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A KNOWLEDGE-BASED
METHOD FOR FUZZY
QUERY PROCESSING
FOR DOCUMENT
RETRIEVAL
SHYI-MING CHEN
Published online: 29 Oct 2010.
To cite this article: SHYI-MING CHEN (1997) A KNOWLEDGE-BASED
METHOD FOR FUZZY QUERY PROCESSING FOR DOCUMENT RETRIEVAL,
Cybernetics and Systems: An International Journal, 28:1, 99-119, DOI:
10.1080/019697297126272
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http://dx.doi.org/10.1080/019697297126272
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A KNOWLED GE-BASED METHOD FOR
FUZZY QUER Y PR OC ESSING FOR
D OC UMENT R ETR IEVAL
SHYI-MING C HEN WEN-HOAR HSIAO YIH-JEN HOR NG
Department of Computer and Information Science, National Chiao Tung University, Hsinchu, Taiwan, Republic of China
This pape r pre se nts a knowle dge -base d m ethod for proce ssing fuzzy que rie s and we ighte d-fuzzy que rie s for docume nt re trie val, whe re fuzzy conce pt m atrice s are use d for knowle dge re pre se ntation and the e lem ents in a fuzzy conce pt matrix are re pre se nte d by trape zoidal fuzzy numbe rs param eterized
s .
by quadruple s a, b, c, d , whe re 0( a( b( c( d( 1. Inte llige nt re -trie val capability and flexible use r’ s que rie s are conse que ntly provide d for.
s .
Salton and McGill 1983 pointed out that information re trieval is conce rned with the re prese ntation, storage , organization, and acce ssing of information item s. Most comme rcial information re trie val systems still adopt the B oolean logic model for information retrie val. H owe ve r, the information retrie val systems based on the Boole an logic mode l are
The authors would like to thank the re fere e s for providing very he lpful com me nts and sugge stions. The ir insight and comme nts led to a be tter pre se ntation of the ide as e xpre sse d in this pape r.
This work was supporte d in part by the National Scie nce Council, Republic of China, unde r grant NSC 83-0408-E-009-041.
Addre ss corre sponde nce to Shyi-Ming Che n, De partm ent of Compute r and Inform a-tion Scie nce , Naa-tional Chiao Tung Unive rsity, Hsinchu, Taiwan, Republic of China.
Cybernetics and Systems: An International Journal, 28:99] 119, 1997
CopyrightQ1997 Taylor & Francis
0196-97 22 ¤97 $12.00 + .00 9 9
rathe r re stricted in applications because these systems cannot process fuzzy queries. Se veral fuzzy information retrie val me thods based on
s .
fuzzy set theory Z adeh, 1965 have be e n proposed for improving the disadvantage of the Boolean logic mode l, such as those in Her and Ke s1983 , Kraft and Bue ll 1983 , Miyamoto 1990 , Murai e t al. 1989 ,. s . s . s .
s . s . s .
Rade chi 1979 , Tahani 1976 , and Z e mankova 1989 . Although the se fuzzy information retrie val me thods have the fuzzy query proce ssing capability, the efficiency and effectivene ss of the se methods are not
s .
satisfactory. Lucare lla and Morara 1991 pre sented a fuzzy information re trieval system FIRST based on conce pt networks. In Chen and W ang s1993, 1995. and W ang and Chen s1993 , we have pre sented some. me thods for de aling with docume nt retrie val using knowle dge-based fuzzy information re trieval te chniques. The me thods we prese nte d in
s . s .
Che n and W ang 1993, 1995a and W ang and Che n 1993 allow the system’s use rs to pe rform simple queries, we ighted que rie s, inte rval que rie s, and we ighte d-inte rval queries. In this pape r, we exte nd the
s . s .
works of Chen and W ang 1993, 1995a , Lucare lla and Morara 1991 ,
s .
and W ang and Che n 1993 to pre se nt a knowle dge-based me thod for dealing with fuzzy que rie s and we ighted-fuzzy que ries for docum ent re trieval, whe re fuzzy conce pt m atrices are use d for knowle dge re pre-se ntation, the eleme nts in a fuzzy concept m atrix repre pre-sent fuzzy re le vant values betwe e n conce pts, and the fuzzy relevant value s be twe e n conce pts are re pre sented by trape zoidal fuzzy numbe rs. The transitive closure of the fuzzy concept matrix is calculated by the fuzzy numbe r arithmetic ope rations to e valuate the im plicit fuzzy re le vant value s be twe e n conce pts. The propose d method is more flexible than the one s
s .
prese nte d in Che n and W ang 1993, 1995a , Lucare lla and Morara s1991 , and W ang and Che n 1993 because it allows the system’s users. s . to pe rform fuzzy queries and we ighte dfuzzy que rie s. Intelligent re -trie val capability and flexible user’ s que rie s are consequently provided for.
BASIC C ONC EPTS OF FUZZY SET THEOR Y
In 1965, Z adeh propose d the the ory of fuzzy sets. In the following, we
s
briefly review some basic de finitions of fuzzy sets from Che n 1992a, b,
. s . s . s c; 1994 , Chen e t al. 1991 , Kande l 1986 , Kaufman and Gupta 1985,
. s .
