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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 ).
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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 • FuzzyLogic 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)
Background • 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) • We must deal between the information available to us and the amount of uncertainty we allow. • Sometimes we can obtain a more robust conclusion by presenting an uncertain description instead of a precise description. (e.g., the description of weather)
Fuzziness is one feature of natural language;it does not necessarily imply the loss of meaningful semantics. • 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multipletruth values的問題之處理效率不足 • 你如何定義一個集合：老年人?
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
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. • 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 • 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?
Fuzzy logic and It’s Applications Contents: • Introduction of Fuzzy Set theory • Basic of Fuzzy Logic • Fuzzy Inference • 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 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
Membership Function 1 3060Ages Introduction Knowledge Representation example: age (Man Old) traditional Age (Man Gt 60)
Introduction Fuzzy logic-based Age (Man Old) Membership Function 1 0.5 3060Ages
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 Mamdani 法 A B 1 1 0 0
Application 2Air Conditioner System TEMP. SENSOR TEMP. ERROR TEMP. CHANGE FUZZY INFERENCE INVERTER FREQ. FUZZY RULES MEMBERSHIP FUNCTIONS COMP VALVE FAN SPEED • 50 RULES (HEATING&A/C) • MAX-PRODUCT INFERENCING • DEFUZZIFICATION: • CENTROID METHOD
Application 3Fuzzy Automatic Washing Machine laundry volume FUZZY CONTROL Stream strength fabric quality optimum water level Washing time Stream strength = Weak Washing time = Short Stream strength = Strong Washing time = Short Stream strength = Strong Washing time = Long (Optimal Washing Cycle)
Application 3Fuzzy-Neuro Washing Machine(Panasonic) (OUTPUT) (INPUT) Quantity Water Level FUZZY INFERENCE Water Stream Strength Turbidity Washing Cycle Time (Optical sensor) Rinse Cycle Time Change Rate Of Turbidity Drain Cycle Time Tuning membership functions NEURAL NET
Application 3Fuzzy-Neuro Washing Machine(Hitachi/Sanyo) (OUTPUT) (INPUT) Water Stream Strength FUZZY INFERENCE Quality(4) Washing Cycle Time Rinse Cycle Time Quantity(3) Drain Cycle Time NEURAL NET Quality(4) Quantity(3) COMPENSATION Conductivity Sensor(5) (Room Temp (8) – Sanyo)
Advantages of fuzzy system modeling • 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: • Fewer rules, • 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.
