Fuzzy Disjunctive Inference from the Perspective of a Dweeb Robert J. Marks II.
Transcript of Fuzzy Disjunctive Inference from the Perspective of a Dweeb Robert J. Marks II.
Fuzzy Disjunctive Inference from the Perspective of a Dweeb
Robert J. Marks II
CONJUNCTIVE Approach
Do this1 and this2 and this3 and this4 and this5 to get that.
Result: Highly complex and brittle design. Loose this4
and your system can fail.
Conjunctive statement:
CAj
j
DISJUNCTIVE Approach
(Do this1 to get that ) or (Do this2 to get that ) or (Do this3 to get that ) or (Do this4 to get that )
Result: Highly robust and fault tolerant
design. Loose this4 and you’re still in business.
Disjunctive statement:
CAjj
Is… DISJUNCTIVE = CONJUNCTIVE?
Is…
(Do this1 to get that ) or (Do this2 to get that ) or (Do this3 to get that ) or (Do this4 to get that )
= (Do this1 and this2 and this3 and this4 ) to get that.
???
CAjj CA
jj
In a Boolean sense,
Disjunctive vs. Conjunctive
Disjunctive reasoning sometimes referred to as “The Combs Method”*
Examples of Complex Disjunctive SystemsExamples of Complex Disjunctive Systems
1.1. Swarms: Insects & PeopleSwarms: Insects & People
2.2. Your BodyYour Body
3.3. Animal motor functionsAnimal motor functions
4.4. Genomic symbiogenesisGenomic symbiogenesis William E. Combs
* Earl Cox, The Fuzzy Systems Handbook, Academic Press/ Morgan Kaufman.
• J. J. Weinschenk, W. E. Combs, R. J. Marks II, “Avoidance of rule explosion by mapping fuzzy systems to a disjunctive rule configuration,” IEEE Int’l Conference on Fuzzy Systems, St. Louis, MO, 2003, pp 43-48.
• J. J. Weinschenk, R. J. Marks II, W. E. Combs, “Layered URC fuzzy systems: a novel link between fuzzy systems and neural networks,” Proc. IEEE Intl’ Joint Conf. on Neural Networks, Portland, OR, 2003, pp. 2995-3000.
• Jeffrey J. Weinschenk, William E. Combs, Robert J. Marks II, "On the avoidance of rule explosion in fuzzy inference engines, " International Journal of Information Technology and Intelligent Computing, vol.1, #4 (2007).
DR vs. CR Scorecard
Property Conjunctive Reasoning (CR) Disjunctive Reasoning (DR)
Scalability Exponential Linear
Plasticity Rigid Plastic
Coupling High Low
Robustness Low High
Fault Tolerance
Low High
Cognitive Parallel
For low order systems, CR most closely parallels human cognitive inference..
For complex systems, DR most closely parallels human cognitive inference.
Parallel & Distributed Processing
Ability
Parallel and distributed processing increases the complexity of most properties.
DR is readily applied to distributed processing as each unit has a relationship with the consequent that is independent of the other units.
Bullies and Dweebs
Physics of Dweebs & Bullies
Fixed Playground
Momentum
Bounce off of walls
Maximum Speed
Bullies
Fixed Speed
Fixed twiddle
Follows closest dweeb
Bullies and Dweebs
Dweeb Variables
Avoid Walls
Avoid Bullies
Adjustable Twiddle
Avoid infected dweebs (?)
Other?
A Disjunctive Rule...
IF the Dweeb is VERY CLOSE to the right wall, THEN increase the speed to the left A LOT.
IF the Dweeb is CLOSE to the right wall, THEN increase the speed to the left SOME.
IF the Dweeb is NOT CLOSE to the right wall, THEN leave the speed AS IS.
A Disjunctive Rule...
0 L
Not Close Close Very Close
LL ML Z MR LR
- Delta Vx MAX 0 Delta Vx MAX
Distance to Right Wall
Aggregate at fuzzy level? Or after defuzzification?
A Disjunctive Rule...
0 L
Not Close Close Very Close
LL ML Z MR LR
- Delta Vx MAX 0 Delta Vx MAX
Distance to Right Wall
After defuzzification
A Disjunctive Rule...
0 L
Not Close Close Very Close
LL ML Z MR LR
- Delta Vx MAX 0 Delta Vx MAX
Distance to Right Wall
A Disjunctive Rule...Same As
L
-Delta Vx MAX
-Delta Vx
Distance to the Right
Wall
Another Disjunctive Rule...
x Distance to closest Bully
LL ML Z MR LR
- Delta Vx MAX 0 Delta Vx MAX
NL NM Z PM P L
SAME CONSEQUENT!
A Disjunctive Rule...Same As
0
-Delta Vx MAX
-Delta Vx
Distance to Nearest
Bully
Disjunctively Combine
0
How do aggregate these two consequents?
• Weighted Average?
• Most urgent?
A Disjunctive Rule...
- Delta Vx MAX 0 Delta Vx MAX
Before defuzzificationBefore defuzzification
Distance to Right Wall
LL ML Z MR LR
LL ML Z MR LR
Dweeb Distance
Disjunctive Aggregatation Followed by
Defuzzification
Bullies and Dweebs
Dweeb Variables
Avoid Walls (Velocity x & y)
Avoid Bullies (Velocity x & y)
Avoid infected dweebs (Velocity x & y)
Avoid infected dweebs (?)
Other?
Assume...
The Dweebs will have sensors allowing them to detect:– The closest bully– The distance to all walls– The distance to all four corners– The closest infected Dweeb– Other??
Assignment
Write a Bullies & Dweeb simulation. The Bullies will have twiddle and maximum
speed. They pursue dweebs. They are fixed. Choose disjunctive mappings so that the
dweebs survive well. Sample software for similar simulation is at
NeoSwarm.com We will later evolve the swarm.