1988 , and Z adeh 1965 . Le t U be the unive rse of discourse, Us
v u , u , . . . , u . A fuzzy set1 2 n4 A in U is a se t of orde re d pairs
v s u , f1 As u1.. s, u , f2 As u2.., . . . , u , fs n As un..4, where fA is the mem bership
w x s .
function of A, f : UA ª 0, 1 , and fA ui indicate s the grade of me m-be rship of u in A. A fuzzy se t A is convex if and only if for all u , u ini 1 2 U,
s s . . s s . s . . s .
fA l u1q 1 y l u2 0 Min fA u1 , fA u2 1 w x
whe re l g 0, 1 . A fuzzy se t A of the unive rse of discourse U is calle d s .
a norm al fuzzy se t if ’ uig U, f u s 1. A fuzzy number is a fuzzyA i
subset in the universe of discourse of U that is both conve x and normal. A fuzzy num ber M of the universe of discourse U may also be characte rize d by a trape zoidal distribution parame trize d by a quadruple
s a, b, c, d shown in Figure 1..
Le t A and B be two trape zoidal fuzzy numbers, where As
s a , b , c , d1 1 1 1. and Bs a , b , c , d . The trape zoidal fuzzy numbe rss 2 2 2 2.
s .
A and B are called e qual i.e ., As B if and only if a s a , b s b ,1 2 1 2
c1s c , and d s d .2 1 2
Le t A and B be two trape zoidal fuzzy numbers, where As
s a , b , c , d1 1 1 1. and Bs a , b , c , d . B ased on Chens 2 2 2 2. s1992a. and
Figur e 1. A trape zoidal fuzzy numbe r.
s .
Kaufman and Gupta 1985, 1988 , the addition, subtraction, multiplica-tion, division, AND, O R, and ratio ope rations of the trape zoidal fuzzy numbe rs A and B can be define d shown as follows.
Fuzzy numbe r addition
Å
:s . s .
A
Å
Bs a , b , c , d1 1 1 1Å
a , b , c , d2 2 2 2s . s .
s a q a , b q b , c q c , d q d1 2 1 2 1 2 1 2 2 Fuzzy numbe r subtraction ] :
s . s .
A] B s a , b , c , d1 1 1 1 ] a , b , c , d2 2 2 2
s . s .
s a y d , b y c , c y b , d y a1 2 1 2 1 2 1 2 3 Fuzzy numbe r multiplication m :
s . s . Am B s a , b , c , d1 1 1 1 m a , b , c , d2 2 2 2 s . s . s a = a , b = b , c = c , d = d 4
Ç
1 2 1 2 1 2 1 2Ç
Fuzzy numbe r division`
/
:s . s . A`
/
s a , b , c , d `1 1 1 1/
a , b , c , d2 2 2 2 s . s . s ar d , b r c , c r b , d r a 5Ç
1 2 1 2 1 2 1 2Ç
n Fuzzy numbe r ANDD
:n s . n s .
A
D
Bs a , b , c , d1 1 1 1D
a , b , c , d2 2 2 2s s . s . s . s . . s .
s Min a , a , Min b , b1 2 1 2 , Min c , c1 2 , Min d , d1 2 6 k
Fuzzy numbe r O R
D
:k s . k s .
A
D
Bs a , b , c , d1 1 1 1D
a , b , c , d2 2 2 2s s . s . s . s . . s .
s Max a , a , Max b , b1 2 1 2 , Max c , c1 2 , Max d , d1 2 7
% Fuzzy numbe r ratio
D
:% s . % s .
A
D
Bs a , b , c , d1 1 1 1D
a , b , c , d2 2 2 2s . s .
s a r a , b r b , c r c , d r d1 2 1 2 1 2 1 2 8 Le t k be a real numbe r be twe en ze ro and one and A be a
s .
trape zoidal fuzzy number, As a , b , c , d . The n, we can see that1 1 1 1
s . s .
km A s k , k , k , k m a , b , c , d1 1 1 1
s . s .
s k= a , k = b , k = c , k = d1 1 1 1 9 In the following, we introduce a de fuzzification technique for trape
-s .
zoidal fuzzy numbers Kaufmann & Gupta, 1988; Che n, 1994a . Le t us conside r the trape zoidal fuzzy numbe r shown in Figure 2, whe re e is a defuzzification value of the trape zoidal fuzzy number. From Figure 2, we can se e that 1 1 s ey b 1 q. s . 2s by a 1 s c y e 1 q. s . s . s . 2s dy c 1. s . 1 1 s . s . s . s . « ey b q 2 by a s c y e q 2 dy c 1 1 s . s . s . s . « ey b y c y e s 2 dy c y 2 by a aq d y b y c 2 bq 2 c « 2 es q 2 2 aq b q c q d « 2 es 2 aq b q c q d s . « es 10 4 s .
In the following, we pre sent a similarity measure Che n, 1995b for me asuring the de gre e of similarity be twe e n two trape zoidal fuzzy
Figu re 2. De fuzzification of a trape zoidal fuzzy num be r.
be rs. Le t A and B be two trapezoidal fuzzy numbe rs, where As s a , b , c , d1 1 1 1.and Bs a , b , c , d . The de gree of similarity be twee ns 2 2 2 2. the trape zoidal fuzzy num bers A and B can be m easured by the sim ilarity function S,
<a1y a q b y b q c y c q d y d2< < 1 2< < 1 2< < 1 2<
s . s .
S A , B s 1 y 11
4
s . w x s .
whe re S A, B g 0, 1 . The larger the value of S A, B , the greater the sim ilarity betwe en the trape zoidal fuzzy numbers A and B. It is obvious
s . s .
that if As 1, 1, 1, 1 and B s 0, 0, 0, 0 , then <1y 0 q 1 y 0 q 1 y 0 q 1 y 0< < < < < < <
s . s .
