IntroductionIntroduction 11

問題問題 電腦可以打敗棋王 電腦可以打敗棋王 vs. vs. 電腦不能和平凡人聊電腦不能和平凡人聊

天？天？ 機械臂可以舉重、插件… 機械臂可以舉重、插件… vs. vs. 機械臂是否可機械臂是否可

以協助採橘子？以協助採橘子？ 甲的表現還不錯甲的表現還不錯；；乙的表現讓人滿意…，誰乙的表現讓人滿意…，誰

的考績較佳？的考績較佳？ 甲活力十足；乙頭腦冷靜…誰適合當總經理？甲活力十足；乙頭腦冷靜…誰適合當總經理？ 明年的市場需求大約十萬件…明年的市場需求大約十萬件…

IntroductionIntroduction 22

Real situations are very often not crisp and deterministic and they cannot be described precisely.

The complete description of a real system often would require by far more detailed data than a human being could ever recognize simultaneously, process and understand.

IntroductionIntroduction 33

數學的分類數學的分類 確定性數學確定性數學

事物的現象具事物的現象具必然性必然性與與精確性精確性。。 不確定性數學不確定性數學

機率論機率論研究和處理隨機性問題的數學，把數學的應用範圍研究和處理隨機性問題的數學，把數學的應用範圍

從從必然現象擴大到偶然現象必然現象擴大到偶然現象。。模糊數學模糊數學 (fuzzy mathematics)(fuzzy mathematics)

研究和處理模糊性問題的數學，把數學的應用範圍研究和處理模糊性問題的數學，把數學的應用範圍從從精確現象擴大到模糊現象精確現象擴大到模糊現象。。

IntroductionIntroduction 44

創立者創立者L. A. ZadehL. A. Zadeh ，， 19651965Fuzzy setsFuzzy sets Information and controlInformation and control ，， 88 ，， pp. 338-pp. 338-

353353

IntroductionIntroduction 55

模糊性模糊性 (fuzziness)(fuzziness) 之意義之意義 指客觀事物的差異在中介過渡時所呈現的指客觀事物的差異在中介過渡時所呈現的

「「亦此亦彼亦此亦彼」性。」性。 例如：高、矮、胖、瘦、美、醜、好、壞例如：高、矮、胖、瘦、美、醜、好、壞

……

IntroductionIntroduction 66

模糊理論之特點模糊理論之特點 11

不是讓數學變成模模糊糊的事物，而是讓不是讓數學變成模模糊糊的事物，而是讓數學進數學進入模糊現象入模糊現象的領域。的領域。

使數學吸取使數學吸取人腦人腦識別識別和和判決的判決的模糊特點模糊特點，使部份，使部份自然語言自然語言能够作為能够作為演算語言演算語言直接進入程序直接進入程序，使人，使人能以簡易之程序調動機器，完成複雜的任務，從能以簡易之程序調動機器，完成複雜的任務，從而提高機器的活性。而提高機器的活性。 例如：機械臂採橘子…例如：機械臂採橘子…

具具個性、主觀、模糊性個性、主觀、模糊性 擁有擁有特殊技能或知識的專家特殊技能或知識的專家都較具都較具個性、主觀與模糊個性、主觀與模糊

性性，模糊理論則具備描述該種特徵之符號與語言。，模糊理論則具備描述該種特徵之符號與語言。 例如：今天天氣很熱例如：今天天氣很熱 oror 適中？適中？

IntroductionIntroduction 77

模糊理論之特點模糊理論之特點 22

求不出數學模式的對象亦可簡易表達求不出數學模式的對象亦可簡易表達 (( 非線非線性問題亦容易處理性問題亦容易處理 ) ) 。。

具精準度具精準度雖為模糊理論但卻能更快、更平穩的獲致精準雖為模糊理論但卻能更快、更平穩的獲致精準

度度 近似概念近似概念 (( 模糊推論模糊推論 )) 語言資訊語言資訊

將將語言變數語言變數 (linguistic variable)(linguistic variable) 以以隸屬函數隸屬函數方式充分表達語言資訊。方式充分表達語言資訊。

IntroductionIntroduction 88

模糊理論之特點模糊理論之特點 33

與與人類思考人類思考方式較契合方式較契合可將語言資訊納入推論，與人類思考之契合性可將語言資訊納入推論，與人類思考之契合性

較佳。較佳。 系統構築系統構築容易容易

可遵循人類思考方式構築。可遵循人類思考方式構築。 不限定不限定研究領域研究領域

凡與人類心理有關之科學均可應用。凡與人類心理有關之科學均可應用。

IntroductionIntroduction 99

模糊理論的演進模糊理論的演進 11

1965 L. A. Zadeh, ”1965 L. A. Zadeh, ”Fuzzy setsFuzzy sets”.”.1968 R. E. Bellman and L. A. Zadeh, ”1968 R. E. Bellman and L. A. Zadeh, ”DeDe

cision makingcision making in a fuzzy environment”. in a fuzzy environment”.1968 L. A. Zadeh, “1968 L. A. Zadeh, “Fuzzy algorithmFuzzy algorithm”.”.1968 J. A. Goguen, “The logic of inexac1968 J. A. Goguen, “The logic of inexac

t concepts”.t concepts”.1972M. Sugeno, “fuzzy integral”.1972M. Sugeno, “fuzzy integral”.

