Linguistic Variable

 

fuzzy set ÀÇ Áß¿äÇÑ ÀÀ¿ëÁß¿¡ computational linguistics °¡ ÀÖ´Ù. ÀÌ°ÍÀº logicÀ» logic statement·Î¼­ ¹¦»çÇϵíÀÌ computer ¿¡ ÀÚ¿¬¾î ¹®ÀåÀ» ¹¦»çÇϱâ À§ÇÑ °ÍÀÌ´Ù. Áï fuzzy set ¿Í linguistic variable Àº Á¶ÀÛÇÒ¼ö ÀÖµµ·Ï ÀÚ¿¬¾îÀÇ Àǹ̸¦ Á¤·®È­Çϱâ À§Çؼ­ÀÌ´Ù. linguistic variableÀº ÀÚ¿¬¾î ¶Ç´Â Àΰø¾ð¾î¿¡¼­ÀÇ words, phrases, sentences °°Àº Ç¥ÇöÀ¸·Î linguistic value¸¦ °®´Â´Ù. ´ÙÀ½Àº linguistic variable°ú linguistic valueÀÇ ¿¹ÀÌ´Ù.  

 

Linguistic Variable

Linguistic Value

    Å°

    dwarf(³­ÀïÀÌ), short, average, tall, giant

    ¼ýÀÚ

    almost none, several, few, many

    stage of life

    infant, toddler(°È´Â ¾Æ±â), child, teenager, adult

    »ö±ò

    red, blue,green, yellow, orange

    ºû

    dim, faint, normal, bright, intense

    µðÀúÆ®

    pie, cake, ice cream, baked alaska

 

ÀÌ·¯ÇÑ linguistic value·Î¼­ÀÇ red ¿Í °°Àº °ªÀº ¼ºÁú»ó ¸Å¿ì ÁÖ°üÀûÀÌ´Ù. ¿¹¸¦µé¾î »ö±ò red ´Â Àΰ£ÀÌ red ¶ó°í °¨ÁöÇÏ´Â ÁÖÆļöÀÇ ¹üÀ§¿Í »óÀÀÇÑ´Ù. Áï ÇϳªÀÇ ÁÖÆļö °ªÀÌ ¾Æ´Ï¶ó´Â °ÍÀÌ´Ù. aquamarine (³²·Ï»ö) Àº blue ¿¡ °¡±î¿î°¡ green¿¡ °¡±î¿î°¡?  linguistic variable´Â heuristic rule¿¡¼­ ÈçÈ÷ »ç¿ëµÇ¸ç ´ÙÀ½Àº ±×¿¹ÀÌ´Ù.

 

    IF   TV°¡ ³Ê¹« ¾îµÎ¿ì¸é  THEN  ¹à±â¸¦ Á¶Á¤Çضó : picture quality

    IF  ³Ê¹« ¶ß°Å¿ì¸é  THEN  Âù °ÍÀ» ´õ ³Ö¾î¶ó : water temperature

    IF   ¾Ð·ÂÀÌ ³Ê¹« ³ôÀ¸¸é   THEN  relief valve¸¦ ¿­¾î¶ó

    IF  ÀÌÀÚÀ²ÀÌ ¿Ã¶ó°¡¸é  THEN  Ã¤±Ç (bond)¸¦ »ç¶ó

    IF  ÀÌÀÚÀ²ÀÌ ³»·Á°¡¸é  THEN  ÁÖ½Ä (stock)À» »ç¶ó

 

À§¿¡¼­ picture quality ´Â color, tint, brightness, noise, consistency µîÀÇ value¸¦ °¡Áø´Ù. ¶ÇÇÑ brightness µîµîÀº closed interval [0, 1] ÀÇ ¼öÄ¡¹üÀ§¸¦ °®´Â linguistic value¸¦ °®´Â´Ù. µû¶ó¼­ picture quality´Â fuzzy set of order 2 ¶ó°í ÇÏ°í brightness ´Â fuzzy set of order 1 À̶óÇÏ¸ç µÑ´Ù linguistic variable ÀÌ´Ù. µû¶ó¼­ linguistic variable´Â hierarchy ±¸Á¶·Î Ç¥ÇöÇÒ¼ö ÀÖ´Ù.

