Chapter 5 FUZZY NUMBER Chi-Yuan Yeh.

Slides:

Advertisements

Similar presentations

THE WELL ORDERING PROPERTY Definition: Let B be a set of integers. An integer m is called a least element of B if m is an element of B, and for every x.

Advertisements

Chapter 6 FUZZY FUNCTION Chi-Yuan Yeh. Kinds of fuzzy function Crisp function with fuzzy constraint Fuzzy extension function which propagates the fuzziness.

ผศ. ดร. สุพจน์ นิตย์ สุวัฒน์ ตอนที่ interval, 2. the fundamental concept of fuzzy number, 3. operation of fuzzy numbers. 4. special kind of fuzzy.

Chapter 5 Fuzzy Number.

PART 2 Fuzzy sets vs crisp sets

Extension Principle — Concepts

Theory and Applications

August 12, 2003II. BASICS: Math Clinic Fall II. BASICS – Lecture 2 OBJECTIVES 1. To define the basic ideas and entities in fuzzy set theory 2. To.

f has a saddle point at (1,1) 2.f has a local minimum at.

Properties of Real Numbers. Closure Property Commutative Property.

Write reasons for each step

1 Example 1 (a) Estimate by the Midpoint, Trapezoid and Simpson's Rules using the regular partition P of the interval [0,2] into 6 subintervals. (b) Find.

PROPERTIES REVIEW!. MULTIPLICATION PROPERTY OF EQUALITY.

4.6 Numerical Integration Trapezoid and Simpson’s Rules.

Least Common Multiple, Greatest Common Factor, & Decimals

Integration Copyright © Cengage Learning. All rights reserved.

Finding Square Roots Grade 8 Ms. Stewart COPY SLIDES WHEN YOU SEE THIS.

Ch. 2 of Neuro-Fuzzy and Soft Computing. Fuzzy Sets: Outline Introduction Basic definitions and terminology Set-theoretic operations MF formulation and.

5.1.  When we use the midpoint rule or trapezoid rule we can actually calculate the maximum error in the calculation to get an idea how much we are off.

Chapter 8 – Exponents and Exponential Functions 8.1/8.3 – Multiplication and Division Properties of Exponents.

Topic 2 Fuzzy Logic Control. Ming-Feng Yeh2-2 Outlines Basic concepts of fuzzy set theory Fuzzy relations Fuzzy logic control General Fuzzy System R.R.

Measurement Sub. :- Mathematics Std. :- 5 th Chapter no. 16.

Fuzzy Logic Notes by Dr. Ashraf Abdelbar American University in Cairo

“Principles of Soft Computing, 2 nd Edition” by S.N. Sivanandam & SN Deepa Copyright  2011 Wiley India Pvt. Ltd. All rights reserved. CHAPTER 11 FUZZY.

4-5 Exploring Polynomial Functions Locating Zeros.

Chapter Definite Integrals Obj: find area using definite integrals.

1 + 2 × 3 – 4 Division / Multiplication × 3 – 4 Division / Multiplication Addition / Subtraction.

By: Tameicka James Addition Subtraction Division Multiplication

2.2 Solving Two- Step Equations. Solving Two Steps Equations 1. Use the Addition or Subtraction Property of Equality to get the term with a variable on.

Chapter 10 FUZZY CONTROL Chi-Yuan Yeh.

Fuzzy Numbers. Definition Fuzzy Number Convex and normal fuzzy set defined on R Convex and normal fuzzy set defined on R Equivalently it satisfies Equivalently.

Multiplication and Division Properties

Name: _____________________________

Subtraction Addition Multiplication Fractions Division 1pt 1 pt 1 pt

Addition/ Subtraction

Solving Two-Step Equations

Integration Review Problems

1 Step Equation Practice + - x ÷

Multiplication and Division by Powers of Ten

II. BASICS: Math Clinic Fall 2003

دانشگاه شهیدرجایی تهران

Multi-Step Equation.

Chapter 1 Real Numbers.

Properties of Whole Numbers

تعهدات مشتری در کنوانسیون بیع بین المللی

Properties of Definite Integrals

بسمه تعالی کارگاه ارزشیابی پیشرفت تحصیلی

Year 1 Number – number and place value

Commutative and Associative Properties

Year 5 Number – number and place value

Copyright © Cengage Learning. All rights reserved.

Solving Quadratics Using Square Roots

Multiplication and Division Property of Radicals

Rational Expressions and Equations

Review of Section 1 Write as an algebraic expression

A mathematical phase containing numbers.

Aim: How do we solve first degree equations and inequalities?

A mathematical phase containing numbers.

X y y = x2 - 3x Solutions of y = x2 - 3x y x –1 5 –2 –3 6 y = x2-3x.

Properties of Definite Integrals

Numerical Integration

Rational Expressions and Equations

Objectives Approximate a definite integral using the Trapezoidal Rule.

Year 2 Number – number and place value

Multiplication with Subtraction

Year 4 Number – number and place value

Justification Equations Lesson 7.

FUZZY SETS AND CRISP SETS PPTS

Presentation transcript:

Chapter 5 FUZZY NUMBER Chi-Yuan Yeh

Outline Interval and Fuzzy number Operations of interval Operations of fuzzy number α-cut extension principle Triangular fuzzy number Trapezoidal fuzzy number

Interval

α-cut

α-cut

α-cut

Fuzzy number Definition: a fuzzy set A on R must posses at least the following three properties A must be a normal fuzzy set must be a closed interval for every (convex) the support of fuzzy set A, , must be bounded

Operations of Interval

Operations of Interval

Operations of Interval

Operations of Interval

Operations of Interval

Operations of Fuzzy Number α-cut Addition:

Operations of Fuzzy Number α-cut Subtraction: Multiplication: Division: Minimum: Maximum:

Operations of Fuzzy Number

Operations of Fuzzy Number α-cut α = 0.5 α = 1.0

Operations of Fuzzy Number Extension principle Addition: Subtraction: Multiplication: Division: Minimum: Maximum:

Operations of Fuzzy Number

Operations of Fuzzy Number

Operations of Fuzzy Number

Operations of Fuzzy Number

Operations of Fuzzy Number

Operations of Fuzzy Number

Operations of Fuzzy Number

Operations of Fuzzy Number

Triangular fuzzy number

Triangular fuzzy number

Triangular fuzzy number

Triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Operations of triangular fuzzy number

Approximation of Triangular Fuzzy Number

Approximation of Triangular Fuzzy Number

Approximation of Triangular Fuzzy Number

Operations of triangular fuzzy number

Operations of triangular fuzzy number 4

Approximation of Triangular Fuzzy Number 4

Approximation of Triangular Fuzzy Number

Trapezoidal fuzzy number

Operations of Trapezoidal Fuzzy Number

Operations of Trapezoidal Fuzzy Number

Operations of Trapezoidal Fuzzy Number

Approximation of Trapezoidal Fuzzy Number

Operations of Trapezoidal Fuzzy Number

Exercise Is B a convex fuzzy set? Is B a fuzzy number?

Exercise

Thanks for your attention!