XFL3: A NEW FUZZY SYSTEM SPECIFICATION LANGUAGE
F. J. Mo eno-Velo, S. Sánchez-Solano, A. Ba iga, I. Ba u one, D. R. López
Ins i u o de Mic oelec ónica de Se illa - Cen o Nacional de Mic oelec ónica
A da. Reina Me cedes s/n, (Edi . CICA),
E-41012, Se illa, Spain
5 h WSES /IEEE Mul icon e ence on Ci cui s, Sys ems,
Communica ions and Compu e s (CSCC 2001),
pp. 361-366, Re hymnon, Julio 2001
© 2001 IEEE. Pe sonal use o his ma e ial is pe mi ed. Howe e , pe mission o ep in / epublish his ma e ial o ad e -
ising o p omo ional pu poses o o c ea ing new collec i e wo ks o esale o edis ibu ion o se e s o lis s, o o euse
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mission o he copy igh holde .
1 In oduc ion
The de ini ion o o mal languages o uzzy sys em
speci ica ion is usual o i s se e al ad an ages
[3][4].Howe e , woobjec i esmaycon lic .Onone
side, a high exp essi e language, able o apply all he
uzzy logic-based o malisms, is desi ed. On he o h-
e side, he inal sys em implemen a ion cons ain s
ha e o be conside ed. In his sense, some languages
ocus on exp essi eness [5][6], while o he s a e o-
cused on so wa e o ha dwa e implemen a ions [7].
When ou g oup begun o design a uzzy sys em en-
i onmen , ou aim was o mee bo h objec i es. This
led us o he de ini ion o he o mal language XFL
[2], which is he base o se e al ha dwa e- and so -
wa e-o ien ed de elopmen ools ha cons i u e he
X uzzy 2.0 design en i onmen [1].
As a s a ing poin o he 3.0 e sion o X uzzy, a
new language, XFL3, which ex ends he ad an ages
o XFL, has been de ined. XFL3 allows he use o
de ine new membe ship unc ions and pa ame ic op-
e a o s, and admi s he use o linguis ic hedges which
pe mi o desc ibe mo e complex ela ionships
among a iables [8]. In o de o inco po a e hese im-
p o emen s, some modi ica ions ha e been made in
he XFL syn ax. In addi ion, he new language XFL3,
oge he wi h he ools based on i , employ Ja a as
p og amming language. This means he use o an ad-
an ageous objec -o ien ed me hodology and he
lexibili y o execu ing he new e sion o X uzzy in
any pla o m wi h JRE (Ja a Run ime En i onmen )
ins alled.
2 The XFL3 language
XFL3 is a uzzy sys em speci ica ion language which
p o ides he use wi h a g ea lexibili y o de ine he
unc ions associa ed wi h he uzzy ope a o s and lin-
guis ic a iables and which allows o exp ess com-
plex ule bases.
An XFL3 speci ica ion consis s o se e al objec s
de ining ope a o se s, a iable ypes, and ule bases.
The de ini ion o ma o hese elemen s is desc ibed
in he ollowing.
2.1 Ope a o se s
An ope a o se in XFL3 is an objec con aining he
ma hema ical unc ions ha a e assigned o each
uzzy ope a o . Fuzzy ope a o s can be bina y (like
he T-no ms and S-no ms employed o ep esen lin-
guis ic a iable connec ions, implica ion, o ule ag-
g ega ions), una y (like he C-no ms o he ope a o s
ela ed wi h linguis ic hedges), o can be associa ed
wi h de uzzi ica ion me hods [9].
XFL3 de ines he ope a o se s wi h he ollowing
o ma (Figu e 1):
ope a o se iden i ie {
ope a o assigned_ unc ion(pa ame e _lis );
ope a o assigned_ unc ion(pa ame e _lis );
........... }
I is no equi ed o speci y all he ope a o s. When
one o hem is no de ined, i s de aul unc ion is as-
XFL3: A New Fuzzy Sys em Speci ica ion Language
F. J. MORENO-VELO, S. SÁNCHEZ-SOLANO, A. BARRIGA, I. BATURONE, D. R. LÓPEZ
Ins i u o de Mic oelec ónica de Se illa (IMSE-CNM)
A da. Reina Me cedes, s/n Edi . CICA. E-41012 Se illa.
