CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. ?aeaioeo?eaoe?y ia’?eoo iieyaa? a iiaoaeia? eiai
iaoaiaoe/ii? iiaeae?, oiaoi iia?aoi?a ca’yceo i?ae ao?aeieie oa
aeo?aeieie ci?iieie ca a?aeiieie aenia?eiaioaeueieie aeaieie. No/ania
oai??y ?aeaioeo?eaoe??, yea aaco?oueny ia iiaeaethaaii? aeeiai?/ieo
ia’?eo?a ??aiyiiyie (aeeoa?aioe?eieie, ??ciinoieie oiui), iiaaii
i?enoiniaaia aei aeei?enoaiiy ?ioi?iaoe?? i?i ia’?eo o aeaeyae?
aenia?oieo i?e?iaeiuei-iiaieo aeneiaethaaiue oeio: «sseui oaeaee?noue
aaoiiia?eth aeoaea aeniea, oi aeo?aoe iaeeaa aaeee?», «sseui oaiia?aoo?a
iecueea, oi iieiaeaiiy ae?inaey iecueea», «sseui aeniea oaiia?aoo?a
oai?iai o?eia?oueny aeae?eueea aei?a, oi iiaeeeaa caiaeaiiy eaaai?a».

Oae? nooi iae?i?ei? caeaaeiino? yaeythoue niaith eiioeaio?aoe?th
aeina?aeo niaoe?ae?no?a ? a?ae?a?athoue cia/io ?ieue a i?aeoe/iiio
ae??oaii? ethaeeiith aaaaoueio neeaaeieo e?aa?iaoe/ieo caaea/:
oi?aae?iiy oaoiieia?/ieie i?ioeanaie, i?iaiicoaaiiy, ae?aaiinoeee,
?ici?ciaaaiiy ia?ac?a oiui. Oi?iaeueiei aia?aoii aeey ia?iaee
i?e?iaeiuei-iiaii? aenia?oii? ?ioi?iaoe?? ? oai??y ia/?oeeo iiiaeei.
Aiia aeicaiey? caaeaaaoe iiaeaeue ia’?eoo o aeaeyae? oae caaii? ia/?oei?
aace ciaiue, ui yaey? niaith noeoii?noue aeneiaethaaiue «ssEUI-OIAe?»,
ye? iia’ycothoue aoiaee oa aeoiaee ia’?eoo. Aaeaeaaoi?noue ia/?oei?
iiaeae? aenia?eiaioaeueiei aeaiei aecia/a?oueny oi?iaie ooieoe?e
iaeaaeiino?, yeeie oi?iae?cothoueny e?iaa?noe/i? ioe?iee. Ine?eueee
ooieoe?? iaeaaeiino? aecia/athoueny aenia?oieie iaoiaeaie, oi ye?noue
ia/?oei? iiaeae? oe?eeii caeaaeeoue a?ae eaae?o?eaoe?? aenia?o?a. ?ioeie
neiaaie, ieoaiiy aaeaeaaoiino? a?aeiieo ia/?oeeo iiaeaeae caeeoa?oueny
a?aee?eoei.

Ia’?eoii aeine?aeaeaiiy yaeythoueny iae?i?ei? nenoaie, a yeeo
caeaaei?noue i?ae ao?aeieie oa aeo?aeieie ci?iieie iieno?oueny ca
aeiiiiiaith i?e?iaeiuei-iiaieo aeneiaethaaiue «ssEUI-OIAe?», ui
oi?iae?cothoueny ia/?oeith eia?eith.

I?aaeiaoii aeine?aeaeaiiy ? iaoaiaoe/i? iiaeae? oa aeai?eoie
?aeaioeo?eaoe?? caeaaeiinoae «ao?ae-aeo?ae» ca aeiiiiiaith ia/?oeeo aac
ciaiue, ui yaeythoue niaith noeoii?noue aenia?oieo aeneiaethaaiue «ssEUI
, OIAe? ».

Oe?eue ?iaioe iieyaa? a iiaoaeia? iaoiaeo ?aeaioeo?eaoe?? iae?i?eieo
ia’?eo?a ia iniia? ia/?oei? eia?ee. Oeae iaoiae ii?aeio? noeoii?noue
iaoaiaoe/ieo iiaeaeae, aeai?eoi?a oa i?ia?aiiiai caaacia/aiiy aeey
i?iaeooaaiiy oa iioeiaeueii? iano?ieee ia/?oeeo aac ciaiue ca e?eoa???i
i?i?iaeueii? ?ica?aeiino? i?ae aaaeaiei (aenia?eiaioaeueiei) oa
iiaeaeueiei (oai?aoe/iei) aeoiaeaie ia’?eoo.

Aeey ?aae?caoe?? i?ia?aie aeine?aeaeaiue aoei iaiao?aeii:

a) i?iaiae?coaaoe caaea/? i?eeiyooy ??oaiue ia i?aenoaa? ia/?oei?
eia?ee, iieacaoe iaiaaeaiiy eeane/ieo iaoiae?a ?aeaioeo?eaoe?? aei
aeei?enoaiiy aenia?oii? ?ioi?iaoe??, noi?ioethaaoe i?eioeeie
?aeaioeo?eaoe?? iae?i?eieo ia’?eo?a ca aeiiiiiaith ia/?oeeo aac ciaiue
(aeaaa 1);

a) ?ic?iaeoe iiaeae? ai?ieneiaoe?? iae?i?eieo caeaaeiinoae ia/?oeeie
aacaie ciaiue aeey ia’?eo?a c iaia?a?aiei oa aeene?aoiei aeoiaeaie, a
oaeiae aeey ???a?o?/ieo caeaaeiinoae (aeaaa 2);