 

linguistic variable ÀÇ term-set ,T(L) Àº ´ÙÀ½°ú °°Àº value¸¦ °®´Â´Ù.

T(PIE) = CHOCOLATE + APPLE + STRAWBERRY + PECAT

À§ÀÇ CHOCOLATE ´Â ¶Ç´Ù¸¥ subsetÀ» ±¸¼ºÇÑ´Ù.

CHOCOLATE = SEMI-SWEET CHOCOLATE + MILK CHOCOLATE + DUTCH CHOCOLATE + ...

 

´ÙÀ½°ú °°Àº CHOCOLATE fuzzy set ÀÇ ¶Ç´Ù¸¥ ÇüÅÂÀÇ Á¤ÀÇ´Â set ÀÇ Àǹ̸¦ º¯Çü½ÃÅ°´Â hedge¸¦ Æ÷ÇÔÇÒ¼ö ÀÖ´Ù.

CHOCOLATE = very CHOCOLATE + very very CHOCOLATE + more or less CHOCOLATE + slightly CHOCOLATE + plus CHOCOLATE + not very CHOCOLATE + ...

fuzzy set, F ¿Í fuzzy set operator ¿ë¾î·Î Ç¥ÇöÇÑ standard hedge´Â ´ÙÀ½°ú °°´Ù.

 

Hedge

Operator definition

    very F

    CON(F) =F

    more or less F

    DIL(F) = F

    plus F

    F

    not F

    1 - F

    not very F

    1 - CON(F)

    slightly F

    INT [ NORM (plus F AND not (very F)) ]

 

operator µéÀ» °áÇÕÇÏ¿© compound hedgeµéÀ» ¸¸µé¼ö ÀÖ´Ù. "slightly" hedge¿¡¼­ º¸µíÀÌ fuzzy set  plus F ¿Í not(very F)¿¡¼­ ÀÛ¿ëÇÏ´Â intersection AND (¡û) °¡ ¹Ù·Î ±× fuzzy set operatorÀÌ´Ù.

 

¶ÇÇÑ Appetite linguistic variableÀ» º»´Ù¸é LIGHT and HEAVY fuzzy set µéÀº S-functionÀ» º¸ÀÌ°í MODERATE fuzzy set ´Â ¥Ð-functionÀ» º¸ÀδÙ. Áï y Ãà¿¡ membership grade, x Ãà¿¡ calories eaten per day¸¦ µÎ´Â ±×¸²À» »ý°¢Çغ»´Ù.

 

fuzzy setÀÇ °æ¿ì´Â LIGHT, MODERATE °£ÀÇ overlapÀÌ Á¸ÀçÇÒ¼ö ÀÖÀ¸¸ç, ½ÉÁö¾î LIGHT ¿Í HEAVY »çÀÌ¿¡µµ overlapÀÌ ÀÖÀ»¼ö ÀÖ´Ù. ±×·¯³ª crisp setÀÇ °æ¿ì´Â disjoint (ºÐ¸®,ÇØü) Çϱ⠶§¹®¿¡ overlapÀÌ ÀÖÀ»¼ö ¾ø´Ù. crispÀÇ °æ¿ì´Â LIGHT appetite´Â µµÀúÈ÷ HEAVY appetiteÀϼö ¾ø´Â °ÍÀÌ´Ù.

 

¿©±â¼­ hedged setÀº fuzzy setÀÇ °æ°è¼±³»¿¡¼­ curve¸¦ ±×¸®°Ô µÈ´Ù. Áï very ¶ó´Â hedge´Â linguistic variable¿¡ ´ëÇÑ modifier·Î¼­ ÀÛ¿ëÇÏ¿© very LIGHT, very MODERATE, very HEAVY ¶ó´Â fuzzy setÀ» ¸¸µç´Ù.

