Fuzzy Disjunctive Inference from the Perspective of a Dweeb Robert J. Marks II

CONJUNCTIVE Approach Do this 1 and this 2 and this 3 and this 4 and this 5 to get that. Result: Highly complex and brittle design. Loose this 4 and your system can fail. Conjunctive statement:

DISJUNCTIVE Approach (Do this 1 to get that ) or (Do this 2 to get that ) or (Do this 3 to get that ) or (Do this 4 to get that ) Result: Highly robust and fault tolerant design. Loose this 4 and you’re still in business. Disjunctive statement:

Is… DISJUNCTIVE = CONJUNCTIVE? Is… (Do this 1 to get that ) or (Do this 2 to get that ) or (Do this 3 to get that ) or (Do this 4 to get that ) = (Do this 1 and this 2 and this 3 and this 4 ) to get that. ??? In a Boolean sense,

Disjunctive vs. Conjunctive Disjunctive reasoning sometimes referred to as “The Combs Method”* Examples of Complex Disjunctive Systems Examples of Complex Disjunctive Systems 1.Swarms: Insects & People 2.Your Body 3.Animal motor functions 4.Genomic 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 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 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 PropertyConjunctive Reasoning (CR)Disjunctive Reasoning (DR) ScalabilityExponentialLinear PlasticityRigidPlastic CouplingHighLow RobustnessLowHigh Fault Tolerance LowHigh 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 V x 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 V x 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 V x 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 V x 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 V x MAX 0 Delta Vx MAX Before defuzzification Distance to Right Wall 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.