a) ?ic?iaeoe iinoaiiaee caaea/ iioei?caoe?? oa a?aeiia?aei? aeai?eoie
iano?ieee ia/?oeeo aac ciaiue aeey ?aeaioeo?eaoe?? ia’?eo?a c
iaia?a?aiei oa aeene?aoiei aeoiaeaie (aeaaa 3);

a) aenia?eiaioaeueii aeiaanoe iiaeeea?noue ?aeaioeo?eaoe?? iae?i?eieo
ia’?eo?a ia/?oeeie aacaie ciaiue ca aeiiiiiaith eiii’thoa?iiai
iiaeaethaaiiy (aeaaa 4);

ae) ?ic?iaeoe i?ia?aiia caaacia/aiiy aeey aaoiiaoecaoe?? i?ioeaaeo?
?aeaioeo?eaoe?? ia aac? ia/?oei? eia?ee oa ai?iaaaeeoe eiai a aenia?oieo
nenoaiao aeey iiaeaethaaiiy oaoiieia?/ieo i?ioean?a, ioe?iee yeino?
?iiaaoe?eieo i?iaeo?a, iaaee/ii? ae?aaiinoeee oa ?ioeo (aeaaa 5).

Iaoiaee aeine?aeaeaiiy. Aeena?oaoe?y aaco?oueny ia ?aeayo oa i?eioeeiao
ooo/iiai ?ioaeaeoo, oai??? ?aeaioeo?eaoe??, ia/?oei? eia?ee, aaiaoe/ieo
aeai?eoi?a iioei?caoe??, oai??? aenia?eiaioo oa eiii’thoa?iiai
iiaeaethaaiiy.

Iaoeiaa iiaecia ?iaioe iieyaa? a cai?iiiiiaaieo iaoaiaoe/ieo iinoaiiaeao
oa aaiaoe/ieo aeai?eoiao oiiei? iano?ieee ia/?oei? iiaeae?. Oiiea
iano?ieea caaacia/o? i?aea?? oaeeo eiao?oe??io?a aaaiiino? aenia?oieo
i?aaee «ssEUI-OIAe?» oa oaeeo ia?aiao??a ooieoe?e iaeaaeiino?, i?e yeeo
aeinyaa?oueny iaeiaioa a?aenoaiue i?ae aaaeaiei (aenia?eiaioaeueiei) oa
iiaeaeueiei (oai?aoe/iei) aeoiaeaie ia’?eoo.

Ia caoeno aeiinyoueny ianooii? iia? iaoeia? ?acoeueoaoe:

1. I?eioeei ?aeaioeo?eaoe?? iae?i?eieo ia’?eo?a ca aeiiiiiaith ia/?oei?
eia?ee oa aaiaoe/ieo aeai?eoi?a.

?acoeueoao iieyaa? a cai?iiiiiaai?e aeaioaoaii?e i?ioeaaeo?? iano?ieee
ia/?oei? aace ciaiue: ia?oee aoai — a?oaa iano?ieea ia i?aenoaa?
aeinooiii? aenia?oii? ?ioi?iaoe??; ae?oaee aoai — oiiea iano?ieea c
aeei?enoaiiyi iaa/aeueii? aea??ee oa aaiaoe/ieo aeai?eoi?a iioei?caoe??.

2. Iaoaiaoe/i? iiaeae? ai?ieneiaoe?? iae?i?eieo caeaaeiinoae c
iaia?a?aiei oa aeene?aoiei aeoiaeii ca aeiiiiiaith ia/?oeeo aac ciaiue.

?acoeueoao iieyaa? a iiaoaeia? oi?iaeueieo i?aaee ia?aoiaeo a?ae
aenia?oii-e?iaa?noe/ieo aeneiaethaaiue «ssEUI , OIAe? »
aei aiae?oe/ieo caeaaeiinoae «aoiaee-aeo?ae» a aeaio aeiaaeeao:
iaia?a?aiee aeo?ae — caaea/? i?iaiicoaaiiy oa oi?aae?iiy, aeene?aoiee
aeo?ae — caaea/? aaoiiaoe/ii? eeaneo?eaoe??.

3. Iaoaiaoe/i? iinoaiiaee caaea/ iioeiaeueii? iano?ieee ia/?oeeo aac
ciaiue c iaia?a?aiei oa aeene?aoiei aeoiaeaie.

?acoeueoao iieyaa? a oi?ioethaaii? caaea/ iaoaiaoe/iiai i?ia?aioaaiiy,
aei yeeo caiaeeoueny aea?? ia?aiao??a ooieoe?e iaeaaeiino? oa aaaiiinoae
aenia?oieo i?aaee ca e?eoa???i i?i?ioio ?ica?aeiino? i?ae iiaeaeueiei oa
aenia?eiaioaeueiei aeoiaeaie ia’?eoo.

4. Aaiaoe/i? aeai?eoie ae??oaiiy iae?i?eieo caaea/ iioei?caoe?? i?e
iano?ieoe? ia/?oeeo aac ciaiue.

?acoeueoao iieyaa? a aecia/aii? cania?a eiaeoaaiiy aa??aio?a ??oaiue —
o?iiinii, a oaeiae iia?aoe?e no?auoaaiiy oa iooaoe??, ye? ii?aeiai?
aaiaoe/iith i?ioeaaeo?ith naeaeoe?? iioeiaeueieo ia?aiao??a ia/?oei?
aace ciaiue.

