io n M o dule

I f the sp ec i f ied search predica tes are too t igh t so tha t the D BM S do no t ret rievea n y d a t a d e si re d b y t h e u s e r, t h e n F u z z y B a s e c an re lax som e p r e d ic a te s c on ta in ingc ond i t ions on se a r c h ke ys , so tha t i t p r ov ide s a ne w que r y s im i lar to the user def inedque r y tha t ha s f a i l e d , bu t l e s s se l e c t ive a nd wi th be t t e r c ha nc e s to r e tr ie ve tup le s f romthe da ta ba se . T he se tup le s w i l l no t e x a c t ly be thos e wa n te d by the use r , bu t th e y wi l lb e t h e m o s t s im i lar to tho se des i red: e . g . i f the re a re no objec ts w i th w e i g h t = 10l b ., F u z z y B a s e m a y r e t ri e v e a n o b j e c t w i t h w e i g h t = 9 lb. 6 oz.!3.6 .1 S imilar ity Q uery M odu le Arc hitecture

The e xe c u t ion flow. o f th is m o du le , t ha t i s ope r a t ive f o r num e r ic a l f ie lds on ly , i sthe f o l lowing :1 . The spe c if ie d se a rc h ke y s a re c ons ide r e d one a t a t im e o r de r ed by the s im i l a r i tyorder th a t be t te r f i t s s im i lar objec ts in the par t icu la r da ta base . Th e f i r st predicatestha t a re re laxed a re those w ho se search keys less d if fe rentiate the objec ts repre -se n te d in the da ta ba se , a s de sc r ibe d by the o r d e r n u m b e r in the sta t is t ical infor-m a t ions t ab le . I f no da ta f i e ld i s kn ow n b e ing a be t t e r c ho ic e to s t a rt t he r e la x ingprocedure , sea rch keys can be ordered e . g . by ascending se lec t iv i ty fac tor of i t spredica te . Th is choice perm i ts to re lax the mo st se lec t ive predica tes f i rs t , anda vo ids r e l a x ing the sa m e p r e d ic a te too m a n y t im e s subse qu e n t ly . Th e r e la x ingte c hn ique i s c a l l e d o r - c u t a nd w or ks b y c om pa r ing the use r- spec i fi e d sea rc hin te rva l , s a y f r o m rmin to rmax, a nd the d om a in o f the a t t r ibu te , s a y f r om valminto valmax . Fo r o~ = 1 , the sys t em consid ers a search in te rva l equ a l to the onerequired by the user . For {x = 0 , th e search in te rva l i s the w hole in te rva l ~ fposs ib le va lue s o f tha t a tt r ibu te in the da ta ba se . F o r in t e r m e d ia te va lue s o f tx thew id th i s g ive n by the t r a pe z ium o f F igu r e 2a . I n i t i a l ly , c t i s s e t t o I .2 . In orde r to re lax t he que r y , t he m od u le e n la rge s the c o ns ide r e d sea r ch in t e r va l byr e duc ing the m e m be r sh ip de g r e e cr a nd use s a s se a rc h in t e rva l t he ne w se g m e n tp r oduc e d by the p r o je c t ion o f the t~ - c u t on the c on t inue un ive r se o f d i sc ourse(F igure 2b) .


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The ne w se a r ch in t e rva l , ob ta ine d r e duc ing the m e m be r sh ip de g r e e, p r oduc e s al o w e r similarity degree o f t h e n e w q u e r y in c o m p a r i s o n w i t h t h e p r e v i o u s o n e . T h eque r y s im i l a r i ty de g r e e i s c om pute d c o ns ide r ing i t a s the f uz z y log ic c o m p uta t ion o fthe se l e c t ion p r e d ic a te o f the que r y us ing a s va lue s the m e m b e r sh ip de g r ee o f ea chsearch ke y to i t s fuzzy in te rva l . Mo reover , to th is re laxed query i s a ssoc ia ted an en-la rged se lec t iv i ty fac tor : the new qu ery i s less se lec t ive .

v a m m ~ i n H a v B t m ~ xa ) v a ~ m ~ i n r m ~ x v a m a xb)FIGURE 2 - RELAXING QUERY PREDICATES