SPAIN
[email p o ec ed]. h p://www.imse.cnm.es
Abs ac : - This pape p esen s he main ea u es o XFL3, a new language o uzzy sys em speci ica ion, which
has been de ined as he s a ing poin o he 3.0 e sion o ou uzzy sys em design en i onmen , X uzzy [1].
I s main ad an ages wi h espec o i s p ecu so , XFL [2], a e i s capabili y o admi use -de ined membe ship
unc ions, pa ame ic ope a o s, and linguis ic hedges. Taking his language as he basis, di e en uzzy sys em
de elopmen ools a e being implemen ing, which a e also summa ized b ie ly.
Key-Wo ds: - Fo mal languages, CAD ools, Fuzzy sys ems.
___________________
This wo k has been pa ially suppo ed by he Spanish CICYT P ojec TIC98-0869 and he FEDER P ojec (Nº 1FD97-0956-C3-02).
sumed. Table 1 shows he ope a o s (and hei de aul
unc ions) cu en ly used in XFL3.
The assigned unc ions a e de ined in ex e nal
iles which we name as packages. The o ma o iden-
i y a unc ion is “package. unc ion”. The package
name (x l in Figu e 1) could be emo ed i he pack-
age has been impo ed p e iously (using he com-
mand “impo package;”).
2.2 Types o linguis ic a iables
An XFL3 ype is an objec which desc ibes a ype o
linguis ic a iable. This means o de ine i s uni e se
o discou se, o name he linguis ic labels co e ing
ha uni e se,and ospeci y hemembe ship unc ion
associa ed o each label. The de ini ion o ma o a
ype is as ollows (Figu e 2):
ype iden i ie [min, max; ca d]{
label membe ship_ unc ion(pa ame e _lis );
label membe ship_ unc ion(pa ame e _lis );
............. }
whe e min and max a e he limi s o he uni e se o
discou se and ca d (ca dinali y) is he numbe o i s
disc e e elemen s. I ca dinali y is no speci ied, i s
de aul alue (cu en ly, 256) is assumed. When lim-
i s a e no explici ly de ined, he uni e se o dis-
cou se is aken om 0 o 1.
The o ma o he linguis ic label iden i ie is sim-
ila o he ope a o iden i ie , ha is, “package. unc-
ion” o simply “ unc ion” i he package whe e he
use has de ined he membe ship unc ions has been
al eady impo ed.
XFL3 suppo s inhe i ance mechanisms in he
ype de ini ions (like i s p ecu so , XFL). To exp ess
inhe i ance, he heading o hede ini ion is as ollows
(Figu e 2):
ype iden i ie ex ends iden i ie {
The ypes so de ined inhe i au oma ically he uni-
e se o discou se and he labels o hei pa en s. The
labels de ined in he body o he ype a e ei he added
o he pa en labels o o e w i e hem i hey ha e he
same name.
2.3 Rule bases
A ule base in XFL3 is an objec con aining he ules
which de ine he logic ela ionships among he lin-
guis ic a iables. I s de ini ion o ma is as ollows
(Figu e 3):
ulebase iden i ie (inpu _lis : ou pu _lis )
using ope a o se {
[ ac o ]i (an eceden )-> consequen _lis ;
[ ac o ]i (an eceden )-> consequen _lis ;
............. }
The de ini ion o ma o he inpu and ou pu a i-
ables is “ ype iden i ie ”, whe e ype e e s o one o
he linguis ic a iable ypes p e iously de ined. The
ope a o se selec ion (sys emop in Figu e 3) is op-
ional, so ha when i is no explici ly de ined, he de-
Table 1: Ope a o s cu en ly de ined in XFL3.
