Fuzzy easoning in con idence e alua ion o speech ecogni ion
Gus a o He n´andez- ´
Ab ego and Jos´e B. Ma i˜no

TALP Resea ch Cen e
Dep Teo ia del Senyal i Comunicacions, Uni e si a Poli `ecnica de Ca alunya
Jo di Gi ona 1-3, Campus No d D-5, Ba celona 08034, Spain
(ab ego/can on)@gps. sc.upc.es
Abs ac
Con idence measu es ep esen a sys ema ic way o ex-
p ess eliabili y o speech ecogni ion esul s. A common
app oach o con idence measu ing is o ake p o i o he
in o ma ion ha se e al ecogni ion- ela ed ea u es o e
and o combine hem, h ough a gi en compila ion mecha-
nism, in o a mo e e ec i e way o dis inguish be ween co -
ec and inco ec ecogni ion esul s. We p opose o use
a uzzy easoning scheme o pe o m he in o ma ion com-
pila ion s ep. Ou app oach opposes he p e iously p o-
posed ones because ou s ea s he unce ain y o ecogni-
ion hypo heses in e ms o “possibili y” con as ed o he
“p obabili y” no ion o simila wo ks. Expe imen al e-
sul s o e isola ed wo ds, con inuous speech and keywo d
spo ing ecogni ion asks show highe pe o mance o ou
sys em compa ed agains s anda d compila ion me hods.
He e we demons a e ha , due o hei app oach o un-
ce ain y; o hei capabili ies o handle expe knowledge
and o hei e sa ili y, Fuzzy In e ence Sys ems ep esen
a na u al way o add up ecogni ion in o ma ion in o con-
idence measu es.
1. In oduc ion
In spi e o he mul iple e o s done o da e on au o-
ma ic speech ecogni ion echnology,i s esul s a e no pe -
ec . E e y ime a ecognizedwo dsequence is conside ed,
he e is some deg ee o unce ain y abou i s co ec ness.
Con idence measu es (CM’s) ep esen a easible way o
exp ess which o he ecognized sequences a e likely o
be co ec and which can be dis ega ded as inco ec . A
a he simple echnique, ha has shown ema kable esul s,
o gene a e con idence measu es is known as “Likelihood
sco e a io” (LSR) [10]. I is done by no malizing he like-
lihood sco e esul ing om he Vi e bi decoding p ocess

This esea ch was suppo ed by CONACyT and by CICYT unde
con ac TIC98-0423-C06-01
by he likelihood sco e p oduced by an al e na i e ecog-
ni ion ne wo k. In ou wo k, we add o he in o ma ion
ela ed o he speech ecogni ion p ocess o he LSR by
means o a uzzy in e ence sys em in o de o build a mo e
eliable measu e o con idence. This pape is o ganized
as ollows: i s , in sec ion 2, ea u es ex ac ed om he
ecogni ion p ocess a e conside ed. In sec ion 3, he im-
po ance o g adual e ms in con idence measu ing is e-
ma ked and uzzy logic is p esen ed as a sui able ame-
wo k o deal wi h deg ees o con idence. Some con igu a-
ions o he ea u e-compila ion s ep a e desc ibed on sec-
ion 4. The expe imen al amewo ks in which ou sys em
is es ed a e desc ibed on sec ion 5 and he esul s ob ained
a e discussed in sec ion 6. Conclusions and u u e lines o
esea ch a e enume a ed on sec ion 7.
2. Fea u es o exp ess deg ees o con idence
Con idence measu es can be gene a ed by combining
in o ma ion abou he ecogni ion sys em in a ea u e-
compila ion ashion [2]. This app oach has p o en o ise
he disc imina i epowe o CM’s when he ea u es a e ex-
ac ed om he compa ison o al e na i e ecogni ion hy-
po heses o om mul iple hypo heses ecogni ion schemes
[11]. Some ea u es, by hemsel es, can be di ec ly ea ed
as CM’s, howe e , no e e y ea u e p esen s high dis-
c imina ion capabili ies and some o hem may ep esen
a high e o o be calcula ed wi hou high pe o mance as
compensa ion. Th ough ca e ul s udy o he na u e o he
ecogni ion p ocess, we ha e o mula ed h ee ea u es o
be he basis o ou expe imen a ion:
2.1. Likelihood sco e a io (LSR)
Ou i s ea u e is he likelihood sco e a io (LSR) i -
sel . Fo i s calcula ion, he likelihoodsco e o he ecogni-
ion hypo hesisis no malized by he sco e o an al e na i e
ecogni ion ne wo k:
LS R
=
log
L
(
~
X
j