S A , B s 1 y s 0 12
4
s . s
Furthe rmore, if As B s a , b , c , d1 1 1 1 i.e., A and B are identical .
trape zoidal fuzzy numbers , then
<a1y a q b y b q c y c q d y d1< < 1 1< < 1 1< < 1 1<
s . s .
S A , B s 1 y s 1 13
4
Le t x and y be two re al values be twe e n zero and one. It is obvious that x and y can be repre sented by trape zoidal fuzzy numbe rs, that is,
s . s . s .
xs x, x, x, x and y s y, y, y, y . B ased on formula 11 , the de gree of similarity betwe en x and y can be e valuated shown as follows:
<xy y q x y y q x y y q x y y< < < < < < <
s . < < s .
S x, y s 1 y s 1 y x y y 14
4
s .
This result is coincide nt with the one we show in Chen et al. 1989 .
C ONC EPT NETWOR KS AND C ONC EPTS MATR IC ES
s .
Lucare lla and Morara 1991 prese nte d conce pt ne tworks for fuzzy information re trieval. A concept ne twork include s node s and dire cted links, whe re each node repre se nts a conce pt or a document and e ach dire cted link conne cts two concepts or is dire cte d from one conce pt Ci
to one docum ent d and is labe led with a re al value betwe en ze ro andm j
one. If Ciª C , the n it indicates that the de gree of rele vance fromj m
w x
conce pt C to conce pt C isi j m , where m g 0, 1 . If Ciª d , the n itj
indicates that the de gre e of relevance of document d with re spe ct toj
w x
conce pt C isi m , where m g 0, 1 . Figure 3 shows a concept network
s .
adapte d from Lucarella and Morara 1991 , whe re C , C , . . . , and C1 2 7 are conce pts; d , d , d , and d are docume nts.1 2 3 4
s . s .
In Che n and W ang 1993, 1995 and W ang and Che n 1993 , we
s .
have e xtende d the work of Lucarella and Morara 1991 to allow the
Figure 3. A conce pt ne twork.
dire cted links in a concept network to be associate d with real intervals w x
in 0, 1 . Howe ve r, if we can allow the directe d links in a conce pt network to be associate d with linguistic te rms or trapezoidal fuzzy
s .
numbe rs parame terized by a, b, c, d , whe re 0( a ( b ( c ( d ( 1, the n the re is room for more fle xibility. Thus, in this pape r, we furthe r
s .
e xtend the works of Chen and W ang 1993, 1995a , Lucare lla and
s . s .
Morara 1991 , and W ang and Che n 1993 to allow the dire cte d links in a conce pt ne twork to be associate d with linguistic te rms or trape zoidal fuzzy numbe rs. The se t of linguistic term s we use d in this pape r and the ir corre sponding trape zoidal fuzzy numbe rs are shown in Table 1.
s . s .
In Che n and W ang 1993, 1995a and W ang and Che n 1993 , we have prese nte d the definitions of conce pt matrice s for modeling conce pt networks. The de finitions of concept matrice s and the transitive closure of the conce pt m atrices are reviewe d as follows.
v 4
Definition 1: Le t C be a se t of concepts, Cs C , C , . . . , C . A1 2 n
s . s .
conce pt matrix M is a fuzzy m atrix Kande l, 1986 ; M C , Ci j re pre se nts
s .
the re le vant value from conce pt C to concept C , where M C , Ci j i j g w0, 1 .x
A concept matrix M has the following propertie s:
1. Refle xivity,
s .
M C , Ci i s 1 , ; Cig C
Table 1. Linguistic terms and the ir corre sponding trape zoidal fuzzy numbe rs
Linguistic terms Trape zoidal fuzzy numbe rs
s . Nonre levant 0, 0, 0, 0 s . V ery low 0, 0, 0.02, 0.07 s . Low 0.04, 0.1, 0.18, 0.23 s . Me dium low 0.17, 0.22, 0.36, 0.42 s . Me dium 0.32, 0.42, 0.58, 0.65 s . Me dium high 0.58, 0.63, 0.80, 0.86 s . H igh 0.72, 0.78, 0.92, 0.97 s . V ery high 0.975, 0.98, 1, 1 s . Fully re levant 1, 1, 1, 1
2. M may not be symme tric, s . s . M C , Ci j / M C , Cj i 3. Transitivity, s . s . s . M C , Ci k 0 Max Min M C , C , M C , C
s
i j j k.
Cjg CDefinition 2: Le t M be a concept matrix,
f11 f12 ? ? ? f1 n f21 f22 ? ? ? f2 n ? ? ? ? ? ? Ms ? ? ? ? ? ? ? ? ? ? ? ? fn1 fn 2 ? ? ? fn n w x whe re n is the numbe r of conce pts in a conce pt ne twork, fi jg 0, 1 , 1( i ( n , 1 ( j ( n , and le t M2s Mª M s f n f . s f n f . ? ? ? s f n f .
E
1i i1E
1 i i2E
1 i i n is 1 , . . . , n is 1 , . . . , n is 1 , . . . , n s f n f . s f n f . ? ? ? s f n f .E
2 i i1E
2 i i2E
2 i i n is 1 , . . . , n is 1 , . . . , n is 1 , . . . , n s ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? s f n f . s f n f . ? ? ? s f n f .E
n i i1E
n i i 2E
n i i n is 1 , . . . , n is 1 , . . . , n is 1 , . . . , n s 15. whe re k and n are the maximum and minimum operators, respe c-tive ly. The n, the re e xists an integer p( n y 1, such that MPs MPq 1Pq 2 s . P
s M s ? ? ? please se e Kandel, 1986, p. 117 . Le t Qs M . Q is called the transitive closure of the conce pt matrix M.