5. Iaieiiea i?ia?aiii? nenoaie FUZZY EXPERT aeey ae??oaiiy caaea/
?aeaioeo?eaoe?? iae?i?eieo ia’?eo?a ia aac? ia/?oei? eia?ee.

Iaieiiea ?aae?ciaaia ia iia? i?ia?aioaaiiy C++ (eiii?eyoi? MSVisual C++
v1.5 aeey IN Windows 95).

Aeinoia??i?noue ?acoeueoao?a ia?aa??yeanue ca aeiiiiiaith eiii’thoa?ieo
aenia?eiaio?a c ia’?eoaie-aoaeiiaie oa i?e ?ic?iaoe? ?aaeueieo
aenia?oieo nenoai.

I?aeoe/ia oe?ii?noue oa ?acoeueoaoe ai?iaaaeaeaiiy. I?ia?aiia iaieiiea
FUZZY EXPERT ?aae?ciaaia ia ieaooi?i? Wintel ? iiaea aeei?enoiaoaaoenue
ye ?ino?oiaioaeueiee can?a aeey iiaoaeiae aaoiiaoeciaaieo nenoai
?ioaeaeooaeueii? i?aeo?eiee ??oaiue a ??cieo aaeocyo.

?acoeueoaoe aeena?oaoe?? ai?iaaaeaeai? a aea?aeathaeaeaoieo oaiao:

46-Ae-176 «Iiaeaethaaiiy ? iioei?caoe?y ethaeeii-iaoeiieo nenoai ia aac?
ia/?oeeo iiiaeei oa aaiaoe/ieo aeai?eoi?a» (? aea?ae?a?no?aoe??
0197U013137); 46-Ae-144 «?ic?iaea oai??? aiae?co oa neioaco
aeai?eoi?/ieo i?ioean?a a oiiaao iaaecia/aii? ?ioi?iaoe??» (?
aea?ae?a?no?aoe?? 0196U007375 ); 82-Ae-165 «Aeine?aeaeaiiy
aaaaoioaeoi?iiai aieeao i?aai?/ieo a?aeoiae?a ia aeieia?/iee noai
aeiae?eey oa ?ic?iaea cania?a eiai iie?ioaiiy ca aeiiiiiaith
a?ieiiaa?n??» (? aea?ae?a?no?aoe?? 0197U012876); a oaeiae a o/aiaiio
i?ioean? eaoaae?e eiii’thoa?ieo nenoai oi?aae?iiy.

Ai?iaaoe?y ?iaioe. Iniiai? iieiaeaiiy aeena?oaoe?eii? ?iaioe
aeiiia?aeaeenue oa ?ai?acaiooaaeenue ia i?aeia?iaei?e eiioa?aioe??
«Fuzzy Logic and Its Applications — FUZZY’97» (Zichron, ?c?a?eue, 1997
?.), V-e oa VI-e i?aeia?iaeieo eiioa?aioe?yo «European Congress on
Intelligent Techniques and Soft Computing -EUFIT» (Aachen, I?ia//eia,
1997, 1998 ??.), i?aeia?iaei?e eiioa?aioe?? «International Workshop.
Biomedical Engineering & Medical Informatics -BEMI’97» (Gliwice,
Iieueua, 1997 ?.), i?aeia?iaei?e eiioa?aioe?? «Annual Meeting of North
American Fuzzy Information Processing Society — NAFIPS’98» (Tampa, NOA,
1998 ?.), ia III-e oa IV-e iaoeiai-oaoi?/ieo eiioa?aioe?yo e?a?i NIAe
«Eiio?ieue ? oi?aae?iiy a oaoi?/ieo nenoaiao -EOON» (A?iieoey, 1995,
1997 ??.), iaoeiai-oaoi?/i?e eiioa?aioe?? «I?eeaaeiaoaeoaaiiy-95»
(Euea?a, 1995 ?.), a oaeiae ia iino?eii ae?th/eo nai?ia?ao eaoaae?e ENO
AAeOO.

Ioae?eaoe??. Ii iaoa??aeai aeena?oaoe?? iioae?eiaaii 14 ?ia?o.

No?oeoo?a oa ia’?i ?iaioe. ?iaioa neeaaea?oueny c anooio, i’yoe aeaa,
aeniiaeo, nieneo e?oa?aoo?e c 96 iaeiaioaaiue oa o?ueio aeiaeaoe?a.
Iniiaia /anoeia ?iaioe aeeeaaeaia ia 195 noi??ieao ae?oeiaaiiai oaenoo.
?iaioa aeeth/a? 52 ?enoiea oa 31 oaaeeoeth.

INIIAIEE CI?NO ?IAIOE

Anooi aei aeena?oaoe?? i?noeoue iaa?oiooaaiiy aeooaeueiino? oaie,
ie?aneaiiy ia’?eoo oa i?aaeiaoo aeine?aeaeaiiy, iien iniiaieo iaoeiaeo
?acoeueoao?a, ?o iiaecie, aeinoia??iino?, i?aeoe/ii? oe?iiino?,
a?aeiiino? i?i ai?iaaaeaeaiiy, ai?iaaoe?th oa no?oeoo?o ?iaioe.

