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Fuzzy Disjunctive Inference from the Perspective of a Dweeb

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:.

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Fuzzy Disjunctive Inference from the Perspective of a Dweeb

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

  2. CONJUNCTIVE Approach Do this1andthis2andthis3andthis4andthis5to getthat. Result: Highly complex and brittle design. Loose this4 and your system can fail. Conjunctive statement:

  3. DISJUNCTIVE Approach (Do this1to getthat ) or (Do this2to getthat ) or (Do this3to getthat ) or (Do this4to getthat ) Result: Highly robust and fault tolerant design. Loose this4 and you’re still in business. Disjunctive statement:

  4. Is… DISJUNCTIVE = CONJUNCTIVE? Is… (Do this1to getthat ) or (Do this2to getthat ) or (Do this3to getthat ) or (Do this4to getthat ) = (Do this1andthis2andthis3andthis4 ) to getthat. ??? In a Boolean sense,

  5. Disjunctive vs. Conjunctive • Disjunctive reasoning sometimes referred to as “The Combs Method”* • Examples of Complex Disjunctive Systems • Swarms: Insects & People • Your Body • Animal motor functions • Genomic symbiogenesis William E. Combs • 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). • * Earl Cox, The Fuzzy Systems Handbook, Academic Press/ Morgan Kaufman.

  6. DR vs. CR Scorecard

  7. Bullies and Dweebs • Physics of Dweebs & Bullies • Fixed Playground • Momentum • Bounce off of walls • Maximum Speed • Bullies • Fixed Speed • Fixed twiddle • Follows closest dweeb

  8. Bullies and Dweebs • Dweeb Variables • Avoid Walls • Avoid Bullies • Adjustable Twiddle • Avoid infected dweebs (?) • Other?

  9. 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.

  10. Not Close Close Very Close 0 L A Disjunctive Rule... Distance to Right Wall Aggregate at fuzzy level? Or after defuzzification? LL ML Z MR LR - Delta Vx MAX 0 Delta Vx MAX

  11. Not Close Close Very Close 0 L A Disjunctive Rule... Distance to Right Wall After defuzzification LL ML Z MR LR - Delta Vx MAX 0 Delta Vx MAX

  12. Not Close Close Very Close 0 L A Disjunctive Rule... Distance to Right Wall LL ML Z MR LR - Delta Vx MAX 0 Delta Vx MAX

  13. -Delta Vx L Distance to the Right Wall -Delta Vx MAX A Disjunctive Rule...Same As

  14. SAME CONSEQUENT! Another Disjunctive Rule... NL NM Z PM P L x Distance to closest Bully LL ML Z MR LR - Delta Vx MAX 0 Delta Vx MAX

  15. -Delta Vx 0 Distance to Nearest Bully -Delta Vx MAX A Disjunctive Rule...Same As

  16. 0 Disjunctively Combine • How do aggregate these two consequents? • Weighted Average? • Most urgent?

  17. Before defuzzification LL ML Z MR LR Before defuzzification A Disjunctive Rule... LL ML Z MR LR Distance to Right Wall Disjunctive Aggregatation Followed by Defuzzification Dweeb Distance - Delta Vx MAX 0 Delta Vx MAX

  18. 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?

  19. 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??

  20. 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.

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