1. I f the new query i s too dif fe rent from the previo us one , or i f the se lec t iv i ty factorr a t e d f o r the ne w que r y ha s r a ise d enough, t he n the m odu le s tops the r e l a x ingpha se , o the r wise i t c ons ide r s the ne x t s e a r c h ke y a nd r e pe a t s s t e ps 2 , 3 , a nd 4 .Remarks:9 I f the tx-cu t assoc ia ted to a search in te rva l reaches ze ro , then the w ho le in te rva l ofposs ib le va lues i s used as search in te rva l : i t s se lec t iv i ty i s reduced to ze ro and i two r ks a s i f the q ue r y d id no t c on ta in tha t s e l e c tion p re d ic a te .9 I f a l l the ye t spec i f ied search va lues a re re laxed and the des i red leve l of s imi la r -i ty /se lec t iv i ty i s s t i l l not reachable , then the program res ta r ts the re laxing proce-

dur e f r om the be g inn ing , a lwa y s o r de r ing the se a r c h ke ys by the c hose n f i t o rde r .9 The r e is a m a x im um num be r o f i t er a t ions o f th i s a lgo r i thm tha t c a use s the de fini-t ive s top o f the r e l a x ing pha se . I t ha s b e e n a r r a nge d in o r de r to a vo id in fin it eloop ing , e ve n i f t ha t e ve n tua l i ty ha s no t oc c ur r e d du r ing so f tw a r e t e s ting t ri a ls .9 The who le p r oc e dur e de sc r ibe d a bove is s t i ll va l id e ve n i f t he in i t i a l s e a rc h va lueis n ot an in te rva l , in fac t w e kn ow tha t a t rapezoida l fuzzy se t can degenera te invar iou s shapes , such as a l ine , a t r iangle or a square .

3 . 6 .2 T h e Q u e r y a s a F u z z y V a l u eR a the r the n r e ga r d ing f uz z y the o r y a s a s ing le the o r y , we shou ld r e ga r d the p r oce ssof fuzzyf ica tion as a m eth od olo gy to genera lize any spec if ic theo ry f rom a c risp(disc re te ) to a cont inu ous ( fuzzy) form [1] .Therefore , the que ry i t se l f i s fuzzyfiable . As a m at te r of fac t Fu zzy Ba se m anagestwo dif fe rent quer ies : the user def ined query an d the fuzzy re laxed q uery . Th e la t te r

prod uces an in te r roga t ion s imi la r to the former . I f the m em bersh ip degrees ct o f eachsearch in te rva l to the fuz zy se t asso c ia ted to the poss ib le search va lues in te rva l a re se tto 1, t he n the use r de f ine d que r y i s be ing p r oc e ssed . I f t he s im i l a r i ty m odu le r e duc ese ve n on ly one o f the se m e m be r sh ip de g r e e s be low 1 , t he n a q ue r y s im i l a r to the in i -t i a l one i s be ing p r oc e ssed : by c om put ing the f uz z y log ic a l va lue re su l t ing f r om thec om bina t ion o f f uz z y va lue s a s soc iat e d to e a c h se a rc h ke y a c c or d ing to the se l e c tionpr e d ic a te in the que r y i t i s poss ib le to ob ta in a f uz z y va lue ind ic a t ing the similarity


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S E L E C T * F R O M d a t aW H E R E a = 1 A N D b = 5 O R d = i 0a nd the f uz z y- r e l a xe d que r y ge ne r a te d by the s im i l a r i ty m odu le i siS E L E C T * F R O M d a t a [a]W H E R E a > 0 . 8 A N D a < 1 . 2 0 . 6A N D b > 4 . 9 A N D b < 5 . 1 0 . 9O R d > 8 . 3 A N D d < i i . i 0 . 7 5

then , the boole an se lec t ion predica te , eva lua ted according to fuzzy logic us in gva lues , g ives : o~ (a ) AN D cx (b) OR o~ (d) = 0 .6 A N D 0.9 O R 0 .75 - - 0 .75 . T he v a lue0 .75 i s a s su m e d to be the fuzzy similarity degree be twe e n the in i t i a l u se r que r y a ndthe que r y ge n e r a te d by the s im i l a r i ty m o du le .3.6.3 Statistical Com puta tion vs. Fuz zy Inference

W e h a v e j u s t i n t r o d u c e d t h e c o n c e pt of uzzy query. B u t w e m u s t n o t i c e t h a t t h ea lgo r i thm tha t p r oduc e s the g r a dua l re l a x ing o f p r e d ic a tes in the que r y i s ba se d a l soon s t a t is t i c al va lue s . F o r in s t anc e , t he c o m p uta t ion m e th od o f the se l e c t iv i ty fa cto rsbe lon gs to s ta t i s t ica l concepts . T he se lec t iv i ty fac tor of the predica tes o f a qu ery i s ob-t a ine d by the we l l kno w n e m p i r ic a l f o r m ula s g ive n in [ 10 ].