Ia?oee ?icae?e i?enay/aii iaeyaeo noaio ieoaiiy oa oi?ioethaaiith caaea/
aeine?aeaeaiiy. A iueiio ?icaeyiooi ??ciiiai?oi? caaea/? i?eeiyooy
??oaiue ia i?aenoaa? ia/?oeeo aac ciaiue, aiae?cothoueny ?nioth/?
iaoiaee ?aeaioeo?eaoe?? iae?i?eieo caeaaeiinoae, aea?oueny iaa?oiooaaiiy
iaiao?aeiino? aeei?enoaiiy aia?aoa ia/?oeeo iiiaeei aeey oi?iae?caoe??
i?e?iaeiuei-iiaieo aeneiaethaaiue, a oaeiae iaiao?aeiino? iioeiaeueii?
iano?ieee ia/?oeeo iiaeaeae, i?iiiiothoueny i?eioeeie ?aeaioeo?eaoe??
iae?i?eieo caeaaeiinoae ia aac? ia/?oei? eia?ee.

Ia/?oea iiaeaeue iae?i?eiiai ia’?eoo «aoiaee-aeo?ae» aecia/a?oueny
noeoii?noth aenia?oieo i?aaee «ssEUI , OI », a yeeo
ao?aei? oa aeo?aeia ci?ii? iiaeooue i?eeiaoe e?euee?ni? oa ye?ni?
cia/aiiy. Aeei?enoaiiy ia/?oeiai eia?/iiai aeniiaeo aea? iiaeeea?noue
io?eioaaoe cia/aiiy aeoiaeo ia’?eoo i?e ??cieo cia/aiiyo ao?aeieo
ci?iieo.

Aeey ?aeaioeo?eaoe?? iae?i?eieo ia’?eo?a ia i?aenoaa? ia/?oeeo aac
ciaiue i?iiiio?oueny aeei?enoiaoaaoe ianooii? i?eioeeie:

1. I?eioeei e?iaa?noe/iino? ao?aeieo oa aeo?aeii? ci?iii?. Ca oeei
i?eioeeiii aoiaee oa aeoiaee ia’?eoo ?icaeyaeathoueny ye e?iaa?noe/i?
ci?ii?, ui ioe?iththoueny ye?nieie oa?iaie (term — a?ae aiae. iaceaaoe).

2. I?eioeei ai?ieneiaoe?? caeaaeiino? «aoiaee-aeo?ae» ca aeiiiiiaith
ia/?oei? aace ciaiue. Ia/?oea aaca ciaiue yaey? niaith noeoii?noue
aeneiaethaaiue «ssEUI , OIAe? », ye? a?aeaeca?eaeththoue
aeina?ae aenia?oa ? eiai ?icoi?iiy i?e/eiii-iane?aeeiaeo ca’yce?a a
caaea/? i?eeiyooy ??oaiue (oi?aae?iiy, ae?aaiinoeee, i?iaiicoaaiiy
oiui).

3. I?eioeei ???a?o?/iino? aac ciaiue. Aeei?enoaiiy oeueiai i?eioeeio
aeicaiey? aoaeoaaoe iiaeae? ?aeaioeo?eaoe?? aeey ia’?eo?a c aaeeeei
/eneii ao?aeieo ci?iieo. Iiaoaeiaa iiaeae? a?aeaoaa?oueny ca?aeii c
aea?aaii eia?/iiai aeaaaeaiiy, yea a?aeaeca?eaeth? ???a?o?/iee
aca?iica’ycie ia/?oeeo aac ciaiue a eiaeiiio eean? ao?aeieo ci?iieo.

4. I?eioeei aeaioaoaiii? iano?ieee ia/?oeeo aac ciaiue. Oe? aoaie
a?aeiia?aeathoue a?aeiiei a eeane/i?e oai??? aoaiai no?oeoo?ii? oa
ia?aiao?e/ii? ?aeaioeo?eaoe??. Ia ia?oiio aoai? aoaeo?oueny a?oaa
iiaeaeue ia’?eoo ia i?aenoaa? aeinooiii? aenia?oii? ?ioi?iaoe??, yea
caaea?oueny o aeaeyae? ia/?oeeo i?aaee «ssEUI-OIAe?». Ia ae?oaiio aoai?
a?aeaoaa?oueny iioei?caoe?y ia/?oei? iiaeae? ca aeiiiiiaith iaa/aeueii?
aea??ee, oiaoi aenia?eiaioaeueieo aeaieo «aoiaee-aeo?ae». Ea?iaaieie
ci?iieie, ui i?aeeyaathoue iano?ieoe?, ? oi?ia ooieoe?e iaeaaeiino? oa
eiao?oe??ioe aaaiiino? ia/?oeeo i?aaee.

Ae?oaee ?icae?e i?enay/aii ?ic?iaoe? iiaeaeae ai?ieneiaoe?? iae?i?eieo
caeaaeiinoae ca aeiiiiiaith ia/?oeeo aac ciaiue. ?icaeyaeathoueny
iae?i?ei? ia’?eoe

(1)

iiaea aooe:

,

,

.

Aeene?aoecaoe?y iaia?a?aiiai aeoiaeo iiaea a?aeaoaaoenue ca i?aaeeii:

. (2)

Oiio aeey cai?o aenia?oii? ?ioi?iaoe?? i?i ia’?eoe iaio aeae?a
aeei?enoiao?oueny ?aeeia iao?eoey ciaiue (oaae. 1).

Oaaeeoey 1

Iao?eoey ciaiue

. . .

Oe?e iao?eoe? a?aeiia?aea? nenoaia aeneiaethaaiue:

. . .

,

, (3)

.

C aeei?enoaiiyi oai??? ia/?oeeo iiiaeei oa nenoaie aenia?oieo
aeneiaethaaiue (3) io?eiaia ianooiia iiaeaeue ia/?oei? ai?ieneiaoe??
ia’?eoo (1):

, (4)

. Aeey oi?iae?caoe?? ia/?oeeo oa?i?a, yeeie ioe?iththoueny aoiaee
ia’?eoo, a ?iaio? i?iiiio?oueny aeei?enoiaoaaoe ooieoe?? iaeaaeiino?:

, (5)

; c — ia?aiao? noeniaiiy-?icoyaoaaiiy.