p
)

log
L
(
~
X
j

a
)
:
(1)
~
X
is he ec o o acous ic ea u es ela ed o he ac ual in-
pu u e ance and

p
and

a
a e he se s o hidden Ma ko
models o he p incipal and al e na i e ecogni ion ne -
wo ks espec i ely. Due o i s uncons ained (and inac-
cu a e) na u e, he pu pose o he al e na i e ne wo k is o
model he un es ic ed signal p obabili y,
P
(
~
X
)
. This p o-
cedu e ends o app oxima e Bayes law in pos e io p oba-
bili y calcula ion. Because i s simplici y and i s high pe -
o mance [10], we conside his ea u e as ou baseline.
2.2. Sequence alignmen sco e (SAS)
Ou second ea u e is wha we call “sequence alignmen
sco e” (SAS). In he calcula ion o likelihood sco e a io,
he sco es o bo h ecognize s ha e been conside ed, bu
he decoded s ings ( he main p oduc o ecogni ion) ha e
been dis ega ded. We ha e epo ed in a p e ious pape
[3] ha a p ope compa ison be ween he p incipal ecog-
ni ion hypo hesis and he al e na i e one can esul in an
e icien ea u e o con idence measu ing. The easoning
behind his ea u e is o conside he al e na i e sequence
as a “second opinion”. Al hough his sequence canno be
conside ed as a ecogni ion hypo hesis, i can p o ide in-
o ma ion abou he na u e o he ecogni ion p ocess. This
app oach is di e en om conside ing mul iple hypo he-
ses o ecogni ion since bo h “opinions” a e aken om
wo comple ely di e en ecognize s. To calcula e SAS,
he p incipal ecogni ion hypo hesis is ansc ibed in o he
phone ic uni s used by he al e na i e ecognize . This
“p incipal” s ing is ime aligned agains he “al e na i e”
ecogni ion s ing. The cos o he alignmen o e e y pai
o uni s (p incipal and al e na i e) is aken om a con-
usion ma ix p e iously calcula ed ha co e s he ypi-
cal hi s, con usions, dele ions and inse ions p esen when
ecogni ionis made wi h he al e na i euni s se . The o e -
all alignmen sco e o bo h s ings is wha we call SAS. A
g aphical ep esen a ion o he calcula ion o SAS is p e-
sen ed on igu e 1 and exp essed in o mulae by:
S AS
= max
j
(
i
)
Y

(
p
i
j
q
j
(
i
)
)
p
i
2
P ; q
j
(
i
)
2
Q
(2)
whe e
P
is he p incipal s ing and
Q
he al e na i e
one.

(
p
i
j
q
j
(
i
)
)
is he con usion p obabili y o he pai o
uni s
p
i
; q
j
(
i
)
. The index
j
is a unc ion o
i
acco ding o
he es ic ions shown on he igh pa o igu e 1.
This ea u e ends o model he dis ance be ween wo
di e en ecogni ion opinions. The al e na i e hypo he-
sis will only be close o he p incipal one when bo h o
hem p esen simila esul s. In o de o a oid high sco es
om common con usions, phone ic uni s ha e been ga h-
e ed in g oups unde con usabili y c i e ia and penal ies o
he alignmen sco e a e applied acco dingly. This ea u e,
by i sel , has a medium disc imina i e powe ha does no
su pass he pe o mance o LSR (see igu es 4 h ough 6).
p l a
a oG
n
P incipal
Al e na i e
Allowed mo emen s
Subs i u ion Inse ion
o Hi
Dele ion
Figu e 1. Calcula ion o SAS
2.3. Rela i e speaking a e (RSR)
When dealing wi h con inuous speech, ecogni ion e -
o s a e no jus o con usion na u e. Ins ead, inse ions
and dele ions a e a common p esence. Ou hi d ea u e is
concei ed o handle his so o e o s. We call i “Rela i e
speaking a e” (RSR) and i is calcula ed acco ding o:
RS R
=
N
T