Ope a o Type De aul unc ion
and bina y min(a,b)
o bina y max(a,b)
implica ion
imp bina y min(a,b)
also bina y max(a,b)
no una y (1-a)
s ongly una y (a)2
mo eo less una y (a)1/2
sligh ly una y 4*a*(1-a)
de uzzi ica ion
de uz de uzzi ica ion cen e o a ea
ope a o se sys emop {
and x l.min();
o x l.max();
imp x l.min();
s ongly x l.pow(3);
mo eo less x l.pow(0.4);
}
Fig. 1: Example o ope a o se de ini ion.
ype inpu 1 [0,100] {
sho x l. iangle(0,25,50);
medium x l. iangle(25,50,75);
all x l. iangle(50,75,100);
}
ype inpu 2 ex ends inpu 1 {
e y_sho x l. iangle(-10,0,25);
e y_ all x l. iangle(75,100,110);
}
Fig. 2: Example o a iable ype de ini ion.
aul ope a o s a e employed. I is also shown in
Figu e 3 how con idence weigh s (wi h de aul al-
ues o 1) can be applied o he ules.
A ule an eceden desc ibes he ela ionships
among he inpu a iables. XFL3 allows o exp ess
complex an eceden s by combining basic p oposi-
ions wi h connec i es o linguis ic hedges (Table 2
and Figu e 4). On he o he side, each ule conse-
quen desc ibes he assigna ion o a linguis ic a i-
able o an ou pu a iable as “ a iable = label”
(Figu e 3).
2.4 Sys em global beha io
The desc ip ion o he sys em global beha io means
o de ine he global inpu and ou pu a iables o he
sys em as well as he ule base hie a chy. This de-
sc ip ion in XFL3 is as ollows (Figu e 5):
sys em (inpu _lis : ou pu _lis ) {
ule_base_iden i ie (inpu s : ou pu s);
ule_base_iden i ie (inpu s : ou pu s);
............. }
The de ini ion o ma o he global inpu and ou -
pu a iables is he same o ma employed in he de -
ini ion o he ule bases. The inne a iables which
may appea es ablish se ial o pa allel in e connec-
ions among he ule bases. Inne a iables mus i s -
ly appea as ou pu a iables o a ule base be o e
being employed as inpu a iables o o he ule bases
(Figu e 5).
3 Func ion packages
Fou ypes o unc ions can be de ined in XFL3: bi-
na y unc ions, una y unc ions, membe ship unc-
Table 2: Example o uzzy p oposi ions
Basic p oposi ions Desc ip ion
a iable == label equal o
a iable >= label equal o g ea e han (Fig. 3a)
a iable <= label equal o smalle han (Fig. 3b)
a iable > label g ea e han (Fig. 3c)
a iable < label smalle han (Fig. 3d)
a iable != label no equal o (Fig. 3e)
a iable %= label sligh ly equal o (Fig. 3 )
a iable ~= label mo eo less equal o (Fig. 3g)
a iable += label s ongly equal o (Fig. 3h)
Complex p oposi ions Desc ip ion
p oposi ion & p oposi ion and ope a o
p oposi ion | p oposi ion o ope a o
! p oposi ion no ope a o
% p oposi ion sligh ly ope a o
~ p oposi ion mo eo less ope a o
+ p oposi ion s ongly ope a o
ulebase base1(inpu 1 x, inpu 2 y : ou pu z) using sys emop
{
i ( x == medium & y == medium) -> z = all;
[0.8] i ( x<=sho | y != e y_ all ) -> z = sho ;
i ( +(x> all) & (y ~= medium) ) -> z = all;
............. }
Fig. 3: Example o ule base de ini ion.
sys em (inpu 1 x, inpu 2 y : ou pu z) {
ulebase1(x, y : inne 1);
ulebase2(x, y : inne 2);
ulebase3(inne 1, inne 2 : z);
}
Fig. 4: Example o sys em beha io de ini ion.