, aecia/a?oueny ca aeiiiiiaith (4) oaeei /eiii:

. (6)

Ia/?oea ai?ieneiaoe?y ia’?eoo c iaia?a?aiei aeoiaeii cae?enith?oueny ca
aeiiiiiaith iia?aoe?? aeaoacceo?eaoe?? (a?ae aiae. defuzzification), yea
ia?aoai?th? ?acoeueoaoe ia/?oeiai eia?/iiai aeniiaeo (4) a /?oea /enei:

. (7)

O?ao?e ?icae?e i?enay/aii ?ic?iaoe? iinoaiiaie caaea/ oa aeai?eoi?a
iioei?caoe??, ye? iaiao?aei? aeey iano?ieee ia/?oeeo iiaeaeae ia’?eoo
(1), ui a?aeiia?aea? aoaio ia?aiao?e/ii? ?aeaioeo?eaoe??.

Iiaeaeue ia’?eoo c iaia?a?aiei aeoiaeii ia? aeaeyae:

, (8)

— iia?aoi? «aoiaee-aeo?ae», yeee aecia/a?oueny ni?aa?aeiioaiiyie
(3),(4),(5),(7).

ia? aenia?eiaioaeueieo aeaieo «aoiaee-aeo?ae»:

. (9)

, yeee caaeiaieueiy? iaiaaeaiiyi

(10)

? caaacia/o? i?i?ioi

. (11)

Iiaeaeue ia’?eoo c aeene?aoiei aeoiaeii — oea aaeoi? nooiai?a
iaeaaeiino? aei eiaeiiai eeano:

, (12)

yeee ia/eneth?oueny ca ni?aa?aeiioaiiyie (4),(5).

ia? aeaieo:

. (13)

, yeee caaeiaieueiy? iaiaaeaiiyi (10) ? caaacia/o? i?i?ioi

, (14)

.

-??aiaai? aeaeiiiiceoe??. E??i oiai, noi?ioeueiaai? e?eoa??? yeino?
iiaeaeae c iaia?a?aiei oa aeene?aoiei aeoiaeaie, ye? aeicaieythoue
aeine?aeaeoaaoe aeeiai?eo iaa/aiiy ia/?oei? aace ciaiue.

Aeey ae??oaiiy caaea/ (11) oa (14), ui a?aeiinyoueny aei iae?i?eii?
iioei?caoe??, iiaeooue aeei?enoiaoaaoenue ??ciiiai?oi? /enaeuei?
iaoiaee, na?aae yeeo iaea?eueo i?inoei ? oi?aa?naeueiei ? iaenei??oee
nione. Aea aeei?enoaiiy oeueiai iaoiaeo aeey iioei?caoe?? ?aaeueieo aac
ciaiue iio?aao? aaeeeeo aeo?ao iaoeiiiai /ano, oea iia’ycaii c
iaiao?aei?noth i?aai?caoe?? iiooeo iine?aeiaii c ??cieo ii/aoeiaeo
oi/ie. Oiio a ?iaio? cai?iiiiiaaii aeei?enoaiiy aaiaoe/ieo aeai?eoi?a,
ye? iiaeooue ?icaeyaeaoenue ye aiaeia aeiaaeeiaiai iiooeo, ui aaaeaoueny
ia?aeaeueii c ??cieo ii/aoeiaeo oi/ie. Aaiaoe/iee aeai?eoi aeei?enoiao?
ii/aoeiao iiiaeeio aa??aio?a-??oaiue (aaouee?a), ui eiaeothoueny ye
o?iiiniie ? i?aeeyaathoueny iia?aoe?yi no?auoaaiiy ? iooaoe??. Iia?aoe?y
no?auoaaiiy «ia?iaeaeo?» iia? aa??aioe-??oaiiy, a iooaoe?y caaacia/o?
«ia?aneiee» a ??ci? ii/aoeia? oi/ee.

Aa??aio-??oaiiy eiaeo?oueny o aeaeyae? no??/ee:

.

) aeiaaeeiaeo oi/ie:

Iia?aoe?y iooaoe?? icia/a? aeiaaeeiao ci?io aeiaaeeiai ia?aiiai
aeaiaioa o?iiiniie a aeiionoeieo iaaeao (10)

,

,

,

aeiaaeeiaiai /enea.

sseui P(t) — iiiaeeia o?iiinii-aaouee?a, a C(t) — iiiaeeia
o?iiinii-ae?oae ia ?oa?aoe?? c iiia?ii t, oiae? aaiaoe/iee aeai?eoi
iioei?caoe?? i?aoeth? ca ianooiiith noaiith:

begin

t:=0 ;

Caaeaoe ii/aoeia? cia/aiiy P(t) ;

Ioe?ieoe P(t) c aeiiiiiaith ooieoe?? a?aeiia?aeiino?;

while (iaia? oiia caaa?oaiiy) do

No?auoaaoe P(t), uia io?eiaoe C(t) ;

Ioe?ieoe C(t) c aeiiiiiaith ooieoe?? a?aeiia?aeiino?;

Aea?aoe P(t+1) c P(t) oa C(t) ;

t:=t+1 ;

end ;

end.