In this paper, we allow the directe d links in a concept network to be associated with linguistic te rms shown in Table 1 or trapezoidal fuzzy
s .
numbe rs parame terized by a, b, c, d , whe re 0( a ( b ( c ( d ( 1,
and we use fuzzy conce pt matrice s to modeling the concept networks. The definition of fuzzy conce pt matrice s is pre sented as follows.
v 4
Definition 3: Le t C be a set of conce pts, Cs C , C , . . . , C , and F1 2 n
s . s .
be a fuzzy concept m atrix. F C , Ci j s a , b , c , di j i j i j i j indicate s that the fuzzy re le vant value from conce pt C to conce pt C is repre sented byi j
s .
trape zoidal fuzzy numbe r a , b , c , di j i j i j i j , where 0( a ( b ( c (i j i j i j di j( 1.
Definition 4: Le t F be a fuzzy conce pt matrix,
A11 A12 ? ? ? A1 n A21 A22 ? ? ? A2 n ? ? ? ? ? ? Fs ? ? ? ? ? ? ? ? ? ? ? ? An 1 An 2 ? ? ? An n
whe re n is the number of concepts, Ai j are trapezoidal fuzzy numbe rs,
s . Ai js a , b , c , di j i j i j i j , 0( a ( b ( c ( d ( 1, 1 ( i ( n , and 1 (i j i j i j i j j( n , and let F2 s F( F k
s
A1 in Ai1.
ks
A1 in Ai 2.
? ? ? ks
A1 in Ai n.
D
D
D
D
D
D
is 1 , . . . , n is 1 , . . . , n is 1 , . . . , n ks
A2 in Ai1.
ks
A2 in Ai 2.
? ? ? ks
A2 in Ai n.
D
D
D
D
D
D
is 1 , . . . , n is 1 , . . . , n is 1 , . . . , n ? ? ? ? ? ? s ? ? ? ? ? ? ? ? ? ? ? ? ks
An in Ai1.
ks
An in Ai 2.
? ? ? ks
An i n Ai n.
D
D
D
D
D
D
is 1 , . . . , n is 1 , . . . , n is 1 , . . . , n s 16.n k
whe re
D
andD
re prese nt the AND and O R ope rators of the trape zoidal fuzzy numbe rs, respectively. The n the re exists an integer p,p( n y 1, such that FPs FPq 1s FPq 2s ? ? ?
. Le t Qs FP
. Q is called the transitive closure of the fuzzy conce pt matrix F .
FUZZY QUER Y PR OC ESSING TEC HNIQUES FOR D OC UMENT R ETR IEVAL
v 4
Le t D be a set of docume nts, Ds d , d , . . . , d1 2 m , and C be a se t of
v 4
conce pts, Cs C , C , . . . , C . A document in a docume nt re trieval1 2 n
system is gene rally described by a se t of concepts with each conce pt re pre senting a topic. The relations betwe en documents and conce pts can be repre sented by a document descriptor matrix D shown as follows: C1 C2 ? ? ? Cn d1 B11 B12 ? ? ? B1 n d2 B21 B22 ? ? ? B2 n Ds ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? dm Bm 1 Bm 2 ? ? ? Bm n
whe re m is the number of docume nts, n is the numbe r of conce pts, Bi j
is a trapezoidal fuzzy num ber param eterized by a quadruple re prese nt-ing the de gree of relevance of docume nt d with re spe ct to concept C ,i j
1( i ( m , and 1 ( j ( n . In a docume nt de scriptor m atrix D, the degree of relevance of each docume nt with respe ct to a spe cific conce pt is de te rmine d by e xperts. Howe ver, an e xpe rt may possibly ne gle ct the degree of relevance of a ce rtain docume nt with respe ct to some specific conce pts. Be cause concepts may be not indepe nde nt of each othe r, the transitive closure Q of the fuzzy concept matrix F can be use d to e valuate the implicit re le vant value s of e ach docume nt with respe ct to specific concepts to improve this. Le t D be a document de scriptor matrix and Q be the transitive closure of the fuzzy concept matrix F ,
whe re C1 C2 ? ? ? Cn d1 B11 B12 ? ? ? B1 n d2 B21 B22 ? ? ? B2 n Ds ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? dm Bm 1 Bm 2 ? ? ? Bm n S11 S12 ? ? ? S1 n S21 S22 ? ? ? S2 n ? ? ? ? ? ? Qs ? ? ? ? ? ? ? ? ? ? ? ? Sn1 Sn 2 ? ? ? Sn n
whe re Bi j and Si j are trape zoidal fuzzy num bers parametrized by quadruples, 1( i ( n and 1 ( j ( n. Le t DUs D( Q k
s
B1 in Si1.
ks
B1 in Si 2.
? ? ? ks
B1 in Si n.
D
D
D
D
D
D
is 1 , . . . , n is 1 , . . . , n is 1 , . . . , n ks
B2 in Si1.
ks
B2 in Si 2.
? ? ? ks
B2 in Si n.
D
D
D
D
D
D
is 1 , . . . , n is 1 , . . . , n is 1 , . . . , n s ? ? ? ? ? ? , ? ? ? ? ? ? ? ? ? ? ? ? ks
Bn in Si1.
ks
Bn in Si 2.
? ? ? ks
Bn in Si n.
