FLEB: A FUZZY LOGIC E-BOOK
A. Be múdez, A. Ba iga, I. Ba u one, S. Sánchez-Solano
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
Eu opean Symposium on In elligen Technologies, Hyb id Sys ems and hei implemen a ion on
Sma Adap i e Sys ems (EUNITE-2001), pp. 549-554, Tene i e, Dec. 2001.
This ma e ial is p esen ed o ensu e imely dissemina ion o schola ly and echnical wo k. Copy igh and all igh s he ein
a e e ained by au ho s o by o he copy igh holde s. All pe sons copying his in o ma ion a e expec ed o adhe e o he e ms
and cons ain s in oked by each au ho ’s copy igh . In mos cases, hese wo ks may no be epos ed wi hou he explici pe -
mission o he copy igh holde .
FLEB: A FUZZY LOGIC E-BOOK
And és Be múdez, Ángel Ba iga, Iluminada Ba u one, San iago Sánchez
Ins i u o de Mic oelec ónica de Se illa
A da. Reina Me cedes s/n. Edi CICA
41012-Se illa, España
e-mail: [email p o ec ed]
ABSTRACT: FLEB1is an elec onic book which a emp s o in oduce he basic ma hema ical ounda ions and applica-
ions o uzzy logic h ough a so wa e en i onmen which includes images, hype ex , sensi i e elemen s, anima ions
and in e ac i e demos. I also allows execu ing X uzzy, a de elopmen ool which eases he desc ip ion, e i ica ion, and
syn hesis o uzzy logic-based sys ems. FLEB, like a usual book, is s uc u ed in o chap e s wi h pages h ough which he
eade can na iga e com o ably. In addi ion, he in o ma ion p o ided can be accessed in a non sequen ial way hanks o
he hype ex and sensi i e elemen s ha in e connec linked pages. This capabili y o non sequen ial eading oge he
wi h he exploi a ion o mul imedia so wa e make FLEB a good ool o pedagogically show and explain he basis o
uzzy logic heo y and applica ions.
KEYWORDS: Fuzzy Logic, e-book, e-lea ning, mul imedia so wa e.
1.- MOTIVATION
Fuzzy Logic was in oduced in he mid-1960s as a discipline which changed he concep s o con en ional logic. F om
i s in oduc ion, many publica ions ha e being appea ing o explain i s main heo e ical concep s and applica ions, espe-
cially om he 80s when uzzy logic-based applica ions expe imen a g ea success. The e is cu en ly a g ea biblio-
g aphical eso abou di e en subjec s ela ed o uzzy logic. Howe e , one o he key poin s o co e he o ma ion in
hese subjec s is he a ailabili y o adequa e ools o educa ion. In his sense, he objec i e o he wo k p esen ed he ein
is wo old. Fi s ly, FLEB eases sel -lea ning by o e ing in e ac i e acili ies such as anima ions and demos o applica-
ion examples. Secondly, i pa es he way o gene a e web based ools and con en s o educa ion.
The cons uc ion o he book has h ee ounda ions: 1) he illus a ion o he con en is based on HTML and many
mul imedia e ec s like anima ions a e employed, 2) he de elopmen and applica ion o p ac ical exe cises is ca ied ou
by X uzzy [3], an en i onmen o designing uzzy logic-based sys ems, 3) he explana ion o applica ion examples is
done by a se o demos which ha e been p og ammed wi h Tcl/Tk [4] ( o achie e anima ed and in e ac i e in e aces)
and wi h C ( o implemen he p ocessing algo i hms).
This Fuzzy Logic E-Book, FLEB, is o ganized in o 4 chap e s. The i s one in oduces he ounda ion o he uzzy
logic and summa izes i s nume ous applica ions, showing he c escen e olu ion o his discipline om he beginning
un il i s cu en si ua ion. Chap e 2 e iews he basic ma hema ical o malisms o uzzy se heo y and uzzy in e ence
mechanisms. Chap e 3 explains he de elopmen o uzzy sys ems by using he X uzzy en i onmen . Finally, Chap e 4
explains applica ion examples wi h he aid o in e ac i e demos p og ammed wi h Tcl/Tk language. The con en o hese
ou chap e s is based on he book “Mic oelec onic design o uzzy logic-based sys ems” [1] and on he use manual o
X uzzy [7]. The cu en e sion o FLEB is w i en in Spanish al hough i is planned i s ansla ion o English o pe mi a
mo e widesp ead di usion.