*aoaa?oee ?icae?e i?enay/aiee ?acoeueoaoai eiii’thoa?ieo aenia?eiaio?a,
iaoa yeeo iieyaa? a ia?aa??oe? iiaeeeaino? ?aeaioeo?eaoe?? iae?i?eieo
ia’?eo?a c iaia?a?aiei oa aeene?aoiei aeoiaeii ca aeiiiiiaith iiaeaeae
oa aeai?eoi?a, ?ic?iaeaieo a ?icae?eao 2 oa 3.

Iaoiaeeea eiii’thoa?iiai aenia?eiaioo neeaaea?oueny c aeeiiaiiy
ianooiieo e?ie?a.

1(. Iae?i?eiee ia’?eo caaea?oueny aoaeiiiith iiaeaeeth o aeaeyae?
aiae?oe/ieo oi?ioe.

2(. C aoaeiiii? iiaeae? aaia?o?oueny aenia?oia aaca ciaiue.

3(. Ii aenia?oi?e aac? ciaiue cae?enith?oueny ?aeaioeo?eaoe?y
iae?i?eiiai ia’?eoa c aeei?enoaiiyi iiaeaeae oa aeai?eoi?a, ?ic?iaeaieo
a ?icae?eao 2 oa 3.

4(. ?acoeueoaoe ?aeaioeo?eaoe?? c aeiiiiiaith ia/?oeeo aac ciaiue, ye?
io?eiai? ia e?ioe? 3(, ii??aiththoueny c aoaeiiieie iiaeaeyie, ui
caaeai? ia e?ioe? 1(. I?e oeueiio aoaeothoueny e?ea? iaa/aiiy, ui
iieacothoue ci?io yeino? ?aeaioeo?eaoe?? ii i??? ca?eueoaiiy ia’?io
iaa/ath/i? aea??ee.

?acoeueoaoe eiii’thoa?ieo aenia?eiaio?a iaaaaeai? a oaae. 2, aea
aeei?enoiaothoueny oae? nei?i/aiiy: aeI — aeoaea iecueeee, I — iecueeee,
iN — ieae/a na?aaeiueiai, N — na?aaei?e, aN — aeua na?aaeiueiai, A —
aenieee, aeA — aeoaea aenieee.

I’yoee ?icae?e i?enay/aiee ?ic?iaoe? i?ia?aiiiai caaacia/aiiy FUZZY
EXPERT aeey i?iaeooaaiiy oa iano?ieee

Oaaeeoey 2

I?eeeaaee ?aeaioeo?eaoe?? iae?i?eieo ia’?eo?a

Iiaeaeue-aoaeii ? ia/?oea Ia/?oea iiaeaeue ? ooieoe?? iaeaaeiino?

aaca ciaiue aei iano?ieee i?ney iano?ieee

ia/?oeeo aac ciaiue, a oaeiae ae??oaiith aeayeeo i?aeoe/ieo caaea/
?aeaioeo?eaoe?? c aeei?enoaiiyi ?ic?iaeaiiai iaoiaeo. I?ia?aiia
caaacia/aiiy FUZZY EXPERT neeaaea?oueny c aeaio /anoei (aeea. ?enoiie):
na?aaeiaeua ?ic?iaee (iaieiiee), ui aeicaiey? noai?thaaoe aenia?oi?
nenoaie o aea?ai?e iaeano?, oa iniaenoi aenia?oii? nenoaie, yea ?
e?ioeaaei iacaeaaeii ooieoe?iioth/ei i?iaeoeoii.

C aeiiiiiaith FUZZY EXPERT aoee iiaoaeiaai? aenia?oi? nenoaie aeey:
a) i?iaiicoaaiiy ia’?io a?iaaco ia aeoiae? oaoiieia?/iiai i?ioeano
a?ieiiaa?n??, a) ioe?iee yeino? ?iiiaaoe?eieo i?iaeo?a,
a) ?aeaioeo?eaoe?? eiao?oe??ioo c/aieaiiy eieana aaoiiia?eth c
aei?iaei?i iie?eooyi, a) aeeoa?aioe?eii? ae?aaiinoeee ?oai?/ii? oai?iae
na?oey, ae) i?iaiicoaaiiy e?eueeino? caoai?thaaiue, ?) ioe?iee iaaaciaee
e?iaioa/? i?e iieiaao oa ?io?.

Aeniiaie i?noeoue oi?ioethaaiiy, ci?no, iaoeiao iiaecio, aeinoia??i?noue
oa i?aeoe/io oe?ii?noue ?acoeueoao?a.

Aeiaeaoee i?noyoue aeieoiaioe i?i ai?iaaaeaeaiiy ?iaioe, noeneo
?ioi?iaoe?th i?i ??ci? iaoiaee ia?aiao?e/ii? ?aeaioeo?eaoe??, a oaeiae
n?i iniiaieo ae?aiieo oi?i i?ia?aiiiai caaacia/aiiy FUZZY EXPERT.

AENIIAEE

A oiae? aeeiiaiiy aeine?aeaeaiue ?ic?iaeaii iaoiae ?aeaioeo?eaoe??
iae?i?eieo ia’?eo?a ia iniia? ia/?oei? eia?ee, yeee neeaaea?oueny c
noeoiiino? i?eioeei?a, iaoaiaoe/ieo iiaeaeae, aeai?eoi?a oa i?ia?aiiiai
caaacia/aiiy aeey ai?ieneiaoe?? iaa?aeiii? caeaaeiino? «aoiaee-aeo?ae»
ii aeinooii?e aenia?oi?e ?ioi?iaoe??. I?e oeueiio io?eiai? ianooii?
?acoeueoaoe:

1. Noi?ioeueiaai? i?eioeeie ?aeaioeo?eaoe?? iae?i?eieo ia’?eo?a ia aac?
ia/?oei? eia?ee ? aaiaoe/ieo aeai?eoi?a.

2. ?ic?iaeai? iaoaiaoe/i? iiaeae? ia/?oei? ai?ieneiaoe?? iae?i?eieo
caeaaeiinoae c iaia?a?aiei oa aeene?aoiei aeoiaeii.