D
D
D
D
D
D
is 1 , . . . , n is 1 , . . . , n is 1 , . . . , n s 17. n kwhe re
D
andD
are the AND and O R operators of the trape zoidal fuzzy numbe rs, re spectively. The docume nt de scriptor matrix DU indi-cate s the degree s of re le vance of e ach docume nt with re spect to specific conce pts and is used as a basis for sim ilarity me asure s be twe e n user’ s que rie s and docume nts as describe d late r.In a fuzzy information retrie val system , the use r’ s que ry can be describe d by a query descriptor Q re prese nte d by a que ry de scriptor matrix q, that is,
v s . s . s . 4
Qs C , V , C , V1 1 2 2 , . . . , C , Vn n
w x
qs V , V , . . . , V1 2 n
whe re V is a trapezoidal fuzzy numbe r paramete rize d by a quadruple,i
1( i ( n , repre se nting the degree of strength that the desired docu-me nts contain conce pt C . If the use r considers that certain conce ptsi
may be ne glecte d, then the user doe s not have to assign the degree s of strength with re spe ct to such concepts in the que ry descriptor vector q. The symboly is used for labeling a ne gle cted conce pt. Thus, if V s y ,i it indicate s that conce pt C is a ne gle cted concept. In this case , thei
conce pt C would not be considere d in the docume nt re trie val process.i U Le t d de note the ith row of the docum ent de scriptor matrix D ,i
w x
dis P , P , . . . , P , and let q be the que ry de scriptor matrix, q si1 i2 i n
wV , V , . . . , V , whe re P and V are trape zoidal fuzzy numbe rs,1 2 nx i j j
s .
Pi js a , b , c , di j i j i j i j
s .
Vjs w , x , y , zj j j j
1( j ( n , 1 ( i ( m , n is the numbe r of concepts, and m is the s .
numbe r of docume nts. Le t q j denote the jth compone nt of the query s .
descriptor matrix q. If q j s y , it indicate s that the conce pt C is aj
negle cted concept with respect to the fuzzy query. B ase d on formula s11 , the degree of similarity betwe en d and q can be evaluated as. i
follows: s . S P , V
p
i j j s . q j/ ``y ’ ’ an d js 1 , . . . , n s . s . RS di s 18 k whe re <ai jy w q b y x q c y y q d y zj< < i j j< < i j j< < i j j< s . s . S P , Vi j j s 1 y 19 4s . w x
RS di g 0, 1 , 1( i ( m , and k is the number of concepts not ne -s .
glecte d in the que ry. The re trieval status value RS di indicate s the degree of sim ilarity be twe e n the query and the docume nt d , wherei
s .
1( i ( m . The larger the value of RS d , the highe r the similarityi
be twe e n the query and the document d .i
Conside r the following O R-conne cted query:
q O R q1 2
whe re q and q are query descriptor matrices. In this case, the de gre e1 2 of similarity betwe en the query and the documents can be e valuate d as follows:
Us . s s . s . . s .
RS di s Max RS d , RS d1 i 2 i 20
s .
whe re RS d1 i re pre se nts the de gre e of sim ilarity be twe e n the que ry descriptor matrix q and the i th row of the document de scriptor matrix1
U s .
D , RS d2 i re prese nts the de gre e of similarity be twe e n the query
descriptor matrix q and the ith row of the docume nt descriptor matrix2
U Us .
D , the retrie val status value RS di re pre sents the degree of
similar-ity of the que ry with respe ct to the document d , and 1i ( i ( m . The information re trieval system would display e very docume nt having a w x re trieval status value gre ate r than a thre shold value l , whe re l g 0, 1 , in a se que ntial orde r from the docume nt with the highest de gre e of re trieval status value to that with the lowe st one .
W eighted-fuzzy que rie s can also be proce ssed by our method. In we ighte d-fuzzy que rie s, a que ry e xpression can be re pre sented by a que ry descriptor matrix q shown as follows:
ws . s . s .x
qs V , W , V , W , . . . , V , W1 1 2 2 n n
whe re V and W are trapezoidal fuzzy numbe rs parameterize d byj j
quadruples, W re prese nts the we ights of conce pt C , and 1j j ( j ( n. Le t
U w x
the ith row of the docume nt de scriptor matrix D be P , P , . . . , Pi1 i2 i n , whe re P , P , . . . , and Pi1 i2 i n are trapezoidal fuzzy numbe rs parame te
ized by quadruple s. Then the de gre e of sim ilarity be twe en the we ighte d fuzzy que ry and the docum ent d can be calculated as follows:i
s . s . RSw di s
t
p
S P , Vi j j m Wj/
s . q j/ ``y ’ ’ an d js 1 , . . . , n %p
Wj s 21.D
t
/
s . Q j/ ``y ’ ’ an d js 1 , . . . , n %whe re m and
D
are the multiplication ope rator and the ratio opera-tor of the trape zoidal fuzzy numbe rs, re spe ctively, and p de notes the summation of the trapezoidal fuzzy numbe rs. The re trie val status values .
RSw di is a trape zoidal fuzzy numbe r indicating the degre e of similarity be twe e n the we ighte d-fuzzy que ry and the docume nt d , whe re 1i ( i (
m . Assume that s . s . RSw d1 s a , b , c , d1 1 1 1 s . s . RSw d2 s a , b , c , d2 2 2 2 . . . s 22. s . s . RSw dm s a , b , c , dm m m n s . s .