(a) (b)
(e)
(g) (h)
( )
(c) (d)
Fig. 5: Illus a ing linguis ic hedges.
ions, and unc ions associa ed wi h de uzzi ica ion
me hods. A g ea ad an age o XFL3 is ha hese
unc ions can be de ined eely by he use in ex e nal
iles (named as packages). The de ini ion o ma is as
ollows:
bina y iden i ie { blocks }
una y iden i ie { blocks }
m iden i ie { blocks }
de uz iden i ie { blocks }
The blocks ha de ine a unc ion include i s name
(and possible alias), he pa ame e s which speci y i s
beha io as well as he cons ain s on hese pa ame-
e s, he desc ip ion o i s beha io in he di e en
languages o which i could be compiled (ja a,
ansi_c and cplusplus, o ins ance), and e en he de-
sc ip ion o i s di e en ial unc ion (i i is employed
in g adien -based lea ning mechanisms). This in o -
ma ion is he basis o gene a e au oma ically a Ja a
class ha inco po a es all he unc ion capabili ies
and can be employed by any XFL3 speci ica ion. Re-
ga ding de uzzi ica ion me hods, some o hem can
be only employed wi h ce ain membe ship unc-
ions. To exp ess his dependence, he block de ined-
o indica es hose allowed membe ship unc ions.
The use o packages allows he designe o de ine
any desi ed unc ion. The s anda d package cu en ly
used in XFL3 (and named x l) con ains he mos usu-
al unc ions, as shown in Table 3.
4 Example o an XFL speci ica ion
One o he main ea u es o XFL3 is he inclusion o
linguis ic hedges and hie a chical s uc u es on he
de ini ion o uzzy sys ems. The modula di ision o
he sys em desc ip ion allows he designe o con-
on he de elopmen o complex sys ems. In his
sense, linguis ic hedges can be used o dec ease he
numbe o linguis ic labels employed and o exp ess
logic ules mo e compac ly [10].
As an example o complex sys em modelling, we
ha e conside ed he classic p oblem o pa king a
uck in a loading dock [11]. In his p oblem, only he
case o backwa d d i ing is gene ally conside ed.
Howe e , his makes i e y di icul o he uck o
pa k when s a ing a a bad-o ien ed posi ion as
shown in Figu e 6. The app oxima ion we ha e ol-
lowed is o di ec ly emula e how we will ac as d i -
e s, which o us is a wo s ep decision p oblem: o
decide whe he mo ing o wa ds o backwa ds and,
depending on he case, o selec he p ope angle o
he wheels. This knowledge is, hence, ep esen ed by
a hie a chical sys em. In pa icula , ou ule bases
a e employed, as shown a he bo om o Figu e 7.
The ule base di ec ion emula es ou non uzzy mak-
ing decision abou he di ec ion o mo emen . On he
con a y, he ule bases o wa d and backwa d emu-
la es ou uzzy decision abou he wheel angle when
d i ing o wa d o backwa d. Finally, he ule base
swi ch chooses he p ope u n as a unc ion o he
mo emen di ec ion.
This example does no a emp o illus a e an op-
imum way o sol ing he uck-dock p oblem bu he
e iciency o XFL3 o ep esen ing expe linguis ic
knowledge. In his sense, he ype de ini ions o he
a iables ha e been educed by using he g ea e and
smalle linguis ic hedges, and he ule base de ini-
ions ha e been compac ed hanks o combina ions o
connec i es and hedges, as we exp ess linguis ically.
Figu e 8 shows he esul s o wo simula ions. In
he i s one, he uck s a s a he bo om-le co ne ,
wi h a no h-eas o ien a ion. The sys em decides o
d i e o wa d app oaching he uck o he e ical
and, once a ha posi ion, leads i backwa ds o he
Table 3: The s anda d package x l.
Func ion ype Possible assigned unc ions
Bina y min, p od, bounded_p od,
d as ic_p od, max, sum,
bounded_sum, d as ic_sum,
dienes_ eshe , mizumo o,
lukasiewicz, dubois_p ade, zadeh,
goguen, godel, sha p.
Una y no , sugeno, yage , pow, pa abola.