3. Noi?ioeueiaai? iaoaiaoe/i? iinoaiiaee caaea/ iioeiaeueii? iano?ieee
ia/?oeeo aac ciaiue.

4. ?ic?iaeai? aaiaoe/i? aeai?eoie ae??oaiiy iae?i?eieo caaea/
iioei?caoe??, ui aeieeathoue i?e iano?ieoe? ia/?oeeo aac ciaiue.

5. ?ic?iaeaii i?ia?aiia caaacia/aiiy FUZZY EXPERT aeey ae??oaiiy caaea/
?aeaioeo?eaoe?? iae?i?eieo ia’?eo?a ia aac? ia/?oei? eia?ee.

NIENIE IIOAE?EIAAIEO I?AOeUe

1. ?ioooaei A.I., Eaoaeueieeia Ae.E. Eaeaioeoeeaoeey iaeeiaeiuo iauaeoia
ia aaca ia/aoeie eiaeee //Eeaa?iaoeea e nenoaiiue
aiaeec.-1998.-?5.-N.53-61.

2. ?ioooaei I.I., Ea?thoe?i ?.I., Eao?euei?eia Ae.?. Aaaaoioaeoi?iee
aiae?c oaoiieia?/iiai i?ioeano a?ieiiaa?n?? ia iniia? e?iaa?noe/ii?
?ioi?iaoe?? //A?niee AI?.-1997.-?3.-N.38-45.

3. ?ioooaei I.I., Eao?euei?eia Ae.?. ?aeaioeo?eaoe?y iae?i?eieo ia’?eo?a
ia/?oeeie aacaie ciaiue //A?niee AI?.-1997.-?4.-N.98-103.

4. ?ioooaei I.I., Eieei ?.?., Eao?euei?eia Ae.?., Eieei E.N.
I?iaiicoaaiiy e?eueeino? caoai?thaaiue ia aac? ia/?oei? eia?ee //A?niee
AAeIO.- 1998.-?2.-N.486-489.

5. Rotshtein A. P., Katelnikov D.I. Design and Tuning of Fuzzy If —
Then Rules for Automatic Classification. In Proc. of the International
Conference «Annual Meeting of North American Fuzzy Information
Processing Society — NAFIPS’98», Tampa, USA, 1998.- P.50-55.

6. Rotshtein A. P., Katelnikov D.I. Tuning of Fuzzy Rules for Nonlinear
Objects Identification with Discrete and Continuous Output. In PROC. of
the 6th European Congress on Intelligent Techniques and Soft Computing
(EUFIT’98), Aachen, Germany, 1998.-P. 929-934.

7. Rotshtein A. P., Katelnikov D.I. Fuzzy rule-based system for
psychophysiological testing of the man-operator. In PROC. of the Fifth
European Congress on Intelligent Techniques and Soft Computing
(EUFIT’97), Aachen, Germany, 1997.- P.984-986.

8. Rotshtein A. P., Katelnikov D.I., Zlepko S.M. Fuzzy rule-based expert
system for differential diagnosis of ischemia heart disease. In Proc. of
the International Conference «Fuzzy Logic and Its Applications —
FUZZY’97». Zichron, Israel, 1997.- P.367-372.

9. Rotshtein A. P., Katelnikov D.I., Goldenberg L.N. Design and tuning
of the fuzzy expert systems for medical diagnostics. In PROC. of
International Workshop «Biomedical Engineering & Medical Informatics»
(BEMI’97) Gliwice, Poland, 1997.- P.106-110.

Iniaenoee aianie. An? iniiai? ?acoeueoaoe aeena?oaoe?eii? ?iaioe
io?eiai? aaoi?ii naiino?eii. A ?iaioao, iaienaieo o ni?aaaoi?noa?,
aaoi?o iaeaaeeoue: iaoaiaoe/i? iiaeae? oa aeai?eoie ?aeaioeo?eaoe??
iae?i?eieo ia’?eo?a c iaia?a?aiei aeoiaeii [1,3,6], aeene?aoiei aeoiaeii
[5,6], i?iaeooaaiiy oa iioei?caoe?y iiaeaeae [2,4,8,9], ?ic?iaea
i?ia?aiiiai caaacia/aiiy [7].

AIIOAOe?ss

Eao?euei?eia Ae.?. ?ic?iaea iaoiaeo ?aeaioeo?eaoe?? iae?i?eieo ia’?eo?a
aeey aenia?oieo nenoai ia aac? ia/?oei? eia?ee.-?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe
ca niaoe?aeuei?noth 05.13.06 — Aaoiiaoeciaai? nenoaie oi?aae?iiy ?
ia?niaeoeai? ?ioi?iaoe?ei? oaoiieia??.-Iaoeiai-ae?iaie/a ei?ii?aoe?y
«Ee?anueeee ?inoeooo aaoiiaoeee», Ee?a, 1998.