O ne o f the t e r m ina t ion cr i te r ia o f the re l a xa t ion pha se i s a c ond i t ion a b ou t the ne wquery se lec t iv i ty : i t i s a s ta t i s t ica l condi t ion , which can be cont ra ry to the similaritygrade proper ty . Th is i s n ot a co nt radic t ion of the fuz zy na ture of the re laxing proce-dure , as the s ta t i s t ica l va lu e is only one of the te rm ina t io n c r i te r ia, an d i t can be d is -a b le d a t sys t e m in i t i a li z a t ion t im e .

M or e ove r , e ve n i f t he p r oc e ss o f r e l a x ing a que r y h a s be e n e xp la ine d o n f uz z y ba-s is , i t i s s t il l poss ib le to read in a probabi l i s t ic ke y [9] the beh avio r of th e fuzzy com-pon ent . W e can reca l l [1 , 2 , 3] tha t , in a fuz zy se t , each gener ic e lem ent x o f the uni -ve r se be longs to the set w i th a g r a de e xpr e sse d a s a r e al num be r f r om the in t er va l [ 0,1 ]. S o bo th p r oba b i l i s ti c the o r i e s a nd f uz z y the o r y de sc r ibe unc e r t a in ty a s a num e r ic alp r ope r ty , bo th s ys t e m s c om b ine set s a nd p r opos i t ions a s soc ia t ive ly , c om m uta t ive lya nd d i s t r ibu t ive ly . The ke y d i s t inc t ion c onc e r ns ho w the sys t e m s jo in t ly tr e a t a s e t Aa nd i t s oppos i t e A c : c l a s s ic a l s e t t he o r y de m a nd s tha t A n A c = O , a nd p roba b i l is -t ic the o r y c onf o r m s : P ( A n A c ) = P ( O ) = O . S o A n A c represents , f rom a prob-a b i li s ti c po in t o f v i e w , a n im po ss ib le e ve n t . B u t f uz z yne ss be g ins wh e nA r i a c : ~ 0 [2].4 A n E x a m p l e : G e a r D e s i g n b y S im i l i tu d e C r i t e r ia

Ge a r d e s ign i s l a rge ly de pe nde n t on e xpe r i enc e . Unc e r t a in ty in loa d m a gn i tude a ndappl ica t ion sequence , ma nufac tur ing e r ror and def lec t ion of suppor ts m ay vary servicel i f e by a f a c to r 2 . F o r th i s re a son ne w de s igns a re g r e a t ly in f lue nc e d by da ta m e a su r e don ge a r s tha t w or k in a na logou s c ond i t ion . Th i s a na logy is c a l l e d s im i l i tude . S im i l i -tude c ri t er i a a r e in t r oduc e d e ve n in IS O /DI N /AG M A s ta nda rds a nd a d hoc p roce dure sf o r de s ign a re in tr oduc e d . H ow e ve r a l l t he se te c hn ique s a r e ba se d on f o r m ula s tha t a reba se d on e xpe r im e n ta l m e a s u r e m e n t in t e s t r ig s a nd in t e rpo la t e a nd e x t ra po la te the ser e su l ts to ob ta in ne w d e s ign . The se f o r m ula s s t a rt f r om the be a m the or y o f De S a in tVe n a in t a nd in H e r tz m ode l f o r c on ta c t a nd a re he a v i ly c o rr e cte d by va r ious c~ifi-


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c ients tha t a re mul t ip l ied to the theore t ica l resul t s . In th is paper s im i l i tude i s d i rec t lyide n t i f ie d by a f uz z y se a r ch in a da ta ba se o f e x i s t ing a nd we l l kno w n ge a rs . T he f uz -z y f i c a t ion o f s im i l itude cr i te r i a i s ba se d o n p r e v ious w or ks o f va r ious a u tho r s tha t a rea im ed to a f ir s t choice o f the param eters of a new des ign . In i t ia l r equi rem ents a rem odi f i e d by us in g f uz z y num be r s . Th i s p r oc e ss i s ba se d on f uz z yfi c at ion c r it e ri a f o r aspec ific field.A t the end of the process s im i la r gears a re found . I t i s probable tha t these require-ments a re not fu l f i l led by these exis t ing gears . However , an exper t da ta -base i s de-f ine d in th i s w a y . The se da ta m a y be use d to i t e ra t ive ly de f ine the ne w de s ign by us -ing s t a nda r d f o r m u la s in a m a nn e r ve r y s im i l a r to the t r a d i t iona l d e s ign m e th od . Th edifference is that expe r ience-based factor can b e ob tain ed from th e exp ert data-base.A n o t h e r ap p r o a c h i s t o u se a r u le b a s e d e x p e r t s y s t e m t o m o d i f y t h e m o s t s i m i l ar e x-i s t ing ge a r in o r de r to f u lf il l r e qu i r em e n t s . A n e xpe r t sys t e m o f th i s k ind , wr i t t e n i sP r o log , wa s d e ve lop e d by one o f the a u tho r s in h i s Do c to r a te thes i s .5 C o n c l u s i o n s