IntroductionIntroduction 1010

模糊理論的演進模糊理論的演進 22

1973 L. A. Zadeh, “1973 L. A. Zadeh, “Fuzzy inferenceFuzzy inference”.”.1974 E. H. Mandani, “1974 E. H. Mandani, “fuzzy algorithms ffuzzy algorithms f

or controlor control”.”.1975 L. A. Zadeh, “Extension principle”.1975 L. A. Zadeh, “Extension principle”.1976 E. Sanchez, “1976 E. Sanchez, “Fuzzy relational equaFuzzy relational equa

tionstions”.”.1978 H. J. Zimmermann, “1978 H. J. Zimmermann, “International International

Journal of Fuzzy Sets and SystemsJournal of Fuzzy Sets and Systems”.”.

IntroductionIntroduction 1111

模糊理論的演進模糊理論的演進 33

1980 F. L. Smith co., “1980 F. L. Smith co., “Practical use of fPractical use of fuzzy controluzzy control”.”.

1984 “IFSA (1984 “IFSA (International Fuzzy SystemInternational Fuzzy Systems Associations Association)” established.)” established.

1985 Hitachi co., “1985 Hitachi co., “fuzzy controled subwfuzzy controled subwayay”.”.

1985 M. Togai, “1985 M. Togai, “Fuzzy digital chipFuzzy digital chip”.”.1985 Fuji Electric co., “1985 Fuji Electric co., “Fuzzy controllerFuzzy controller

”.”.

IntroductionIntroduction 1212

模糊理論的演進模糊理論的演進 44

1990 Panasonic co., “1990 Panasonic co., “fuzzy washing fuzzy washing machinemachine”.”.

……1993 IEEE, Transactions on “Fuzzy 1993 IEEE, Transactions on “Fuzzy

Systems” Published.Systems” Published.

IntroductionIntroduction 1313

模糊理論的應用模糊理論的應用 11

FieldsFields ControlControl Expert systemsExpert systems Image processingImage processing Human interfaceHuman interface Information retrievalInformation retrieval MedicalMedical PsychologyPsychology ManagementManagement EconomicsEconomics Data baseData base ComputerComputer RoboticsRobotics Traffic controlTraffic control Civil engineeringCivil engineering

FunctionsFunctions Decision supportDecision support EvaluationEvaluation ModelingModeling DiagnosisDiagnosis PredictionPrediction InferenceInference RecognitionRecognition ClusteringClustering Data analysisData analysis

IntroductionIntroduction 1414

模糊理論的應用模糊理論的應用 22

Consumer productsConsumer productsWashing machinesWashing machinesMicrowave ovensMicrowave ovensRice cookersRice cookersVacuum cleanersVacuum cleanersCamcordersCamcordersTV’sTV’sThermal rugsThermal rugsWord translatorsWord translators

IntroductionIntroduction 1515

模糊理論的應用模糊理論的應用 33

systemssystemsElevatorsElevatorsTrainTrainCranesCranesAutomotive (engines, transmissions, Automotive (engines, transmissions,

brakes)brakes)Traffic controlTraffic control

SoftwareSoftwareMedical diagnosisMedical diagnosisSecuritiesSecuritiesData compressionData compression

IntroductionIntroduction 1616

模糊理論的架構模糊理論的架構

Fuzzy Sets

Fuzzy MeasureFuzzy Logic

Fuzzy Mathematics

IntroductionIntroduction 1717

Fuzzy setsFuzzy sets

Fuzzy set operationsFuzzy set operationsDecomposition principleDecomposition principleExtension principleExtension principle

IntroductionIntroduction 1818

Fuzzy MathematicsFuzzy Mathematics

Fuzzy relationFuzzy relationFuzzy functionFuzzy functionFuzzy numberFuzzy numberFuzzy arithmeticFuzzy arithmetic

IntroductionIntroduction 1919

New Trends of Fuzzy ResearchNew Trends of Fuzzy Research

Neural Networks

ChaosTheory

ProbabilityTheory

Artificialintelligence

GeneticAlgorithms

FuzzyTheory

Soft computing

IntroductionIntroduction 2020

Soft ComputingSoft Computing11

Soft computing attempts to exploit the Soft computing attempts to exploit the tolerance for uncertainty of various tolerance for uncertainty of various types to achieve types to achieve tractabilitytractability, , low costlow cost, , and and robustnessrobustness..

The The primary aimprimary aim of soft computing is to of soft computing is to develop computational methods that develop computational methods that produceproduce acceptable approximate acceptable approximate solutions at low costsolutions at low cost..

IntroductionIntroduction 2121

Soft computingSoft computing22

Soft Computing

Neural Network

Probabilistic Reasoning

Fuzzy Logic

IntroductionIntroduction 2222

ReferencesReferences

George J. Klir, Bo Yuan, Fuzzy Sets and George J. Klir, Bo Yuan, Fuzzy Sets and Fuzzy Logic – Theory and Applications, Fuzzy Logic – Theory and Applications, Prentice Hall.Prentice Hall.

H.-J. Zimmermann, Fuzzy Set Theory – H.-J. Zimmermann, Fuzzy Set Theory – and Its Applications, second edition, Kland Its Applications, second edition, Kluwer Academic Publishers.uwer Academic Publishers.

區奕勤區奕勤 , , 張先迪張先迪 , , 模糊數學原理及應用模糊數學原理及應用 , , 儒林圖書有限公司儒林圖書有限公司 ..