Membe ship
unc ions apezoid, iangle, isosceles,
slope, bell, sigma, ec angle, sin-
gle on
De uzzi ica ion
me hods Cen e O A ea, Fi s O Maxima,
Las O Maxima, MeanO Maxima,
FuzzyMean, Weigh edFuzz-
yMean, Quali y, GammaQuali y.
angle
(x,y)
Fig. 6: Example o he uck-dock p oblem.

dock. The second simula ion begins a he bo om-
igh co ne in a sou h-wes di ec ion. In his case, he
uck is d i en backwa ds ill an ho izon al o ien a-
ionis eached, henis di ec ed o wa d o he e ical
and inally goes back o he dock.
5 Summa y o he XFL3-based ools
The co e o any applica ion de eloped wi h XFL3 is
based on he use o Ja a classes which con ain he
whole s uc u e and unc ionali y o he speci ica-
ions o be wo ked wi h. Using hese classes and he
Ja a g aphic lib a ies, se e al ools ha e been buil
Fig. 7: Summa y o he XFL3 speci ica ion o a uzzy con ol sys em o he uck-dock p oblem.
ope a o se opse { de uz x l.FuzzyMean(); and x l.p od(); }
ype TC ispX [-50.0,50.0] { ... }
......
ype TWheel [-30.0,30.0] { ... }
ulebase backwa d(TX x, TAngle angle : TWheel wheel) using opse { ... }
ulebase o wa d(TX x, TAngle angle : TWheel wheel) using opse { ... }
ulebase swi ch(TWheel bw, TWheel w, TDi dd : TWheel wheel, TDi di )
using opse { ... }
ulebase di ec ion(TC ispX x,TC ispY y,TC ispAngle angle,TOldDi olddi : TDi di )
using opse {
i (y > a ) -> di = backwa d;
i (y == a & olddi <= ze o ) -> di = backwa d;
i (y == a & olddi > ze o ) -> di = o wa d;
i (y <= nea & x != cen e & angle <= RI & angle >= LE) -> di = o wa d;
i (y <= nea & x != cen e & (angle > RI | angle < LE)) -> di = backwa d;
i (x == cen e & y == nea & angle <= RS & angle >= LS) -> di = backwa d;
i (x == cen e & y == nea & (angle > RI | angle < LE)) -> di = backwa d;
i (x == cen e & y == nea & (angle == LE | angle == RI)) -> di = o wa d;
i (x == cen e & y < nea & angle == CE) -> di = s op;
i (x == cen e & y < nea & (angle > RI | angle < LE)) -> di = backwa d;
i (x == cen e & y < nea & angle < CE & angle >= LE) -> di = o wa d;
i (x == cen e & y < nea & angle > CE & angle <= RI) -> di = o wa d;
}
sys em (TX x,TC ispY y,TAngle angle,TOldDi olddi : TWheel wheel,TDi di ec ion){
di ec ion(x, y, angle, olddi : dd);
backwa d( x, angle : bw);
o wa d( x, angle : w);
swi ch( bw, w, dd : wheel, di ec ion);
}
NB NB
NB NB
NB NM
PB
PB
PB
PB
PB
ulebase backwa d
NM
NS
NS
NS
NS
NS
PS
PS
PS
PS
PS
NM
NMNM
NM
NM
PM PM
PM
PM
PM PM
PM
ZE
<LE
LE
LS
CE
RS
RI
>RI
<LE LE CE RI >RI
x
angle
backwa d
o wa d swi ch
wheel
x
angle
di ec ion
y
olddi
di ec ion
PS PM
PM PB
NS PS
NB
NM
NM
NS
PS
ulebase o wa d
NM
PM
PB
NB
NS
PS
NM
NB
PS
PB
NS
NS
PBPB
PM
NS
NB NB
NM
NS
PS PS
PM
ZE
<LE
LE
LS
CE
RS
RI
>RI
<LE LE CE RI >RI
x
angle
TC ispX
TC ispY
igh cen e le
a nea
TC ispAngle TX
LE LS CE RS RI
TDi
TAngle
TOldDi TWheel
ZE PS PM PBNB NM NSs opbackwa d o wa d
CE RILE
LE LS CE RS RI
ze o
<LE >RI <LE >RI <LE >RI
> ze o< ze o
(a) (b)
Fig. 8: Simula ion esul s on he uck-dock p oblem.
which allow exploi ing he XFL3 ea u es h ough
he di e en de elopmen s ages o a uzzy sys em
design.