2.- DEVELOPMENT ENVIRONMENT
Due o he g ea simila i y be ween he idea o an elec onic book and he concep o a web page, he selec ion o
HTML as he p og amming language o FLEB is appa en . As a ma e o ac , a web page is basically a o ma ed and
enhanced ex which o en con ains links o o he web pages. In in e ne , he linked pages can be placed in emo e hos s,
so ha he na iga o ( he p og am which isualizes hem) has o ask o hem o he co esponding se e , h ough a ne
1. FLEB(O): Wo d whose o igin is he G ecian e m phleps,phlebos, which means ein.
connec ion. I we pu oge he all he pages in o he same machine (bookbinding?), as well as he na iga o and a se o
equi ed p og ams such ne connec ion is no needed and he pages can include calls o any o he equi ed p og ams.
This capabili y is a equi emen ha he selec ed p og amming language o FLEB had o mee , because FLEB had o
allow execu ing se e al p og ams al eady de eloped o Linux (in pa icula , he de elopmen en i onmen X uzzy and
he in e ac i e demos o applica ion examples). The mos widely used na iga o in Linux, Ne scape Na iga o , is easily
con igu ed o his pu pose. Al hough wi h limi a ions in he execu ion o some p og ams, FLEB uns in o he pla o ms
and wi h o he na iga o s. This is a g ea ad an age o he p og amming language HTML.
In o de o p o ide he pages wi h a g ea e deg ee o dynamism and in e ac i i y, Ja aSc ip commands ha e been
included in o he HTML code. Among hem, we can ci e he o e LIB [2] lib a y manage commands. The Cascade S yle
Shee s (CSS) ha e also been employed o , among o he inali ies, jus i ying he ex wi hin he pages. In addi ion, he
s yle shee s allow changing he appea ance o he e-book, o ins ance ia he on ypes o he link appea ance, by only
modi ying a single documen . The Ja aSc ip as well he CSS commands a e in e p e ed by he na iga o i sel .
Windows 98 was selec ed in o de o use he de elopmen en i onmen Mic oso F on Page. Howe e , any HTML
edi o wi h p e iewing op ion would ha e se ed ou pu poses because he whole code has been w i en by hand.
Mic oso Pain and Adobe Pho oshop ha e been employed o c ea ing and p ocessing images. The laye echnology o
Adobe has g ea ly helped in de eloping he di e en ames which compound e e y anima ion c ea ed o FLEB; i s
a angemen has been ca ied ou wi h WWW Gi Anima o [6], a use - iendly eewa e u ili y o ab ica ing anima ed
GIFs. Finally, he in e ac i e demos ha e been pe o med wi h he help o he p og amming ool Visual Tcl [5].
3.- VISUALIZATION ENVIRONMENT
3.1.- MAIN PAGE OR GENERAL TABLE OF CONTENTS
The main page o gene al able o con en s o FLEB (illus a ed in Figu e 1) is displayed when he book is open by he
na iga o . FLEB has been designed o a esolu ion o 1024 x 768 pixels, al hough i can be iewed wi h less esolu ion
hanks o he sc ollba s ha appea au oma ically when he size o he page exceeds he window size.
Figu e 1. FLEB main page.
The con en s o a page in FLEB a e shown in he cen al egion o he sc een, be ween wo black s ips. These egions
will be e e ed o as he main ame and supe io o in e io s ips, espec i ely. In he main ame o he i s page, ou
small igu es appea a he le , one below ano he . Each o hese images is associa ed wi h one chap e o he e-book. The
con en able o he co esponding chap e appea s in he main ame when clicking one o hem, ha is, na iga ing
owa ds any pa icula con en o he book is as easy as clicking i .
The FLEB logo, which always pe mi s he e u n o he main page, appea s a he le co ne o he supe io s ip, as
illus a ed in Figu e 1. The igh co ne o he in e io s ip is whe e he na iga ion icons a e displayed. In he case o his
main page, only an X-shaped na iga ion icon appea s. This is he icon p og ammed o close he book.