The pa pe r p r e se n t s F uz z yB a se , a sys t e m f o r the ge ne r a t ion o f s im i l a r i ty que r ie s inr e la t io n a l D B M S s . S i m i l a r it y i s a n i m p o r t a n t d e s ig n t e c h n i q u e i n m a n y t e c h n o l o g ic a la pp l i c a tions , suc h a s ge a r de s ign . F u z z yB a se wa s de ve lope d upo n a D B M S f o r P C :M icrosof t Fo xP ro for W ind ow s, ver . 2 .5 , the re fore i t exhib i t s a comfor table graphicuse r in te rf ac e, pe r f e c tly in t e g r a te d in the M ic r oso f t W ind ow s ope r a t ing sys t e m . Thef i r st t e s t be d w a s the ge a r de s ign p r ob le m d e sc r ibe d in se c tion 4. The s ys t e m i s unde reva lua t ion , but pre l im inary resul ts a re sa t i s fac tory .6 Bi b l i ograp h y[1 ] Z a d e h L . A . : " O u t l i n e o f a n e w a p p r o ac h t o t h e A n a l y s i s o f C o m p l e x S y s t e ma n d d e c is i o n P r o c e ss " . I E E E T r a n s a ct i o n o n S y s t e m s , M a n , a n d C y b e r n e t i cs ,vo l . S M C - 3 , No . 1 Ja nu a r y 1973[2 ] K o s k o B . : " N e u r a l N e t w o r k s a n d F u z z y S y s t em s : a d y n a m i c a l s y s t e m s a p-p r oa c h to m a c h ine in t e l l ige nc e " , P r e n ti c e - H a l l I n t e r na t iona l I nc. , 1992 .[3 ] B e z d e k J. : " F u z z y M o d e l s . W h a t ar e T h e y , a n d W h y ? " , I E E E T r a n sa c t io n s o n

F u z z y S y s te m s , Vo l . 1 , No . 1 , F e br u a r y 1993 .[4 ] Le e C . C . : "F uz z y Lo g ic in c on t r o l sy s t e m s : f uz z y log ic c on t r o l l e r - pa r t 1 a nd2" , I EEE Tr a ns . on S ys te m s , M a n a n d C ybe r ne t i c s , vo l . 20, pp . 404- 435 , 1990 .[5 ] P ia nc a s te l l i L . : "A na l i s i e d im ple m e n ta z ion e eli un m e todo d i c a l c o lo pe r m otedenta te basa to su l la s im i l i tudin e con appl icaz ioni es is tent i e g i /L col lauda te" ,Un ive r s i td d i B o logn a e F i r e nz e P hD the s i s in App l i e d M e c ha n ic s , 1988 .[6 ] L e u n g K . S . , W o n g M . H . , L a i n W . : " A f u zz y e x p e rt d a ta b a se s y s t e m " , I E E ET r a ns . o n K n o w l e d g e a n d D a t a E n g i n e e r i n g , 4 - 1 9 8 9 .[7 ] Va ss i l l i a d i s S . , T r i a n ta f y l lo s G . , K obr o s ly W . : "A F u z z y R e a son in g Da ta ba seQ u e s t i o n A n s w e r i n g S y s t e m " , IE E E T r a n s . o n K n o w l e d g e a n d D a t a E n g in e er -ing , D e c e m be r 1994 .[8 ] Za de h L . A . : "T he r o le o f f uz z y log ic in the m a na ge m e n t o f unc e r t a in ty in e x-pe r t sys t e m s" , F u z z y S e t s a nd S ys te m s 11 ( 1983) .[9 ] Za d e h L . A . : "F u z z y S e ts as a B a s i s fo r a tho r y o f P oss ib i l i t y" , F uz z y S e t s a ndS ys te m s 1 ( 1978).[10] Se l inger , P .G. e t a l . : "A cces s pa th se lec t ion in a re la t iona l da tabase sy s tem " ,A C M S I G M O D C o n f ., B o s t o n, M a y 1 97 9.

1995 - fuzzybase - a fuzzy logic aid for relational database queries

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