How Fuzzy Systems Work

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Disjunctive Swarm Intelligence What We Learn
From Groups of Individually Dumb Bugs
Doing Collectively Smart Things"
Robert J. Marks II
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Applications Warfare Game Theory
Aviation Weekly , Sept 29, 2003
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Applications Business
Swarm Intelligence A Whole New Way to Think
About Business Harvard Business Review, May
2002 Using swarm intelligence optimization,
Southwest Airlines slashed freight transfer rates
by as much as 80. Similar research into the
behavior of social insects has helped Unilever,
McGraw Hill, and Capital One, to develop more
efficient ways to schedule factory equipment,
divide tasks among workers, organize people , and
even plot strategy.
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Applications Telecommunications
Scientific American, March 2000 Several
companies are using swarm intelligence for
handling the traffic on their networks. France
Télécom and British Telecommunications have taken
an early lead in applying antbased routing
methods to their systems The ultimate
application, though, may be on the Internet,
where traffic is particularly unpredictable.
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Applications Optimization
Particle Swarm An (enormously effective!) multi-
agent optimization algorithm based on the
biomimetics of bird flight.
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Application Fiction
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Boundary Marking The Problem

• Solve the equation
• f (x) c
• f ( . ) is a function,
• c is a given constant, and
• x is a vector.
• Assumption
• There are a number of solutions.
• (The problem is ill-posed.)

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Solve for contour
Edge Island In 59
Dimensions Details Notes
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What is Swarm Intelligence?Simple Rules for
Multiple Agents.

• Randys Rules
• Drive Fast
• Turn Left

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Another rule

• Drive Fast
• Turn Left
• Dont hit stuff
• Emergent Behavior
• Competition- Winning!

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Gnat Swarm One Simple Rule
Steady State In Out
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The Dumb Termite Clearing Wood

• RULES
• Run around randomly until you bump into a piece
  of wood.
• Pick it up.
• Run around randomly until you bump into a piece
  of wood.
• Put it down.
• Repeat forever.
• Q What does this do? MOVIE

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The Dumb Termite Clearing Wood

• Run around randomly until you bump into a piece
  of wood.
• Pick it up.
• Run around randomly until you bump into a piece
  of wood.
• Put it down.
• Repeat forever.
• Q What does this do? MOVIE

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Ant Clustering
Ants cluster their dead to clean their nest.
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Termite Wood Moving
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Another Termite Simulation with a Velocity Bias
Click
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Worm Search Looking for Your Lost Pet Turtle
Under a Lamppost

• Agent Rule
• Diminishing Radius Momentum if the visible
  radius decreases, the momentum is increased.
• Dont tred on me.
• Emergent Behavior A parameter to tune between
  the optimization criteria.

• Tradeoffs
• Easier to look under lamppost
• Want to look uniformly in around the area.
• Pareto Optimization (Efficient Frontier)

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Q What does a pile of sand have to do with a
swarm?
A 1. Simple Rules 2. Pareto Statistics (Power
Law) Earthquakes Income Citation Size of
wars Size of cities Dweeb Massacres
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Bullies Dweebs

• Evasion Pursuit

Click
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Let's Get Fuzzy

• Based on intuition and judgment
• No need for a mathematical model
• Relatively simple, fast and adaptive
• Less sensitive to system fluctuations
• Can implement design objectives, difficult to
  express mathematically, in linguistic or
  descriptive rules.

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Example Fuzzy Table for Control
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Lab Test Speed Tracking of IM
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Lab Test Prercision Position Tracking of IM
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Combinatorial Rule Explosion

• For the trajectory example given
• 2 antecedents
• 7 rules each
• 72 rules
• In general
• A antecedents
• R rules each
• RA rules exponential growth
• e.g. 10 antecedents, 10 rules 10 billion rules
  per consequent

The curse of dimensionality
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Dweeb Control

• Antecedents for Dweeb control
• Nearest bully ?x
• Nearest bully ?y
• Nearest Dweeb tracked by Bully ?x
• Nearest Dweeb tracked by Bully ?y
• Nearest Dweeb ?x
• Nearest Dweeb ?y
• Distance from ceiling
• Distance from floor
• Distance from right wall
• Distance from left wall
• Consequents
• Dweebs ?x ?y
• Dweebs ?twiddlex ?twiddley

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Dweeb Control

• Antecedents for Dweeb control
• Nearest bully ?x
• Nearest bully ?y
• Nearest Dweeb tracked by Bully ?x
• Nearest Dweeb tracked by Bully ?y
• Nearest Dweeb ?x
• Nearest Dweeb ?y
• Distance from ceiling
• Distance from floor
• Distance from right wall
• Distance from left wall
• Consequents
• Dweebs ?x ?y
• Dweebs ?twiddlex ?twiddley

• 10 antecedents, 3 rules per 310 rules
• 4 consequents
• 236,196 rules

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Dweeb Control How we Think

• Antecedents for Dweeb control
• Nearest bully ?x ? ? Dweeb ?x ?
• Nearest bully ?y ? ? Dweeb ?y ?
• Nearest Dweeb tracked by Bully ?x ? ? Dweeb ?x ?
• Nearest Dweeb tracked by Bully ?y ? ? Dweeb ?y ?
• Nearest Dweeb ?x ? ? Dweeb ?x ?
• Nearest Dweeb ?y ? ? Dweeb ?x ?
• Distance from ceiling ? ? Dweeb ?y ?
• Distance from floor ? ? Dweeb ?y ?
• Distance from right wall ? ? Dweeb ?x ?
• Distance from left wall ? ? Dweeb ?x ?
• 30 rules for ?x and ?y, not 118,098

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Combs Andrews

• (A?B?C?) ?R ? (A?R)(B?R)(C?R)

Conjunctive inference Disjunctive inference 1.
RA rules per consequent 1. RA rules per
consequent 2. Brittle 2. Plastic 3. Expert
Unmanageable 3. Expert Manageable
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Disjunctive vs. Conjunctive Inferencing
Plasticity Robustness Dynamic Adaptivity
Cognitive Parallels Reasoning In Complex
Situations Under Finite Computational
Resources Tractability
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Multi-Agent Criteria Uncover important search
area.

• Consequents
• Velocity Components
• In direction of new discovery
• In direction of unexplored area
• Away from nearby agents
• In direction of diminished radius

• Antecedents
• Distance from Unexplored Area
• Location of Newly Discovered area
• Distance of Nearest Agent
• Radius Diminishment

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Finis