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FUZZY LOGIC CONNECTIVES  IN ABDUCTIVE INFERENCE AND CLUSTERING.

FUZZY LOGIC CONNECTIVES  IN ABDUCTIVE INFERENCE AND CLUSTERING. Joseph AGUILAR-MARTIN, University of TOULOUSE (France). agenda. What we want to achieve : (Biological process example) Logic  probability  fuzzy membership Aggregation  adequacy

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FUZZY LOGIC CONNECTIVES  IN ABDUCTIVE INFERENCE AND CLUSTERING.

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  1. FUZZY LOGIC CONNECTIVES  IN ABDUCTIVE INFERENCE AND CLUSTERING. Joseph AGUILAR-MARTIN, University of TOULOUSE (France)

  2. agenda • What we want to achieve : (Biological process example) • Logic  probability  fuzzy membership • Aggregation  adequacy • Abductive learning  algorithm (LAMDA) • Industrial supervision tool

  3. 1 • What we want to achieve : (Biological process example)

  4. fermentationprocess supervision Yeast Production (LBB Touluse) Deduce el physiologicalstate from: DOT : oxygen partial pressure O2 : oxygen % in output CO2 : carbon dióxyde % in output pH. OH- ion (consumed) : pH regulator

  5. fermentationprocess supervision data physiological states

  6. fermentationprocess supervision Building Supervision automata

  7. fermentationprocess supervision Using Supervision automaton

  8. 2 Logic  probability  fuzzy membership

  9. LOGIC basic reasoning mechanisms on time Parmenides, Zeno Leibniz Aquinas Lullius Aristoteles 1200 1300 1600 -400 -500

  10. geometry

  11. Probabilistic aspects in deduction

  12. Probabilistic aspects in abduction

  13. Probabilistic aspects in abductionspecial situations

  14. Propositional Logic

  15. Explanatory implication

  16. Explanatory abduction

  17. Likelihood algorithm

  18. 3 Aggregation  adequacy

  19. Adequacies Concept in an universe Adequacy of z to C Adequacy of z with respect to each di

  20. Aggregation functions(junctors)

  21. adequacies & junctors

  22. Compensated adequacies

  23. Copulæ

  24. Frank’s t-norms

  25. partitions

  26. Fuzzy partitions

  27. 4 Abductive learning  algorithm (LAMDA

  28. Knowing and recognizing

  29. abductive learning

  30. x1 Arithmétique (somme pondérée) x2 S/w xi f y xn-1 y = f ( Swi.xi ) xn Fonction « axone » (logistique..) Fonction « synapse » (présence..) Logique (conjonction) m1 x1 m2 x2 & mi xi y mn-1 xn-1 y = (m1 & m2 … & mi …& mn-1 & mn ) mn xn connexionism

  31. class assignment

  32. criterion of quality

  33. Abductive learning algorithm

  34. illustrative exampleinput-output data

  35. training data validation data application illustrative example

  36. 5 Industrial supervision tool

  37. Gazifier supervision

  38. industrial example LAMDA 3. Prétraitement de Données. 1. Lissage 7 Individus Class de Transition Gauss1 Min MAx 0.8 App Supervisée Gauss1 Min Max 1 App Non Supervisée ** Variables:Capteur du signal du commande PI,Capteur Niveau T1(my1),Capteur Niveau T2 (my2),Fluxe de sortie valve P1 (mQp).

  39. SALSA training

  40. SALSA supervisor current data operation information finite state machine built by abductive learning

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