N
i;
T

i;
(3)
whe e
N
T
is he o al numbe o speech uni s (wo ds,
phones, e c) de ec ed in he whole ecogni ion hypo hesis
and
N
i;
is he numbe o uni s de ec ed in he ime in-
e al
(
;
i
)
conside ed.
T
is he du a ion o he whole
u e ance and
i;
is he leng h o he ime in e al. This is
a ela i e measu e because, o calcula e i s alue o a sin-
gle wo d, i akes in o accoun in o ma ion om he whole
ph ase. This ea u e is in ended o de ec he lack o excess
o phone ic uni s in a ecogni ion hypo hesis. I should
be no iced ha his ea u e is only use ul on con inuous
speech and i s use on isola ed wo ds o keywo ds spo ing
is no ecommended because i may lead o w ong alues
o con idence.
3. Fuzzy In e ence Sys ems in con idence mea-
su ing
P obabili y, unde s ood om a equency poin o iew,
deals wi h unce ain y in e ms o occu ences o known
ac s. In he case o speech ecogni ion esul s, he known
ac s a e whe he he ecogni ion hypo hesis is co ec o
no . P obabili y is use ul when dealing wi h se ial e en s
ha equi e an enume a ion no ion o unce ain y bu is no
e y use ul when he unce ain y is abou he deg ee o ac-
complishmen o a known si ua ion [5]. This is he case o
con idence measu ing whe e he ask is o know o e e y
single ecogni ion hypo hesis, i s deg ee o possible co -
ec ness. The no ion o “possibili y” opposed o “p obabil-
i y” is a ele an con as ha uzzy logic p esen s in on
o p obabili y heo y.
The spi i o con idence measu es is o exp ess he un-
ce ain y o speech ecogni ion esul s in g adual e ms
and no in equency. Unde such conside a ion, uzzy
logic ep esen s na u al ounda ions o con idence mea-
su es. Bu uzzy logic is no jus a heo e ic ool o ep e-
sen unce ain y, a good sha e o i s success is due o he
se e al p ac ical implemen a ions i has. Fuzzy logic sys-
ems o Fuzzy In e ence Sys ems (FIS) a e schemes ha
(among o he capabili ies) allow o map a numbe o uzzy
a iable inpu s in o a numbe o uzzy ou pu s [7]. The
mapping is done by a se o uzzy ules ha ela es inpu s
wi h ou pu s in an “i ... hen” ashion. Inpu s and ou -
pu s can be ep esen ed by means o uzzy a iables able
o con ain language e ms and uzzy hedges. By analyz-
ing he his og ams o each o he ea u es ha we ha e
p oposed, some cha ac e is ics o hem a e obse ed and
some uzzy h esholds o sepa a e hei alues when he e
is a co ec o inco ec esul a e p oposed. This analysis
allows us o de ine some ules o beha io acco ding o he
co ec ness s a us o he hypo heses. The collec ed expe
knowledge can be condensed in a uzzy in e ence sys em.
In his applica ion, he uzzy sys em can be unde s ood as
a non-linea classi ie (jus as a neu al ne wo k) ha ans-
o ms se e al inpu s in o a unique ou pu ha compiles all
he in o ma ion gi en.
4. Fea u e compila ion schemes
I is cus oma y ha he compila ion s ep o he in o -
ma ion included in he ecogni ion ea u es is pe o med
by means o a uni ing ool based on he de elopmen o
condi ional p obabili ies. In such a way, Bayesian classi-
ie s [1], linea disc imina i e analysis [11], decision ees
[9] and neu al ne wo ks [12] ha e been used as easoning
schemes o compile he in ol ed ea u es. We ha e buil
some classi ie s based on some o he schemes men ioned
o compa e hei pe o mance agains uzzy sys ems.
4.1. Bayesian classi ie (BC)
This is a a he simple classi ie ha maps ecogni ion
ea u es in o a con idence measu e by means o a linea
combina ion. The coe icien s o such a combina ion a e
calcula ed om he co a iance ma ix o he ea u es de-
i ed om some aining da a. Th oughou his pape , his
