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.