The X uzzy logo a he le co ne o he in e io s ip opens he X uzzy en i onmen when i is selec ed. The X uzzy
en i onmen is composed o a se o ools co e ing he di e en s ages o desc ip ion, e i ica ion, and syn hesis o uzzy
sys ems. These ools a e in eg a ed in o a g aphical use in e ace and sha e a common o mal speci ica ion language
named XFL [3], [7].
3.2.- CHAPTER AND SECTION PAGES
The con en s a e o ganized in o h ee le els: chap e s, sec ions, and subsec ions. When one o hem is selec ed, i s
con en ela ion is shown a he supe io s ip oge he wi h he FLEB logo. A he same ime, he con en o he main
ame changes o display he selec ed page, and a new se o icons appea a he in e io s ip.
As example, when one o he book sec ions is selec ed, he supe io s ip akes he appea ance illus a ed in Figu e 2.
I displays he chap e , sec ion, and subsec ion i les which he iewed page belongs o. These i les a he supe io s ip,
as also happened o he i les o he con en able in he main page, can be clicked wi h he mouse o na iga ing h ough
FLEB.
Figu e 2. Example o FLEB page.
The main ame con ains images and ex . The wo ds ha appea wi h a pa icula colo (#9900CC) iden i y sensi i e
ex . When he mouse is placed on a sensi i e ex a popup ex ame is displayed and, i he symbol @ appea s a e he
heading, i is possible o access o addi ional in o ma ion by clicking i . The o he way o com o ably na iga e h ough
FLEB is o make use o he na iga ion icons a he igh co ne o he in e io s ip.
The icons a he le co ne o he in e io s ip, close o he X uzzy logo, depend on he page which is cu en ly isual-
ized. In he case o Figu e 2, he e is only one icon, which in o ms abou he possibili y o showing a sequence o images.
Fou o hese icons can appea pe page. Table 1 shows he appea ance o hese ou icons and o he na iga ion icons,
oge he wi h hei unc ionali y. The i s page o a chap e always shows he con en able o ha chap e . When he
mouse is placed on a sec ion o a subsec ion i le, all he icons associa ed wi h ha sec ion o subsec ion appea a he
in e io s ip.
Table 1. Func ionali y o he icons employed in FLEB
4.- APPLICATION ENVIRONMENT
One o he main ad an ages o an e-book is i s abili y o p o ide he ex wi h mul imedia elemen s, which comple-
men s he in o ma ion supplied, acili a es concep unde s anding (due o isualiza ion u ili ies), and allows he eade o
in e ac wi h he book i sel (pe o ming p ac ical exe cises wi h he lea n concep s). In o de o p o ide FLEB wi h
mul imedia capabili y, h ee in e ac i e elemen s ha e been included: anima ions and image sequences, a uzzy sys em
de elopmen en i onmen , and demos o eal applica ions.
The anima ions, which ha e been implemen ed by anima ed GIFs, allow illus a ing di e en concep s. An example is
o explain he union (Figu e 3) o he in e sec ion o uzzy se s by illus a ing how he esul ing uzzy se is c ea ed as he
inpu uni e se o discou se is being swep . The anima ions di e om he image sequences in ha he la e a e sequen-
ially displayed when he use clicks he co esponding icon (see Table 1) while he anima ions a e displayed comple ely
wi h only one click.
Figu e 3. Anima ion illus a ing uzzy se s union.
Close he e-book. This in o ms ha he e is an image sequence. The
images in he sequence a e sequen ially displayed
whene e he icon is clicked.
Re u n o he las
isi ed page. This in o ms ha he e is an in e ac i e demo, which is
execu ed when clicking i .
Go o he p e ious
page. This in o ms ha he page con ains images wi h sensi-
i e egions (which a e associa ed wi h popups ames
like he sensi i e ex egions). When placing he mouse
on hese icons, he sensi i e egions a e shown.
Go o he ollowing
page. When a (sub)sec ion consis s o se e al pages, his icon
shows he si ua ion o he cu en page (i) wi hin he
o al numbe o pages (j).

