MatLab Fuzzy Logic Toolbox An End User Programming Environment

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MatLab Fuzzy Logic Toolbox - An End User
Programming Environment

• Presented By
• Karlene Williams

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Agenda

• What is Fuzzy Logic?
• What is MatLab Fuzzy Logic Toolbox For?
• Who is MatLab Fuzzy Logic Toolbox For?
• Overview Fuzzy Inference Systems
• Fuzzy Set Concept
• Fuzzy Rules
• Membership functions
• How it works
• Building Systems An Example
• Demo
• Discussion

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What Is Fuzzy Logic?
As complexity rises, precise statements lose
meaning and meaningful statements lose
precision
- Lotfi Zadeh
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What Is Fuzzy Logic? (Cont.)

• Fuzzy logic is all about the relative importance
  of precision How important is it to be exactly
  right when a rough answer will do?

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What Is Fuzzy Logic?(Cont.)

• Fuzzy logic trades off between significance and
  precision
• The Fuzzy Logic Toolbox for use with MATLAB is a
  tool for solving problems with fuzzy logic.
• Fuzzy logic is a convenient way to map an input
  space to an output space. E.g. Tell me how good
  your service was at a restaurant, and Ill tell
  you what the tip should be.

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What Is MatLab Fuzzy Logic Toolbox For?

• The Fuzzy Logic Toolbox allows you to create and
  edit fuzzy inference systems.
• Systems can be created using
• Graphical tools or
• Command-line functions
• Features
• High-level script language with interpreter.
• Huge library of functions and scripts.
• Act as an computing environment that combines
  numeric computation, advanced graphics and
  visualization.

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More Features

• Underlying data structure is a multi-dimensional
  array (e.g., scalar, vector, or matrix)
• Case sensitive variables
• Operator precedence. E.g. logical (AND, OR, NOT,
  etc)
• Object oriented capabilities
• Variable number of input and output arguments
• Use interactively or as programming language
  (interpreted or compiled)

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More Features

• Can link to other languages (e.g., compiled C
  code)
• Comprehensive help facility
• Conditionals, looping, functions, globals, etc
• Fast prototyping
• Large number of included examples
• Typically not for real-time operation
• Data analysis visualisation
• GUI interaction

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Who Is MatLab Fuzzy Logic Toolbox For?

• Ideal for engineers, researchers and educators!
• Experienced fuzzy logic designers should find it
  easy to use the system to research, model, test,
  and visualize highly complex systems.

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Overview Fuzzy Inference Systems

• Fuzzy inference - process of formulating the
  mapping from a given input to an output using
  fuzzy logic.
• The mapping provides a basis from which decisions
  can be made, or patterns discerned.
• DOMAIN Fuzzy inference systems have been
  successfully applied in fields such as automatic
  control, data classification, decision analysis
  and expert systems.

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Fuzzy Set Concept

• A fuzzy set is a set without a crisp, clearly
  defined boundary. It can contain elements with
  only a partial degree of membership. E.g.
  classifying the weekend days

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Fuzzy Rules
If-Then Rules statements are used to
formulate the conditional statements that
comprise fuzzy logic. E.g. If service is
poor or the food is rancid, then tip is cheap
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Membership Functions

• A membership function (MF) is a curve that
  defines how each point in the input space is
  mapped to a membership value (or degree of
  membership) between 0 and 1.

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How It Works

• Four Steps
• Step 1. Fuzzify inputs (fuzzification)
• Step 2. Rule evaluation
• Step 3. Aggregation of rule outputs
• Step 4. Defuzzify

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Step 1 Fuzzify Inputs

• Take crisp inputs and determine the degree to
  which they belong to each of the appropriate
  fuzzy sets (via membership functions).

Thus the food is delicious to the degree 0.7
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Step 2 Rule Evaluation

• Process of mapping one or more input(s) to a
  single number that represents the result of the
  evaluation.This number is then applied to the
  output membership function.

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Step 3 Aggregate All Outputs

• Aggregation is the process by which the outputs
  of all rules are unified.
• The membership functions that represent the
  outputs of each rule are combined into a single
  fuzzy set.

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Aggregate All Outputs (Cont)
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Step 4 Defuzzify

• The final output of the fuzzy system must be
• a crisp number. For this process
• The input ? aggregate output from step 3
• The output ? a single number

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Defuzzification (Cont)
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Building Systems With the Fuzzy Logic Toolbox
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Building Systems With the Fuzzy Logic Toolbox
(Cont.)

• There are five GUI tools
• The Fuzzy Inference System or FIS Editor
• Handles the high-level issues How many input and
  output variables? What are their names?
• The Membership Function Editor
• Used to define the shapes of membership functions
  associated with each variable.
• The Rule Editor
• for editing the list of rules that defines the
  behavior of the system.

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Building Systems With the Fuzzy Logic Toolbox
(Cont.)

• 4. The Rule Viewer
• Shows which rules are active, or how individual
  membership function shapes are influencing the
  results.
• 5. The Surface Viewer
• Generates and plots an output surface map for the
  system.

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Building Systems An Example
The Basic Tipping Problem Given a number
between 0 and 10 that represents the quality of
service at a restaurant (where 10 is excellent),
and another number between 0 and 10 that
represents the quality of the food at that
restaurant (again, 10 is excellent), what
should the tip be?
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Step 1 Define Rules

• 1. If the service is poor or the food is rancid,
  then tip is cheap.
• 2. If the service is good, then tip is average.
• 3. If the service is excellent or the food is
  delicious, then tip is
• generous.
• Assume that
• an average tip is 15,
• a generous tip is 25, and
• a cheap tip is 5.

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User Interface Layout Getting Started
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User Interface Layout FIS Editor
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UI Layout MF Editor - Service
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UI Layout MF Editor - Food
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UI Layout MF Editor - Tip
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User Interface Layout Rule Editor
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User Interface Layout Rule Viewer
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User Interface Layout Surface Viewer
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DEMO ?
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Questions ?
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Discussion Points

• System features supplement cognitive resources
• (design features can be used effectively by
  users with different levels of
• cognitive resources ).

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Notes

• Low viscosity a single change usually Requires
  no further actions to restore consistency. The
  GUIs are dynamically linked, in that changes you
  make to the FIS using one of them, are
  automatically propagated across the others.
• Hard mental operations
• The use of the variable Params is not clear.
  Im still trying to figure exactly what it means.
• Cant figure out how to undo changes made to
  membership functions. Hace to exit without saving
  and open FIS again.
• Must specify MF Range before entering Params
  (otherwise strange things happen!)

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A Note on Usability

• Ease of use
• - learning (easy to learn)
• - remembering (facilitates a high level of
  recall)
• Effectiveness
• - time (rapid development)
• - errors (few errors)
• - usefulness (can achieve its desired goal)

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The End

• THANK YOU! ?