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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

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fuzzy logic

Fuzzy Logic

11/6/2001

agenda
Agenda
  • General Definition
  • Applications
  • Formal Definitions
  • Operations
  • Rules
  • Fuzzy Air Conditioner
  • Controller Structure
general definition
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
Applications
  • ABS Brakes
  • Expert Systems
  • Control Units
  • Bullet train between Tokyo and Osaka
  • Video Cameras
  • Automatic Transmissions
formal definitions
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
Operations

A B

A  B A  B A

controller structure
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
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}
rules

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
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