Cai?iiiiiaai? i?eioeeie ?aeaioeo?eaoe?? iae?i?eieo caeaaeiinoae ia aac?
aenia?oii-e?iaa?noe/ii? ?ioi?iaoe?? oeyoii aeaioaoaiii? iano?ieee
ia/?oeeo aac ciaiue. ?ic?iaeai? iiaeae? ai?ieneiaoe?? iae?i?eieo
caeaaeiinoae c iaia?a?aiei oa aeene?aoiei aeoiaeii ia iniia? ia/?oeeo
i?aaee «ssEUI , OIAe? ». Noi?ioeueiaai? caaea/?
iano?ieee iiaeaeae ia/?oei? ai?ieneiaoe?? ye aea?? oaeeo oi?i ooieoe?e
iaeaaeiino? oa eiao?oe??io?a aaaiiino? aenia?oieo i?aaee, ui
i?i?i?cothoue ?ica?aei?noue i?ae oai?aoe/iei oa aenia?eiaioaeueiei
aeoiaeaie ia’?eoo. ?ic?iaeai? aaiaoe/i? aeai?eoie iioeiaeueii? iano?ieee
ia/?oeeo aac ciaiue. I?iaaaeai? eiii’thoa?i? aenia?eiaioe c aoaeiiieie
iae?i?eieie ia’?eoaie, ui aeiaiaeyoue aoaeoeai?noue cai?iiiiiaaiiai
iaoiaeo ?aeaioeo?eaoe??. ?ic?iaeaia i?ia?aiia iaieiiea FUZZY EXPERT aeey
ae??oaiiy i?aeoe/ieo caaea/ ?aeaioeo?eaoe?? ia aac? ?ic?iaeaiiai
iaoiaeo. Iaaaaeai? ?acoeueoaoe aeei?enoaiiy iaieiiee FUZZY EXPERT a
aenia?oieo nenoaiao iaaee/ii? ae?aaiinoeee, i?iaiicoaaiiy caoai?thaaiue,
oa ioe?iee ?iiaaoe?eieo i?iaeo?a.

Eeth/ia? neiaa: iae?i?ei? caeaaeiino?, ?aeaioeo?eaoe?y, ia/?oea eia?ea,
aaiaoe/i? aeai?eoie, i?eeiyooy ??oaiue, aenia?oi? nenoaie.

Eaoaeueieeia Ae.E. ?ac?aaioea iaoiaea eaeaioeoeeaoeee iaeeiaeiuo
iauaeoia aeey i?eiyoey ?aoaiee ia aaca ia/aoeie eiaeee. -?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 05.13.06 — Aaoiiaoece?iaaiiua nenoaiu oi?aaeaiey e
ia?niaeoeaiua eioi?iaoeeiiiua oaoiieiaee.-Iao/ii- i?iecaiaenoaaiiay
ei?ii?aoeey «Eeaaneee einoeooo aaoiiaoeee», Eeaa, 1998.

I?aaeeiaeaiu i?eioeeiu eaeaioeoeeaoeee iaeeiaeiuo caaeneiinoae ia aaca
yenia?oii-eeiaaenoe/aneie eioi?iaoeee iooai aeaooyoaiiie iano?ieee
ia/aoeeo aac ciaiee. ?ac?aaioaiu iiaeaee ia/aoeie aii?ieneiaoeee
iaeeiaeiuo caaeneiinoae. Noi?ioee?iaaiu caaea/e iioeiaeueiie iano?ieee
ia/aoeeo aac ciaiee. Aeey ?aoaiey yoeo caaea/ ?ac?aaioaiu aaiaoe/aneea
aeai?eoiu iioeiecaoeee. I?iaaaeaiu eiiiuethoa?iua yenia?eiaiou n
yoaeiiiuie iiaeaeyie, iiaeoaa?aeaeathuea yooaeoeaiinoue i?aaeeiaeaiiiai
iaoiaea eaeaioeoeeaoeee. ?ac?aaioaia i?ia?aiiiay iaiei/ea FUZZY EXPERT
aeey ?aoaiey i?aeoe/aneeo caaea/ eaeaioeoeeaoeee. I?eaaaeaiu ?acoeueoaou
eniieueciaaiey iaiei/ee FUZZY EXPERT a yenia?oiuo nenoaiao iaaeeoeeineie
aeeaaiinoeee, i?iaiice?iaaiey caaieaaaiee e ioeaiee eiiiaaoeeiiiuo
i?iaeoia.

Eeth/aaua neiaa: iaeeiaeiua caaeneiinoe, eaeaioeoeeaoeey, ia/aoeay
eiaeea, aaiaoe/aneea aeai?eoiu, i?eiyoea ?aoaiee, yenia?oiua nenoaiu.

Katelnikov D.I. Creation of method for nonlinear object identification
for solution making based upon fuzzy logic.-Manuscript.

Candidate of technical science dissertation on speciality 05.13.06 —
Automated control systems and perspective informational
technology.-Scientific and productive corporation «Kiev institute of
automatisation», Kiev, 1998.

The dissertation is devoted to creation of method for nonlinear objects
identification on the basis of fuzzy logic and genetic algorithms.
Dissertation contains new principles of identification, mathematical
models of fuzzy approximation of objects with discrete and continuous
output. Tasks of fuzzy models fine tuning are stated. Genetic algorithms
for solution of these tasks are developed. Achieved new scientific
results were applied during creation of FUZZY EXPERT software. The main
purpose of this software is to facilitate procedures of nonlinear object
identification on the basis of fuzzy logic and genetic algorithms.

Keywords: Information from expert, fuzzy logic, rough tuning of the
model, fine tuning of fuzzy model, genetic algorithms of optimization,
software FUZZY EXPERT.

Aaoi? aeneiaeth? iiaeyeo ae.o.i., i?io. ?ioooaeio I.I. ca aecia/aiiy
iaoe aeine?aeaeaiue oa iinoaiiaee caaea/ ?aeaioeo?eaoe??.

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