模糊邏輯郭耀煌

課程大綱• Fuzzy Sets

• Fuzzy Arithmetic

• Fuzzy Relations

• Fuzzy Logic

• Fuzzy Measure (Possibility Theory)

• Design Process and Design Tools

• Applications: expert systems, fuzzy controllers, pattern recognition, databases and information retrieval, decision making.

教材 ( 一 )• Textbook: Fuzzy Sets and Fuzzy Logic, Theory

and Applications; George J. Klir & Bo Yuan, Prentice Hall, 1995.

• Ref.– Fuzzy sets, Uncertainty, and Information, G. J. Klir and

Tina A. Floger, Prentice Hall, 1988

– Fuzzy Set Theory and Its Applications, H. -J. Zimmermann, 1991

– Fuzzy Logic: Intelligence, Control, and Information, John Yen, Reza Langari, Prentice Hall, 1999.

– 模糊理論及其應用 , 2003

– Fuzzy Logic with Engineering Applications (3rd Ed.), T. J. Ross, WILEY, 2010

選課要求• 期中考、期末考 ( 各 20%)• 平時作業 (25%)• 實作作業 (1次； 15%)• 期末專題 (1~3人團隊完成； 20%)• 上課出席狀況、發言提問等 (15%)• 助教 :(智慧型系統暨媒體處理實驗室 ) 羅群智(cobrageo@ismp.csie.ncku.edu.tw)、

陳慎謙(xol700@ismp.csie.ncku.edu.tw)

Background1. Handle complexity is a common issue in the

information society: complexity originates from huge information and huge uncertainty. 開車即是一個例子、網際網路資訊運用亦然 手排 vs.自排 vs.無人駕駛自動車：手排需要更

多的知識，不確定性程度也增加 ( 不知何時需換檔 )

2. We must deal between the information available to us and the amount of uncertainty we allow.

3. Sometimes we can obtain a more robust conclusion by presenting an uncertain description instead of a precise description. (e.g., the description of weather)

4. Fuzziness is one feature of natural language; it does not necessarily imply the loss of meaningful semantics.

5. Application roadmap of information technology: numerical analysis, large database, knowledge management, social interactions.

So, we must first know the characteristics of the world and its knowledge, then explore the possibility and limitation of knowledge.

傳統的邏輯或數學體系是二元體系，無法處理具有不確定性的問題或者對需要 multiple truth values 的問題之處理效率不足

你如何定義一個集合：老年人 ?

6. Even supercomputer still lacks for the capability of summarization, which is the basis of intelligence and competence of human being. due to the binary logic basis of modern computer model. wait for chemical computer, bio-computer and molecular computer.

– 辨識莫札特的音樂人類無法清楚列出標準– 辨識人種：非超級電腦可行之工作– 有些事情縱使不明確指出其法則，一樣可以去做，

即工作法則是晦暗不明的

7. Traditional AI paradigms: first order logic (John McCarthy, Nilsson Kowalski); ad-hoc techniques and heuristic procedures. (Marvin Minsky (MIT), Roger Schank). L. Zadeh: using fuzzy logic (approximate reasoning, non-discrete) instead of first order logic as the basis of AI in common sense reasoning.

8. 現今的電腦並非計算能力不足，而是因為電腦軟硬體皆非以 fuzzy knowledge(非 discrete的 )及 common-sense reasoning為導向而設計

9. Law of Incompatibility: As complexity rises, precise statements lose meaning and meaningful statements lose precision.

• Fuzzy logic denotes a retreat form unrealistic requirement of precision.( 不是精確的東西就不是科學 )– 古典機率理論被統計技巧取代– 以數值分析解法對微分方程求解，在 3~40 年前無法被

相信的• Paradigm shift: certainty in science uncertainty in

science (molecular; probability theory (statistics; microscopic macroscopic)

• Organized simplicity (Newtonian mechanics, analyzed by Calculus) organized complexity (involve nonlinear systems with large no. of components and rich interactions among the components, which are usually nondeterministic, but not as a result of randomness) disorganized complexity (randomness; statistics)

• Bremetmann limit: No data processing system, whether artificial or living, can process more than

bits per second per gram of its mass. (quantum theory) transcomputational problems

• How to deal with systems and associated problems whose complexities are beyond our information processing limits?

47102

Fuzzy logic and It’s Applications

Contents:

1. Introduction of Fuzzy Set theory

2. Basic of Fuzzy Logic

3. Fuzzy Inference

4. Applications of Fuzzy Logic

Introduction

1965 Fuzzy Set (Prof. Lotfi A.Zadeh,UCB)

1966 Fuzzy logic (Dr. Peter N.Marinos, Bell Lab)

1972 Fuzzy Measure

(Prof.Michio Sugeno)

vs. probability theory

(can only representing

one of several types

of uncertainty)

Fuzzy Set

Fuzzy Event

CrispElement

• 1944 年 , Zadeh 進入 MIT, 此時 computer age 已經發韌 ,– Nobert Winer: cybernetics maintaining order in systems– Claude Shannon: information theory– Warren Mculloch/Walter Pitts: network networks– All these theories would make it possible to create a

world in which information plays a major role• Fuzzy logic combines set theory, vagueness

philosophy, multi-valued logic, Max-Black’s word usage charts.

• Core thinking of fuzzy logic: What is a class?– Categories 遍佈我們的思考，即使動物也隨時在做分類– 語言即是 classes 的最高表示 , 大部分的字都 refer to

categories

• 1970 年 David Marr 認為 handling classes 是腦灰色皮質的永久角色

• 數學家及理則學者以 formal models 來描繪 classes, fuzzy sets 即是這種 model. (19 世紀 Cantor 發展 set theory)

• 字需要有 context 方能給予涵義 (semantics), 集合亦然 , universe of discourse 即充當 set 的 context.

