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模糊邏輯
郭耀煌
課程大綱
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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
• 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.
– Fuzzy Engineering, Bart Kosko, Prentice Hall, 1997.
– 模糊理論及其應用, 2003
選課要求
•期中考、期末考(各20%)
•平時作業(20%)
•實作作業(20%)
•期末專題(20%)
•上課出席狀況、發言提問等(15%)
•助教:蔡仁勝、李振維
Background
1. Handle complexity is a common issue in the
information society: complexity originates from
huge information and huge uncertainty.
2. 手排比自排複雜:手排需要更多的知識,而
且不確定性程度也增加(不知何時需換檔)
3. We must deal between the information available
to us and the amount of uncertainty we allow.
4. 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 so
does not necessarily imply the loss of
meaningful semantics.
5. Application roadmap of information technology:
numerical analysis, large database, knowledge
management. So, we must first know the
characteristics of the world and its knowledge,
then explore the possibility and limitation of
knowledge.
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, nondiscrete) 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)
• Bremetmann limit: No data processing system,
whether artificial or living, can process more than
2 1047 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?
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)
Fuzzy Set
Fuzzy Event
1972 Fuzzy Measure
(Prof.Michio Sugeno)
Crisp
Element
• 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)
Membership Function
traditional
Age (Man Gt 60)
1
30
60
Ages
Introduction
Fuzzy
Membership Function
Age (Man Old)
1
0.5
30
60
Ages
Fuzzy Logic
 A( x) : membershipof the element x in the fuzzy subset A
x : an elementof the reference set E
A, B, Fuzzy subset of E
a  A ( x), b  B ( x), a, b[0,1]
a  b  MIN (a, b)
a  b  MAX (a, b)
 a  1 a
a  b  (a   b)  ( a  b)
Fuzzy Logic
Commutativity a  ()b  b  ()a
Associative (a  b)  c  a  (b  c)
Distributivity a  (b  c)  (a  b)  (a  c)
( a)  a
DeMorgan' stheorems
(a  b)   a   b
(a  b)   a   b
Fuzzy Inference
二值理論推論形式
(事實) 麻雀是鳥
(規則) 鳥會飛
(結論) 麻雀會飛
AI Language as LISP,Prolog “Pattern Matching”
Fuzzy推論形式:
(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 A
(rule) if X is A then Y is B
希望得到的結論是
Mamdani 法
(result) Y is B
1
A
A
1
B
B
0
0
Application 2
Air Conditioner System
TEMP.
SENSOR
TEMP. ERROR
TEMP. CHANGE
FUZZY
INFERENCE
INVERTER
FREQ.
FUZZY RULES
COMP
VALVE
MEMBERSHIP
FUNCTIONS
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50 RULES (HEATING&A/C)
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MAX-PRODUCT INFERENCING
DEFUZZIFICATION:
CENTROID METHOD
FAN SPEED
Application 3
Control laws of a Washing Machine
Laundry volume (V)
Low
Mid
High
Soft
S = Weak
T = Short
S = Weak
T = Short
S = STD
T = STD
More or less
soft
S = Weak
T = Short
S = STD
T = STD
S = STD
T = STD
S = Weak
T = Short
S = STD
T = STD
S = Strong
T = Long
S = Weak
T = Short
S = STD
T = STD
S = Strong
T = Long
fabric
quality
More or less
(Q)
Hard
Hard
Application 3
Fuzzy Automatic Washing Machine
laundry volume
Stream strength
optimum
water level
Laundry
volume
(V)
fabric
quality
(Q)
fabric
quality
FUZZY
CONTROL
Washing time
High
Mid
Low
Stream strength = Weak
Washing time = Short
Hard
Mid
Soft
Stream strength = Strong
Washing time = Long
Stream strength = Strong
Washing time = Short
(Optimal Washing Cycle)
Application 3
Fuzzy-Neuro Washing Machine(Panasonic)
(OUTPUT)
(INPUT)
Quantity
Turbidity
(Optical sensor)
Water Level
Water Stream Strength
FUZZY
INFERENCE
Change Rate
Of Turbidity
Washing Cycle Time
Rinse Cycle Time
Drain Cycle Time
Tuning
membership
functions
NEURAL
NET
Application 3
Fuzzy-Neuro Washing Machine(Hitachi/Sanyo)
(OUTPUT)
(INPUT)
Quality(4)
Quantity(3)
Water Stream Strength
FUZZY
INFERENCE
Washing Cycle Time
Rinse Cycle Time
Drain Cycle Time
Quality(4)
Quantity(3)
Conductivity
Sensor(5)
(Room Temp (8) – Sanyo)
NEURAL
NET
COMPENSATION
Advantages of fuzzy system modeling
1.
2.
3.
4.
5.
6.
The ability to model highly complex business problems.
Improved cognitive modeling of expert systems
 Need not crisply dichotomize rules at artificial
boundary;
 Reduce overall cognitive dissonance
The ability to model systems involving multiple experts.
Reduced model complexity:
a. Fewer rules,
b. Representing rules closer to natural language
Improved handling of uncertainty and possibilities,
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
以往方式的
問題所在
感覺型問題
非線形型問題
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
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應
用 例
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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。
地下鐵乘客的 •
心情控制
汽車的
SUSPENSION •
起重機的操作
控制
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分類型問題
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。
溫度控制
AIRCONDITIONER
位置控制HARD
DISK
速度控制
AUTOIRIS/
AUTOFOCUS
機能
PATTERN認
識
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