A second in e ac i e elemen o FLEB is X uzzy ha can be execu ed om any page. This en i onmen , which is sup-
plied oge he wi h he ex , allows he eade o co e all he s ages o a uzzy sys em design: desc ip ion, simula ion,
uning by lea ning algo i hms, and ei he so wa e o ha dwa e syn hesis. The only equi emen o un X uzzy is ha he
execu ion pla o m has o be Unix. The X uzzy main page is shown in Figu e 3.
Figu e 3. X uzzy main page.
The hi d in e ac i e elemen is a se o demos wi h which he eade can in e ac . These demos ha e been de eloped
wi h he p og amming language Tcl/Tk and using se e al C unc ions so as o achie e independence om he execu ing
pla o m (Unix o Windows). The e a e cu en ly i e demos. One o hem illus a es he uni e sal app oxima ion capa-
bili y o uzzy sys ems. The o he ou demos show he capabili y o a uzzy con olle o sol e di e en con ol p ob-
lems: s abilizing an in e ing pendulum, pa king a uck a a gi en loading dock, main aining a suspended ball wi h an ai
low a a gi en heigh , and con olling a dose sys em. Thanks o hese demos, he eade can design a uzzy con olle and
isualize how is he plan e olu ion. This means ha a i ual lab is included oge he wi h he ex .
Figu e 4 shows he g aphical use in e ace o one o hese demos: he uck-dock con olling p oblem. The do ed
lines a he igu e illus a e se e al pa hs ollowed by he uck o di e en s a ing poin s. The eade can de ine and
modi y he con ol policy o each he desi ed loading dock. Fo ins ance, he eade can execu e X uzzy o modi y he
membe ship unc ions o he inpu con ol a iables, as shown in Figu e 5.
Figu e 4. In e ac i e demo: a uck pa king a a loading dock.
Figu e 5. Window o X uzzy o edi he membe ship unc ions o he inpu and ou pu a iables.
5.- CONCLUSIONS
This pape desc ibes an elec onic book, FLEB, ha includes mul imedia esou ces esul ing om he ensemble o
elemen s such as linked ex , anima ions and image sequences, de elopmen en i onmen , and i ual labo a o y. We
hink his book o e s wo ele an ea u es conce ning con en and s uc u e. As ega ds con en s, his book p o ides a
pedagogic summa y o uzzy logic heo y and applica ions ha , o he bes o ou knowledge, is no p o ided by mos o
cu en books on uzzy logic. Conce ning s uc u e, his book can se e as a pa adigm o o he ex s on di e en sub-
jec s. FLEB is independen o he execu ion pla o m excep o he uzzy sys em de elopmen en i onmen , X uzzy,
which only uns in Unix.
6.- REFERENCES
[1] Ba u one, I., Ba iga, A., Sánchez-Solano, S., Jiménez, C. J., López, D. R., “Mic oelec onic design o uzzy logic-
based sys ems”, CRC P ess, 2000.
[2] Bos up, E ik, “O e LIB” (h p://www.bos up.com/web/o e lib/).
[3] López, D. R., Jiménez, C. J., Ba u one, I., Ba iga, A., Sánchez-Solano, S., “X uzzy: A Design En i onmen o Fuzzy
Sys ems”, 7 h IEEE In e na ional Con e ence on Fuzzy Sys ems (FUZZ-IEEE’98), pp. 1060-1065, Ancho age, May
1998.
[4] Sánchez-Solano, S. Ba iga, A., Ba u one, I., López, D. R., Mo eno, F. J., “Cu so de Diseño de Con olado es Di u-
sos Median e el En o no de Desa ollo X uzzy”, IV Cong eso de Tecnologías Aplicadas a la Enseñanza de la Elec ó-
nica (TAEE’2000), pp. 501-504, Ba celona, Sep . 2000.
[5] Visual Tcl (h p:// cl.sou ce o ge.ne /).
[6] Wasinge , I., Nou bakhch, R., Koma y, R, “WWW Gi Anima o ” (h p://s ud1. uwien.ac.a /~e8925005/).
[7] X uzzy. (h p://www.imse.cnm.es/X uzzy).