• Bart Kosko: everything is fuzzy except numbers.• 人們在面對 complex information 時 , 會利用 summarization 的策

略– Brain 一直在做 summarizing sense data, which reduces

massive details to chunks of perception. we see an almost closed circle as a complete one.

– 語言亦是一種 summarization• Arthur Geoffrion 質疑如何客觀地定義 membership function• Kahan: What we need is more logical thinking, not less

– 沒有一個問題不能被 ordinary logic 執行得更好

Introduction

Knowledge Representation

example: age (Man Old)

traditional

Age (Man Gt 60)

30 　　 60 　　　 Ages

1

Membership Function

Introduction

Fuzzy logic-based

Age (Man Old)

30 　　 60 　　　 Ages

1

Membership Function

0.5

Fuzzy Logic

AsubsetfuzzytheinxelementtheofmembershipxA :)(:x an element of the reference set E

EofsubsetFuzzyBA ,,

]1,0[,),(),( baxbxa BA

),( baMINba

),( baMAXba

aa 1

)()( bababa

Fuzzy LogicabbaityCommutativ )()(

aa )(

stheoremsDeMorgan '

baba )(

)()( cbacbaeAssociativ

)()()( cabacbavityDistributi

baba )(

Fuzzy Inference

二值理論推論形式 : exact symbolic pattern matching by AI Language (LISP, Prolog):（事實）　麻雀是鳥（規則）　鳥會飛（結論）　麻雀會飛Fuzzy 推論形式： numerical inference scheme（事實）　這番茄很紅（規則）　蕃茄若是紅了就熟了（結論）　這蕃茄很熟了

Fuzzy Inference

(facts) X is

(rule) if X is A then Y is B

希望得到的結論是(result) Y is B

A

1

0

1

0

A

B

A B

Mamdani 法

Application 2Air Conditioner System

TEMP.SENSOR

TEMP. ERRORTEMP. CHANGE

FUZZYINFERENCE

INVERTERFREQ.

COMPVALVE

FAN SPEED

FUZZY RULES

MEMBERSHIPFUNCTIONS

• 50 RULES (HEATING&A/C)

• MAX-PRODUCT INFERENCING• DEFUZZIFICATION:

CENTROID METHOD

Application 3Control laws of a Washing Machine

Laundry volume (V)

Low 　　　　　 Mid 　　　　　 High 　　　

fabric quality

(Q)

SoftS = Weak 　　　 S = Weak 　　　 S = STD

T = Short 　　　 T = Short 　　　 T = STD

More or less soft

S = Weak 　　　 S = STD 　　　 S = STD

T = Short 　　　 T = STD 　　　 T = STD

More or less Hard

S = Weak 　　　 S = STD 　　　 S = Strong

T = Short 　　　 T = STD 　　　 T = Long

Hard S = Weak 　　　 S = STD 　　　 S = Strong

T = Short 　　　 T = STD 　　　 T = Long

Application 3Fuzzy Automatic Washing Machine

FUZZYCONTROL

Laundry volume

(V)

High

Mid

Low

fabric quality

(Q)

Hard

Mid

Soft

Stream strength = WeakWashing time = Short

Stream strength = StrongWashing time = Long

Stream strength = StrongWashing time = Short

(Optimal Washing Cycle)

Stream strength

Washing time

laundry volume

optimumwater level

fabricquality

Application 3Fuzzy-Neuro Washing Machine(Panasonic)

FUZZYINFERENCE

NEURALNET

Tuningmembershipfunctions

Water LevelQuantity

(INPUT) (OUTPUT)

Turbidity(Optical sensor)

Change RateOf Turbidity

Water Stream Strength

Washing Cycle Time

Rinse Cycle Time

Drain Cycle Time

Application 3Fuzzy-Neuro Washing Machine(Hitachi/Sanyo)

FUZZY INFERENCE

NEURAL NET

Water Stream StrengthQuality(4)

(INPUT)(OUTPUT)

Quantity(3)

Washing Cycle Time

Rinse Cycle Time

Drain Cycle Time

COMPENSATION

Quality(4)

Quantity(3)

ConductivitySensor(5)(Room Temp (8) – Sanyo)

Advantages of fuzzy system modeling1. The ability to model highly complex business problems.2. Improved cognitive modeling of expert systems

Need not crisply dichotomize rules at artificial boundary;

Reduce overall cognitive dissonance3. The ability to model systems involving multiple experts.4. Reduced model complexity:

a. Fewer rules,b. Representing rules closer to natural language

5. Improved handling of uncertainty and possibilities,6. Less externally complex problems can be isolated

and fixed sooner improved MTTR and MTBF.

表 1 　關於理論應用方面的控制問題

感覺型問題 非線形型問題 分類型問題

以往方式的問題所在

控制目標用數值表現很難。

控制結果的好壞必須要用感覺評估。

由於控制對象的狀況常常變化，故無法完全控制目標值，故OVERSH-OOT很大。

雖然預設的狀況很複雜但卻無法記述所有PATTERN 的對應方法。

應　用　例

• 地下鐵乘客的心情控制

• 汽車的SUSPENSION

• 起重機的操作控制

• 溫度控制AIRCONDIT-IONER

• 位置控制 HARD DISK

• 速度控制

• AUTOIRIS/ AUTOFOCUS機能

• PATTERN 認識