p ocedu e may also be called BC.
4.2. Neu al Ne wo ks (MLP)
Neu al ne wo ks ha e been b oadly used o combine
ecogni ion ea u es in o CM’s. High pe o ming esul s
ha e been epo ed [12] and hei ad an ages o e o he
combina ion sys ems ha e been la gely discussed [11].
Ne wo k opology is always a delica e issue. Rema kable
esul s ha e been achie ed wi h mul i-laye pe cep ons
(MLP’s) when ained unde a back p opaga ion ame-
wo k. Simple con igu a ions ha e been p e e ed ins ead
o complica e ones since pe o mance is qui e simila [11].
Fo ou expe imen a ion, we ha e chosen a eed- o wa d
MLP wi h 1 hidden laye con aining 4 o 6 elemen s, each
wi h a hype bolic angen sigmoid ans e unc ion. The
inpu laye deals wi h he alues o he ea u es and he
ou pu laye deals wi h he CM alue. The pa ame e s o
he ne a e adjus ed in a back p opaga ion lea ning phase
aking examples om a aining da abase.
4.3. Fuzzy In e ence Sys em (FIS)
Fuzzy in e ence sys em, as a classi ica ion engine, can
be equipped wi h expe knowledge capable o sepa a e
class elemen s. Fo wha ou sys em is conce ned, a a he
simple con igu a ion is conside ed. A Sugeno- ype FIS is
chosen due o i s good beha io as classi ie and i s sim-
plici y [4]. The numbe o inpu a iables depends on he
numbe o ea u es used. The ou pu a iable is he alue
o he CM. The uzzy ules a e designed wi h a “ ein o ce-
men ” spi i . Likelihood sco e a io is ea ed as he main
disc imina ion a iable and he es o he ea u es a e em-
ployed o ein o ce i s alues. The ules o he uzzy in e -
ence sys em allows o ac i a e and deac i a e he in luence
o he ein o cing ea u es con enien ly. Figu e 2 shows an
schema ic ep esen a ion o he FIS used o combine like-
lihood sco e a io and sequence alignmen sco e. The se
o ules o his sys em is p esen ed on igu e 3
C3
C5
C6
C7
C8
a e age
CM
C1
C4
C2
weigh ed
SAS
LSR
Figu e 2. FIS o combine LSR and SAS
In igu e 3, he consequen pa s o he ules a e con-
s an s, bu we will p o e ha , e en wi h his simple con ig-
u a ion, FIS pe o ms e ec i ely as uni ing ool o CM’s.
5. Expe imen al amewo k
Expe imen al wo k has been ca ied ou wi h Spanish
Speechda [8] as de eloping and es ing da abase. This is
a da abase collec ed h ough he ixed elephone ne wo k,
1. i LSR = low and SAS = low, hen CM = 0
2. i LSR = low and SAS = midlow, hen CM =0.05
3. i LSR = low and SAS = midhigh, hen CM =0.15
4. i LSR = low and SAS = high, hen CM =0.25
5. i LSR = high and SAS = low, hen CM =0.65
6. i LSR = high and SAS = midlow, hen CM =0.75
7. i LSR = high and SAS = midhigh, hen CM= 0.9
8. i LSR = high and SAS = high, hen CM = 1
Figu e 3. Se o uzzy ules o a FIS o wo
ea u es
sampled a 8 kHz and eco ded unde se e al acous ic en-
i onmen s. Speech was pa ame e ized wi h mel-ceps um
coe icien s. Fi s and second o de di e en ial pa ame e s
plus he di e en ial ene gy we e employed. The ecogni-
ion sys em models he phone ic uni s by Gaussian semi-
con inuous hidden Ma ko models (HMM’s) wi h quan i-
za ion o he 6 (2 o he ene gy) closes codewo ds. The
codebook size was 256 (32 o he di e en ial ene gy).
Nea o 1000 speake s ha e been selec ed o each o he
aining and es ing se s. The e is no speake o e lapping
be ween se s. To co e some o he possible amewo ks
whe e CM a e ele an , we ha e spli ou expe imen a ion
on he ollowing ecogni ion asks:
1. Isola ed wo ds: each speake p onounces a name o
Spanish ci ies aken om he “Ci y” pa o Speech-
da .
2. Con inuous speech: speake s u e p omp ed ime
ph ases. The a e age numbe o wo ds pe ph ase is