B ase d on formula 10 , the retrie val status value RSw di can be defuzzified into a crisp real value, where 1( i ( m . In this case, the
s . s .
defuzzified value of RSw di is e qual to aiq b q c q d r 4, wherei i i s .
1( i ( m . Let the de fuzzified value of RS dw i be e qual to k , wherei
w x w x
k29 g 0, 1 and 1( i ( m , and let l be a thre shold value , l g 0, 1 . The information re trieval system would display e very docume nt having a defuzzified re trie val status value k gre ate r than the threshold valuei l
in a se que ntial orde r from the docume nt with the highest de gre e of defuzzified re trie val status value to that with the lowe st one.
In the following, we use an example to illustrate the we ighted-fuzzy que ry processing process for docume nt re trieval.
Example: Assume that the re trieval threshold value l is 0.65, and
assum e that the re are four concepts C , C , C , C and five docume nts1 2 3 4
d , d , d , d , and d . Furthe rmore, assume that the docume nt de scrip-1 2 3 4 5 tor matrix D and the fuzzy conce pt matrix F have the following forms:
C1 C2 C3 C4 s0 .2, 0.3, 0.4, 0 .5. s0 .5, 0.6, 0.7, 0 .8. s1 , 1 , 1, 1. s0 , 0 , 0 , 0. d1 s1 , 1 , 1, 1. s0 .6, 0.7, 0.8, 0 .9. s0 .3, 0.4, 0.5, 0 .6. s0.5, 0.6, 0 .7 , 0 .8. d2 s . s . s . s . d 0 .5, 0.6, 0.7, 0 .8 1 , 1 , 1, 1 0 .1, 0.2, 0.3, 0 .4 0.7, 0.7, 0 .7 , 0 .7 Ds 3 s . s . s . s . d4 0 , 0 , 0, 0 0 .3, 0.4, 0.5, 0 .6 0 .5, 0.6, 0.7, 0 .8 1 , 1 , 1 , 1 d5 s0 .3, 0.4, 0.5, 0 .6. s0 .4, 0.5, 0.6, 0 .7. s0 , 0 , 0, 0. s0.5, 0.6, 0 .7 , 0 .8. C1 C2 C3 C4 s1, 1 , 1 , 1. s0 .975, 0 .98, 1, 1. s0 , 0 , 0, 0. s0, 0 , 0 , 0. C1 s0, 0 , 0 , 0. s1 , 1 , 1 , 1. s0.58 , 0 .63, 0 .80, 0 .86. s0 .975, 0 .98, 1, 1. C2 Fs s . s . s . s . C3 0, 0 , 0 , 0 0 , 0 , 0 , 0 1 , 1 , 1, 1 0, 0 , 0 , 0 C4 s0, 0 , 0 , 0. s0 , 0 , 0 , 0. s0 , 0 , 0, 0. s1, 1 , 1 , 1.
In this case , the transitive closure Q of the fuzzy concept matrix F can be calculate d as follows: C1 C2 C3 C4 s1, 1 , 1 , 1. s0 .975, 0 .98, 1, 1. s0.58 , 0 .63, 0 .80, 0 .86. s0 .975 , 0 .98, 1 , 1. C1 s . s . s . s . 0, 0, 0 , 0 1 , 1 , 1 , 1 0.58 , 0 .63, 0 .80, 0 .86 0 .975 , 0 .98, 1 , 1 C Qs 2 s . s . s . s . 0, 0 , 0 , 0 0 , 0 , 0 , 0 1 , 1 , 1 , 1 0, 0, 0, 0 C3 s0, 0 , 0 , 0. s0 , 0 , 0 , 0. s0 , 0 , 0 , 0. s1, 1, 1, 1. C4
The docume nt de scriptor matrix DU can be obtained based on the docume nt de scriptor m atrix D and the transitive closure Q of the fuzzy conce pt m atrix F as follows:
DU s D( Q C1 C2 C3 C4 s0 .2 , 0 .3 , 0 .4 , 0 .5. s0 .5 , 0 .6 , 0 .7 , 0 .8. s1 , 1 , 1 , 1. s0 .5 , 0 .6 , 0 .7 , 0 .8. d1 s1 , 1 , 1 , 1. s0 .97 5 , 0 .8 , 1 , 1. s0 .58 , 0 .6 3 , 0 .8 0 , 0 .86. s0 .9 7 5 , 0 .98 , 1 , 1. d2 d s . s . s . s . s 3 0 .5 , 0 .6 , 0 .7 , 0 .8 1 , 1 , 1 , 1 0 .58 , 0 .6 3 , 0 .8 0 , 0 .86 0 .9 7 5 , 0 .98 , 1 , 1 d4 s0 , 0 , 0 , 0. s0 .3 , 0 .4 , 0 .5 , 0 .6. s0 .5 , 0 .6 , 0 .7 , 0 .8. s1 , 1 , 1 , 1. d5 s0 .3 , 0 .4 , 0 .5 , 0 .6. s0 .4 , 0 .5 , 0 .6 , 0 .7. s0 .4 , 0 .5 , 0 .6 , 0 .7. s0 .5 , 0 .6 , 0 .7 , 0 .8.
If the use r’s we ighted-fuzzy query is repre sented by the query descriptor matrix q shown as follows:
ws s . s . .
qs 0 .6 , 0 .7 , 0 .8 , 0 .9 , 0 .6 , 0 .7 , 0 .8 , 0 .9 ,y , y , s s0 .9 , 0 .95, 0 .95 , 1 , 0 .5 , 0 .6, 0 .7 , 0 .8. s . .x
s .