Cu en ly, he eisa ailablea uzzysys emedi ion
ool, named x edi . I allows de ining he ope a o
se s, a iable ypes, ule bases, and sys em s uc u e
h ough a g aphical use in e ace, as shown in Figu e
9. Two g aphic ep esen a ion ools, named x 2dplo
and x 3dplo , ha e been also de eloped. They allow
illus a ing he uzzy sys em beha io by i s ou pu /
inpu su ace in a wo o h ee dimensional space.
A ool o au oma ically adjus ing uzzy sys ems
desc ibed wi h XFL3 is also a ailable. This ool,
named x sl, p o ides he use wi h se e al lea ning
algo i hms and allows selec ing which sys em pa-
ame e s a e going o be uned and which no . Be-
sides, his oolincludes wome hods o p e- and pos -
p ocessing o elimina ing non signi ican ules and
labels and o clus e ing he ou pu a iables, hus
simpli ying hei associa ed ypes.
The inal s ep o any design p ocess is he syn he-
sis s ep which can lead o a so wa e o ha dwa e sys-
em implemen a ion. To ease he so wa e syn hesis,
h ee ools ha e been de eloped, x j,x c and x cpp,
which gene a e, espec i ely, he sys em desc ip ion
in Ja a, C, and C++ languages.
These and o he ools unde de elopmen a emp
o co e all he di e en s ages o a uzzy sys em de-
sign om i s linguis ic desc ip ion o i s inal imple-
men a ion (ei he so wa e o ha dwa e) and will
cons i u e he 3.0 e sion o he X uzzy en i onmen .
6 Conclusions
This pape has in oduced he XFL3 language, which
has been de eloped a e accumula ing expe ience
wi h hedesigno heX uzzy2.0en i onmen .XFL3
eases he desc ip ion and manipula ion o complex
uzzy sys ems hanks o he use o qui e use -de ined
membe ship unc ions, uzzy ope a o s (including
linguis ic hedges), and ule bases (admi ing hie a -
chical s uc u es). An illus a i e example has been
included o show he e iciency o XFL3 o apidly
ansla e linguis ic knowledge. Based on his lan-
guage, se e al ools a e being de eloped o cons i u e
he new e sion o X uzzy, which could be execu ed
on any pla o m con aining he Ja a Run ime En i-
onmen .
Re e ences:
[1] D. R. López, C. J. Jiménez, I. Ba u one, A. Ba iga,
S. Sánchez-Solano. "X uzzy: A Design En i on-
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on Fuzzy Sys ems (FUZZIEEE’98), pp. 1060-1065,
Ancho age, May 1998.
[2] D. López, F. J. Mo eno, A. Ba iga, S. Sánchez-So-
lano. "XFL: A Language o he De ini ion o Fuzzy
Sys ems", P oc. 6 h IEEE In . Con . on Fuzzy Sys e-
ms (FUZZIEEE’97), pp. 1585-1591, Ba celona,
Jul., 1997.
[3] M. Bonne , S. Maye , A. Raggl, W. Slany,
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Logic in A i icial In elligence: Towa ds In elligen
Sys ems, Ma in, T.P., Ralescu, A.L., Eds., Sp in-
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[4] Z. A. Sosnowski, “FLISP - a language o p oces-
sing uzzy da a”, Fuzzy Se s and Sys ems, No 37, pp.
23-32, 1990.
[5] O.G.Dua e, G. Pé ez. “UNFUZZY: Fuzzy Logic
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Fig. 9: Main window o he x edi ool.