a ound 9.4. Ph ases a e aken om he “Time” pa o
Speechda .
3. Keywo dspo ing: ph asescon ainingembeddedkey-
wo ds a e u e ed by he speake s. Each sen ence may
con ain 1 o 4 keywo ds. These sen ences come om
he “KeySen ence” pa o he da abase.
The o e all ask is o alida e he ecogni ion esul s ha
he ecognize p oduces when dealing wi h each o he ex-
pe imen a ion asks. The p incipal ecognize is ailo ed
o be applica ion independen . Fo acous ic modeling, i
is based on high-pe o mance sublexical phone ic uni s
(Demiphones [6]) combined in o ocabula y ins ances by
means o an speci ic language model (LM). Fo isola ed
wo ds a null g amma (all ocabula y wo ds ha e equal
p obabili y) is used. Con inuousspeech ecogni ion is con-
duc ed by a ini e-s a e g amma ha co e s e e y possi-
ble ime ph ase. Keywo d spo ing has an s ochas ic i-
g am as LM. Fo his ask, keywo ds a e ep esen ed by
Demiphones and ou o ocabula y ins ances (OOV) by
a ne wo k o phonemes. Since ou pu pose is o de ec
keywo ds a maximum, he p esence o OOV is es ic ed
by penalizing ansi ions in he phoneme ne wo k. On
he o he hand, he al e na i e ecognize is equipped wi h
loose language es ic ions and Phonemes, ained unde a
disc imina i e c i e ion, as phone ic uni s.
De ec ion a e, measu ed as he pe cen age o co ec ly
ecognized wo ds, as well as he numbe o alse ala ms
and he con igu a ion o he es se s o each o he ecog-
ni ion asks is shown on able 1
isola ed con inuous keywo ds
oc. size 500 59 30
speake s 989 995 993
wo ds 989 9405 1485
alse ala ms 172 377 1132
de ec ion 82.61 % 95.23 % 93.80 %
Table 1. Con igu a ion, alse ala ms and de-
ec ion a e o he ecogni ion asks es ed
The numbe o alse ala ms is he summa ion o in-
se ions and subs i u ions. Wi hou any alida ion o he
ecogni ion hypo heses, o e ie e he gi en de ec ion
a e, would imply o accep he indica ed numbe o alse
ala ms. Some ema k abou he ecogni ion a es is wo h-
while: he de ec ion a e o isola ed wo ds is a he small
due o he la ge numbe o possible wo ds o de ec . De-
ec ion in con inuous speech is e y high o wo ds bu no
o ph ases (78.19 %). In keywo d spo ing, i is possible
o achie e a high de ec ion a e bu wi h a la ge numbe o
alse ala ms as coun e pa .
Gene a ion o con idence measu es passes h ough he
calcula ion o ea u es o each de ec ed wo d. Nex , he
ea u es o e e y ecogni ion candida e a e compiled, by
means o one o he p e iously men ioned combina ion en-
gines, in o a CM o each wo dhypo hesis. Pe o manceo
CM’s is e alua ed in e ms o hei capabili ies o alida e
co ec hypo heses and ejec alse ala ms.
6. Discussion
In a ask o esul s classi ica ion, he e can be wo kinds
o e o s: alse ala ms (i.e. w ong esul s ega ded as co -
ec ones) and alse ejec ions (co ec esul s w ongly e-
ga ded as inco ec ). To show he ela ionship be ween
hese wo ypes o e o s, i is cus oma y o gene a e ROC’s
( ecei e ope a ion cha ac e is ics). In his wo k, ROC’s
a e buil by a ying he alue o he alida ion h eshold
imposed o he esul ing con idence measu es and plo ing
he a e o alse ala ms agains he a e o co ec ly ecog-
nized okens. An ideal classi ie would be able o co ec ly
de ec a la ge numbe o ins ances while accep ing a low
numbe o alse ala ms.
Figu e 4 shows he ROC’s o he ea u es and com-
bined CM’s gene a ed by di e en me hods o he iso-
0 10 20 30 40 50 60 70 80 90 100
0
10
20
30
40
50
60
70
80
90
100
Pe cen age o alse ala ms
Pe cen age o de ec ion
FIS
LSR (baseline)
MLP
BC
SAS
Figu e 4. ROC’s o he isola ed wo ds ecog-