The n based on formula 21 , we can ge t the following results: <0 .2y 0 .6 q 0 .3 y 0 .7 q 0 .4 y 0 .8 q 0 .5 y 0 .9< < < < < < < s . RSw d1 s
t
1y/
4 s . m 0 .6 , 0 .7 , 0 .8 , 0 .9 <0 .5y 0 .9 q 0 .6 y 0 .95 q 0 .7 y 0 .95 q 0 .8 y 1< < < < < < <Å
t
1y/
4 s . m 0 .5 , 0 .6 , 0 .7 , 0 .8 % ws 0 .6, 0 .7 , 0 .8 , 0 .9.Å
s 0 .5 , 0 .6 , 0 .7 , 0 .8.xD
s . s 0 .64545 , 0 .64615 , 0 .64667, 0 .64706 <1y 0 .6 q 1 y 0 .7 q 1 y 0 .8 q 1 y 0 .9< < < < < < < s . RSw d2 st
1y/
4 s . m 0 .6 , 0 .7 , 0 .8 , 0 .9 <0 .975y 0 .9 q 0 .98 y 0 .95 q 1 y 0 .95 q 1 y 1< < < < < < <Å
t
1y/
4 s . m 0 .5 , 0 .6 , 0 .7 , 0 .8 % ws 0 .6 , 0 .7 , 0 .8 , 0 .9.Å
s 0 .5 , 0 .6 , 0 .7 , 0 .8.xD
s . s 0 .84603, 0 .8475, 0 .84859, 0 .84941<0 .5y 0 .6 q 0 .6 y 0 .7 q 0 .7 y 0 .8 q 0 .8 y 0 .9< < < < < < < s . RSw d3 s
t
1y/
4 s . m 0 .6, 0 .7 , 0 .8 , 0 .9 <0 .975y 0 .9 q 0 .98 y 0 .95 q 1 y 0 .95 q 1 y 1< < < < < < <Å
t
1y/
4 s . m 0 .5, 0 .6 , 0 .7 , 0 .8 % ws0 .6 , 0 .7 , 0 .8 , 0 .9.Å
s0 .5 , 0 .6, 0 .7 , 0 .8.xD
s . s 0 .92785 , 0 .92827, 0 .92859, 0 .92882 <0y 0 .6 q 0 y 0 .7 q 0 y 0 .8 q 0 y 0 .9< < < < < < < s . RSw d4 st
1y/
4 s . m 0 .6 , 0 .7 , 0 .8 , 0 .9 <1y 0 .9 q 1 y 0 .95 q 1 y 0 .95 q 1 y 1< < < < < < <Å
t
1y/
4 s . m 0 .5 , 0 .6 , 0 .7 , 0 .8 % ws 0 .6 , 0 .7, 0 .8 , 0 .9.Å
s 0 .5 , 0 .6 , 0 .7 , 0 .8.xD
s . s 0 .56818 , 0 .57308, 0 .57667, 0 .57941 <0 .3y 0 .6 q 0 .4 y 0 .7 q 0 .5 y 0 .8 q 0 .6 y 0 .9< < < < < < < s . RSw d5 st
1y/
4 s . m 0 .6 , 0 .7 , 0 .8 , 0 .9 <0 .5y 0 .9 q 0 .6 y 0 .95 q 0 .7 y 0 .95 q 0 .8 y 1< < < < < < <Å
t
1y/
4% s . ws . s .x m 0 .5 , 0 .6 , 0 .7 , 0 .8
D
0 .6 , 0 .7 , 0 .8 , 0 .9Å
0 .5 , 0 .6 , 0 .7 , 0 .8 s . s 0 .7 , 0 .7 , 0 .7 , 0 .7 s .Based on formula 10 , we can ge t the following re sults: s .
The defuzzified value of RSw d1 is e qual to 0 .64545q 0 .64615 q 0 .64667 q 0 .64706
s 0 .64333
Ç
4
Ç
s .
The defuzzified value of RSw d2 is e qual to 0 .84603q 0 .8475 q 0 .84859 q 0 .84941
s 0 .84788
Ç
4
Ç
s .
The defuzzified value of RSw d3 is equal to 0 .92785q 0 .92827 q 0 .92859 q 0 .92882
s 0 .92838
Ç
4
Ç
s .
The defuzzified value of RSw d4 is equal to 0 .56818q 0 .57308 q 0 .57667 q 0 .57941
s 0 .57434 .
Ç
4
Ç
s .
The defuzzified value of RSw d5 is e qual to 0 .7q 0 .7 q 0 .7 q 0 .7
s 0 .7 . 4
Be cause the retrie val thre shold value l is 0.65, the docum ents d1 and d4 will not be re trie ve d be cause the re trieval status value s of the docume nts d1 and d4 are le ss than the threshold value . From the se re sults, we also can see that the docume nt d is the most suitable to the3 user’ s we ighte d-fuzzy query be cause it has the largest retrie val status value.
C ONC LUSIONS
In this pape r, we have pre sented a knowle dge -based me thod for pro-ce ssing fuzzy que rie s and we ighted-fuzzy queries for docume nt re trieval,
whe re the fuzzy concept m atrices are use d for knowle dge repre sentation and the e le ments in fuzzy concept m atrices are repre sented by trape
-s .
zoidal fuzzy num bers parame te rize d by quadruples a, b, c, d , whe re
0( a ( b ( c ( d ( 1. W e also use an e xample to illustrate the we ighte d-fuzzy query proce ssing process for docum ent re trieval. From the illustrated e xample , we can se e that the propose d method can be e xe cute d very e fficie ntly. The proposed method is a significant im prove-me nt ove r the m ethod based on B oolean algebra because it has the fuzzy query proce ssing capability. Furtherm ore , the proposed me thod is
s .
more flexible than the one s pre sented in Chen and W ang 1993, 1995a ,
s . s .
