Fuzzy Logic

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# Fuzzy Logic - PowerPoint PPT Presentation

Fuzzy Logic. 11/6/2001. Agenda. General Definition Applications Formal Definitions Operations Rules Fuzzy Air Conditioner Controller Structure. General Definition. Fuzzy Logic - 1965 Lotfi Zadeh, Berkely

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### Fuzzy Logic

11/6/2001

Agenda
• General Definition
• Applications
• Formal Definitions
• Operations
• Rules
• Fuzzy Air Conditioner
• Controller Structure
General Definition

Fuzzy Logic - 1965 Lotfi Zadeh, Berkely

• superset of conventional (Boolean) logic that has been extended to handle the concept of partial truth
• central notion of fuzzy systems is that truth values (in fuzzy logic) or membership values (in fuzzy sets) are indicated by a value on the range [0.0, 1.0], with 0.0 representing absolute Falseness and 1.0 representing absolute Truth.
• deals with real world vagueness
Applications
• ABS Brakes
• Expert Systems
• Control Units
• Bullet train between Tokyo and Osaka
• Video Cameras
• Automatic Transmissions
Formal Definitions
• Definition 1: Let X be some set of objects, with elements noted as x.
• X = {x}.
• Definition 2: A fuzzy set A in X is characterized by a membership function mA(x) which maps each point in X onto the real interval [0.0, 1.0]. As mA(x) approaches 1.0, the "grade of membership" of x in A increases.
• Definition 3: A is EMPTY iff for all x, mA(x) = 0.0.
• Definition 4: A = B iff for all x: mA(x) = mB(x) [or, mA = mB].
• Definition 5: mA' = 1 - mA.
• Definition 6: A is CONTAINED in B iff mA  mB.
• Definition 7: C = A UNION B, where: mC(x) = MAX(mA(x), mB(x)).
• Definition 8: C = A INTERSECTION B where: mC(x) = MIN(mA(x), mB(x)).
Operations

A B

A  B A  B A

Controller Structure
• Fuzzification
• Scales and maps input variables to fuzzy sets
• Inference Mechanism
• Approximate reasoning
• Deduces the control action
• Defuzzification
• Convert fuzzy output values to control signals
Rule Base
• Fan Speed
• Set stop {0, 0, 0}
• Set slow {50, 30, 10}
• Set medium {60, 50, 40}
• Set fast {90, 70, 50}
• Set blast {, 100, 80}

Air Temperature

• Set cold {50, 0, 0}
• Set cool {65, 55, 45}
• Set just right {70, 65, 60}
• Set warm {85, 75, 65}
• Set hot {, 90, 80}

Membership function is a curve of the degree of truth of a given input value

default:

The truth of any statement is a matter of degree

Rules

Air Conditioning Controller Example:

• IF Cold then Stop
• If Cool then Slow
• If OK then Medium
• If Warm then Fast
• IF Hot then Blast