ni ion ask
la ed wo ds ask. As p e iously men ioned, LSR is con-
side ed as baseline. SAS is used as ein o ce , al hough
i does no pe o m well enough in isola ion. These plo s
show ha all combina ion p ocedu es p esen highe dis-
c imina i e cha ac e is ics han he baseline. Rema kably,
uzzy sys em p esen s a good beha io along he whole
plo and i is only sligh ly su passed by MLP in a small
egion o i . Compa ed agains he baseline, a a gi en
alse ala ms a e, FIS p esen a no iceable inc emen o de-
ec ion. Fo con inuous speech, a simila beha io can be
obse ed in igu e 5. In his case, baseline has lowe pe -
o mance han any o he combina ions. SAS has a lowe
pe o mance compa ed o he isola ed wo ds case and he e
ela i e speaking a io has also been conside ed as ein-
o ce , hough i canno be conside ed as a sui able con i-
dence measu e by i sel . In his case, combina ions p esen
some i egula beha io : while BC and MLP pe o m well
in he high de ec ion zone, hey d opin he low alse ala ms
egion. In con as , FIS beha es sa is ac o ily a high de-
ec ion bu conside ably be e a he low alse ala ms e-
gion. Fo he keywo d spo ing case, shown in igu e 6,
only SAS, whose pe o mance is qui e ai , is conside ed
as ein o ce . I is wo h no icing ha e e y combina ion
he e clea ly ou pe o ms he baseline and, among combi-
na ions, FIS shows he bes pe o mance along he whole
g aph.
A commonly accep ed summa y o ROC cu es is he
equal-e o a e (EER). This is he poin whe e he a e o
alse ala ms equals he a e o alse ejec ions. Table 2
con ains he EER alues o he ea u es and he combi-
na ion p ocedu es es ed. All o he combina ions p esen
impo an educ ionso he EER compa ed obaseline. FIS
achie es he lowes a es o e e y ecogni ion ask, excep-
ion made o keywo d spo ing whe e i is su passed by
he MLP a he equal e o poin . Howe e , om igu e 6
0 10 20 30 40 50 60 70 80 90 100
0
10
20
30
40
50
60
70
80
90
100
Pe cen age o alse ala ms
Pe cen age o de ec ion
FIS
LSR (baseline)
MLP
BC
SAS
RSR
Figu e 5. ROC’s o he con inuous speech
ecogni ion ask
i can be no iced ha MLP does no ou pe o m FIS in he
low alse ala ms egion.
Isola ed Con inuous Keywo ds
LSR (baseline) 20.75 23.65 21.25
SAS 30.45 34.35 31.90
RSR - 39.00 -
BC 19.45 23.25 19.75
MLP 19.85 22.85 19.05
FIS 18.50 22.05 19.35
Table 2. EER o ea u es and combina ions
In he compa ison o in o ma ion compila ion ools, i
should be conside ed ha he pa ame e s o uzzy in e -
ence sys ems ha e no been uned up by means o he ain-
ing da a as he Bayesian classi ie and mul i-laye pe cep-
on ha e, ins ead hey ha e been adjus ed manually based
on obse a ion. The MLP used o isola ed wo ds and
he one used o keywo d spo ing ha e di e en pa am-
e e s se s whe eas he FIS emains he same on bo h ap-
plica ions. I is expec ed ha some ine uning p ocedu e
conside ing he aining da a (as in an ANFIS amewo k
[4]), would ise he pe o mance o he FIS. Howe e , he
need o speci ic aining da a o adjus pa ame e s u ns
he sys em applica ion dependen . So a , ou compila-
ion ools ha e been designed conside ing in o ma ion ex-
ac ed om each ecogni ion ask esul ing in ask-speci ic
sys ems. This is no he case o FIS. We ha e e icien ly
applied a gene ic sys em o co e bo h, isola ed wo ds
and keywo d spo ing, en i onmen s (whe e wo ea u es
a e used) wi hou any adap a ion s ep and we ha e only
changed he sys em when a hi d ea u e is needed (in con-
inuous speech). This e sa ili y and anspo abili y ep e-
sen s ano he ad an age o FIS o e he es o he sys ems.