Lucare lla and Morara 1991 , and W ang and Chen 1993 because it allows the system’ s use rs to pe rform fuzzy queries and we ighted-fuzzy que rie s. Inte llige nt retrie val capability and fle xible use r’s que rie s are consequently provided for.
R EFER ENC ES
Che n, S. M. 1992a. A fuzzy re asoning technique base d on the a -cuts ope rations of fuzzy num bers. Proceed ings of the Secon d International Con feren ce on
Au tom ation Tech nology, Taipe i, Taiwan, Re public of China, pp. 147] 154.
Che n, S. M. 1992b. An improve d algorithm for inexact re asoning base d on s .
extende d fuzzy production rule s. Cybern. Syst. 23 5 :463] 481.
Che n, S. M. 1992c. A ne w approach to ine xact re asoning for rule-base d syste ms. s .
Cybern. Syst. 23 6 :561] 582.
Che n, S. M. 1993. An inexact reasoning te chnique using linguistic rule matrix transformations. Proceedin gs of the IEE E 23rd In ternational Sym posiu m on
Multiple-Valued Logic, Sacramento, CA, pp. 190] 195.
Che n, S. M. 1994a. Using fuzzy reasoning technique s for fault diagnosis of the J-85 je t e ngines. Proceedings of the Third National Conference of Scien ce and Tech nology of National Defense, Taipe i, Taiwan, Republic of China, pp. 29] 34.
Che n, S. M. 1994b. A ne w me thod for handling multicriteria fuzzy decision-mak-s .
ing proble ms. Cybern. Syst. 25 3 :409] 420.
Che n, S. M. and J. Y. Wang. 1993. A new approach for fuzzy information retrie val. Proceed ings of 1993 National Com puter Sym posiu m , Chiayi, Taiwan, Re public of China, vol. 2, pp. 767] 774.
Che n, S. M. and J. Y. Wang. 1995a. Docum ent re trieval using knowledge -based fuzzy information retrie val technique s. IEEE Trans. Syst. Man Cybern.
s .
25 5 :793] 803.
Che n, S. M. and S. Y. Lin. 1995b. A ne w method for fuzzy risk analysis. Proceed ings of 1995 Artificial Intelligence Workshop, Taipe i, Taiwan, Republic of China, pp. 245] 250.
Che n, S. M., J. S. Ke , and J. F. Chang. 1989. Technique s for handling multicrite -ria fuzzy de cision-making proble ms. Proceed ings of the 4th Internation al Sym posiu m on Com pu ter and In form ation Scien ces, Cesme , Turke y, vol. 2, pp. 919] 925.
Che n, S. M., J. S. Ke , and J. F. Chang. 1991. An inexact reasoning algorithm for de aling with ine xact knowle dge. Int. J. Software Eng. Knowledge Eng.
s .
1 3 :227] 241.
Her, G. T. and J. S. Ke . 1983. A fuzzy information re trie val syste m mode l. Proceed ings of 1983 National Com puter Sym posium , Taiwan, Re public of China, pp. 147] 155.
Kame l, M., B. Hadfield, and M. Ismail. 1990. Fuzzy que ry proce ssing using s .
cluste ring technique s. Inform . Process. Manage. 26 2 :279] 293.
Kande l, A. 1986. Fuzzy m athem atical techniques with applications. Reading, MA: Addison-We sle y.
Kaufman, A. and M. M. Gupta. 1985. Introduction to fu zzy arithm etic: Theory and application s. New York: V an Nostrand Re inhold.
Kaufman, A. and M. M. Gupta. 1988. Fu zzy m athem atical m odels in engineering and m an agem en t science. Amste rdam: North-Holland.
Kraft, D. H. and D. A. Buell. 1983. Fuzzy se ts and generalize d Boolean retrie val s .
syste ms. In t. J. Man Machine Stud. 19 1 :45] 56.
Lucare lla, D. and R. Morara. 1991. FIRST: Fuzzy information retrieval system.
J. Inform. Sci. 17:81] 91.
Miyamoto, S. 1990. Information re trieval based on fuzzy associations. Fuzzy Sets
Syst. 38:191] 205.
Murai, T., M. Miyakoshi, and M. Shimbo. 1989. A fuzzy docum ent retrie val me thod base d on two-valued inde xing. Fuzzy Sets Syst. 30:103] 120.
Radechi, T. 1979. Fuzzy set theore tical approach to docum ent retrie val. In form.
Process. Manage. 15:247] 259.
Salton, G. and M. J. McGill. 1983. In troduction to m odern inform ation retrie¨al. Ne w York: McGraw-Hill.
Tahani, V . 1976. A fuzzy mode l of docum ent retrie val syste m. Inform . Process.
Manage. 12:177] 187.
Wang, J. Y. and S. M. Che n, 1993. A knowle dge-base d me thod for fuzzy information re trieval. Proceed ings of the First Asian Fuzzy System s Sym po-siu m , Singapore, Nove mber.
Z adeh, L. A. 1965. Fuzzy sets. Inform . Con trol 8:338] 353.
Z emankova, M. 1989. FIIS: A fuzzy inte lligent information system. Data Eng. s .
12 2 :11] 20.