 

linguistic variable´Â fuzzy set or rules·Î ÀÎ½ÄµÉ ¼ö ÀÖ´Â valid syntax ¿Í semantics¸¦ °¡Á®¾ßÇÑ´Ù. syntactic rule Àº T(L) °ú °°Àº Ç¥Çö¾ç½ÄÀ¸·Î Á¤ÀÇÇÏ¿©º¸¸é, ¿¹¸¦µé¸é term-set  T(age)´Â

T(age) = {old, very old, very very old,.....}

À§ÀÇ ¹®ÀåÀº ´ÙÀ½°ú °°Àº syntactic ruleÀ» »ç¿ëÇÏ¿© recursivelyÇÏ°Ô »ý¼ºµÈ´Ù

T  = { old } ¡ú { very T }

 

T(L) °ú ¿¬°üµÈ semantic rule Àº term L ÀÇ Àǹ̸¦ ±ÔÁ¤ÇÑ´Ù.

Áï primary termÀº young, old, chocolate,strawberry µîµîÀ» ÀǹÌÇÏ¸ç ±× Àǹ̴ hedge°¡ »ç¿ëµÇ±âÀü¿¡ ÀÌ¹Ì Á¤ÀǵǾî ÀÖ¾î¾ßÇÑ´Ù. hedge´Â very young, very old, slightly chocolate µîµî°ú °°ÀÌ primary termÀÇ Àǹ̸¦ º¯Çü (modify) ½ÃŲ´Ù.

 

¥ìold(x) = S (x; 60, 70, 80)

 

old¿¡ °üÇÑ membership functionÀº À§¿Í°°ÀÌ ÁÖ¾îÁø´Ù. ÀÌ°ÍÀº S-functionÀ¸·Î Á¤ÀǵȴÙ.

ÀÌ °æ¿ì hedged fuzzy setÀÇ Àǹ̴ ÀûÀýÇÑ fuzzy set operator¸¦ Àû¿ëÇÏ¿© ´ÙÀ½°ú°°ÀÌ Á¤ÀÇÇÑ´Ù

 

¥ìvery chocolate = ¥ìchocolate

¥ìnot chocolate =  1 - ¥ìchocolate

¥ìmore or less chocolate = ¥ìchocolate

¥ìnot very chocolate =1 - ¥ìvery chocolate

 

±âÁ¸ ¾ð¾îÀÇ ¹®¹ýÀ» BNF notationÀ¸·Î Á¤ÀÇÇÒ ¼ö ÀÖ´Â °Íó·³ fuzzy grammar ·Î¼­ Ç¥ÇöÇÒ¼ö ÀÖ´Ù.

À̸¦ »ç¿ëÇÏ¿© fuzzy productionÀ» »ý¼ºÇÏ°Ô µÈ´Ù.

 

linguistic variable °³³äÀ» Àß ÀÀ¿ëÇÑ ¿¹·Î¼­ Sugeno °¡ ¸¸µç fuzzy car °¡ ÀÖ´Ù. ±×°ÍÀº »ç°¢ trackÀ» ÀÚµ¿ÀûÀ¸·Î ¿îÇàÇÏ°Ô ¸¸µå´Â fuzzy logic ¿¡ ±âÃÊÇÑ Á¦¾î½Ã½ºÅÛÀ» »ç¿ëÇÏ¿´´Ù.¶ÇÇÑ Æ¯Á¤ Áö¿ª¿¡ ½º½º·Î ÁÖÂ÷ÇÒ ¼ö ÀÖ°í example ·ÎºÎÅÍ ÇнÀÇÑ´Ù. linguistic variableÀº Â÷ÀÇ ¿îµ¿À» Á¦¾îÇÏ´Â rule¿¡ »ç¿ëµÈ´Ù. ÀÌ¿Ü¿¡ ¸¹Àº fuzzy logic control systemÀÌ Á¦¾î¿Í »ê¾÷°øÁ¤°úÁ¤¿¡ »ç¿ëµÇ¾ú´Âµ¥ ¿¹·Î cement¸¦ Á¦Á¶ÇϱâÀ§ÇÑ cement kiln °ú °°Àº process µîÀÌ´Ù.