0 10 20 30 40 50 60 70 80 90 100
0
10
20
30
40
50
60
70
80
90
100
Pe cen age o alse ala ms
Pe cen age o de ec ion
FIS
LSR (baseline)
MLP
BC
SAS
Figu e 6. ROC’s o he keywo d spo ing
ecogni ion ask
Ne e heless, o e e y combina ion p ocedu e, applica-
ion dependency can be ackled by implemen ing sublex-
ical (phonemes o g oups o phonemes ins ead o wo ds)
ea u es and con idence measu es.
A inal ema k is dese ed: he con igu a ion o ou
sys em does no equi e any in o ma ion de i ed om he
ecogni ion p ocess bu only om he ecogni ion esul s
by hemsel es. This allows o build a con idence label-
e s independen ly o he ecognize and a oids he need
o exhaus i e ack o he whole ecogni ion p ocess. As
a coun e pa , i needs o an al e na i e ecogni ion s ep,
whose con igu a ion is e y simple, ha does no ep esen
a se ious inc emen o he compu a ional load.
7. Conclusions
In his pape we ha e shown ha uzzy logic is a na -
u al and e ec i e app oach o measu e he con idence o
speech ecogni ion esul s. The way i handles unce -
ain y, in e ms o possibili y, esul s mo e consis en ha
he way p obabili y heo y does. Fuzzy in e ence sys ems
ha e been e icien ly used o compile ea u es ela ed o he
ecogni ion p ocess in o a mo e disc imina i e con idence
measu e. They add up in o ma ion in o a syne ge ic way
so he esul ing combina ion always su passes he o igi-
nal ea u es on hei own. F om ROC’s i is obse ed
ha he combina ion o ea u es is a p ocess wo hwhile.
Compa ed agains Bayesian classi ie s and mul i-laye pe -
cep ons, uzzy in e ence sys ems show a be e and mo e
s able beha io o he ecogni ion asks ied, being able
o main ain high de ec ion a es while p ope ly ejec ing
alse ala ms, e en when hei con igu a ion is a he sim-
ple. Fu he mo e, uzzy sys ems has demons a ed o be
e sa ile and anspo able be ween applica ions. The p o-
cedu e we p opose akes p o i o in o ma ion ex ac ed ex-
clusi ely om he ecogni ion esul s and does no need o
ha e any pa icula ela ion wi h a conc e e speech ecog-
ni ion scheme a all.
The on-going esea ch abou his opic includes:

o de elop sublexicalp ocedu esand con idencemea-
su es in o de o a oid he need o applica ion speci ic
da a o aining;

o add in o ma ion om he language model in o de
o imp o e he disc imina ion in con inuous speech;

o include a sel -lea ning p ocedu e o he uzzy sys-
ems con igu a ion in o de o inely une i s pa ame-
e s.
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