Fuzzy Logic and Adaptive Sampling Edwin Hernandez HCS - Lab
INTRODUCTION <ul><li>In real life terms like (empty, full) are used to describe queues. Other terms could be (high congest...
Membership functions Triangular T()  and trapezoidal Trap() All parameters are represented as  T(), Trap() or Impulse()
FLC membership functions  deltaV (NC)=T(NC:0, D1, 0)  deltaV (CS)=T(CS:D1, D2,D3)  deltaV (CL)=T(CL:D2, D3, D4)  delta...
Membership functions  deltaT (Low)=Trap(Low:1, T1, T2)  deltaT (med-low)=T(med-low:T1, T2,T3)  deltaT (medium)=T(medium...
Membership Functions  output (DH)=Trap(Low:-O1, -O2, -O3)  output (DM)=T(DM:-O2, O3,0)  output (NC)=T(NC:-O3, 0, O4)  ...
RULES <ul><li>RULES are simple IF X AND Y THEN Z statements. </li></ul><ul><li>There are some techniques to process the ru...
Adaptive Sampling RULES <ul><li>There are 25 rules to be applied and used </li></ul><ul><li>Among them: </li></ul><ul><ul>...
INFERENCING <ul><li>MAX-MIN: this method tests the magnitudes of each rule and selects the highest one. This method does n...
INFERENCING <ul><li>AVERAGING: works but fails with contradictory rules, because it might average zero. </li></ul><ul><li>...
MAX-MIN method
MAX-DOT Pseudo-code float Output[]; Value[] = GetMembership(inputV, DeltaV[]); // returns a value for Value_chLow, Value_n...
Other Applications ATM Admission control and congestion control
FLC:ATM Switcher [1]
FLC : Rules and Membership functions
FLC: Rules for the Fuzzy Congestion Controller
FLC: Defuzzification Rules 1, 2, 4,5,6 apply for IM Tsukamoto’s defuzzification method
References/Related Work <ul><li>[1]  R. Cheng, C. Chuang. &quot;Design of a Fuzzy Traffic Controller for ATM Networks&quot...
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Introduction to Fuzzy Logic in Networks

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Fuzzy logic examples in network applications.

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Introduction to Fuzzy Logic in Networks

  1. 1. Fuzzy Logic and Adaptive Sampling Edwin Hernandez HCS - Lab
  2. 2. INTRODUCTION <ul><li>In real life terms like (empty, full) are used to describe queues. Other terms could be (high congestion, average congestion, congestion, low congestion) </li></ul><ul><li>This can be represented as : T(q) = {Empty(E), Full(F)} </li></ul><ul><li>In fuzzy logic those variables can be represented in what it called: MEMBERSHIP FUNCTIONS </li></ul>
  3. 3. Membership functions Triangular T() and trapezoidal Trap() All parameters are represented as T(), Trap() or Impulse()
  4. 4. FLC membership functions  deltaV (NC)=T(NC:0, D1, 0)  deltaV (CS)=T(CS:D1, D2,D3)  deltaV (CL)=T(CL:D2, D3, D4)  deltaV (CM)=T(CM:D3, D4, D5)  deltaV (CH)=T(CH:D4, D5, D6) NC: No change CS: Change-Slightly CL: Change-Low CM: Change-Medium CH: Change-High DeltaV (Change of Value)
  5. 5. Membership functions  deltaT (Low)=Trap(Low:1, T1, T2)  deltaT (med-low)=T(med-low:T1, T2,T3)  deltaT (medium)=T(medium:T2, T3, T4)  deltaT (med-high)=T(med-high:T3, T4, T5)  deltaT (high)=Trap(high:T4, T5, Tmax) deltaT Timming
  6. 6. Membership Functions  output (DH)=Trap(Low:-O1, -O2, -O3)  output (DM)=T(DM:-O2, O3,0)  output (NC)=T(NC:-O3, 0, O4)  output (IM)=T(IM:0, O3, O4)  output (IH)=Trap(IH:O4, O5, O6) Output Inc/dec timmers DH: decrease high DM: decrease medium NC: No change IM: Increase more IH: Increase High
  7. 7. RULES <ul><li>RULES are simple IF X AND Y THEN Z statements. </li></ul><ul><li>There are some techniques to process the rules, this process is called INFERENCING </li></ul><ul><li>There are several INFERENCE methods: </li></ul><ul><ul><li>MAX-MIN. </li></ul></ul><ul><ul><li>MAX-DOT </li></ul></ul><ul><ul><li>AVERAGING </li></ul></ul><ul><ul><li>ROOT SQUARES </li></ul></ul>
  8. 8. Adaptive Sampling RULES <ul><li>There are 25 rules to be applied and used </li></ul><ul><li>Among them: </li></ul><ul><ul><li>IF DeltaV=Nchange AND deltaT=Low THEN Output = IH </li></ul></ul><ul><ul><li>IF DeltaV=Nchange AND deltaT=Med-Low THEN Output = IH </li></ul></ul><ul><ul><li>IF DeltaV=Change-High AND DeltaT=High THEN Output = DH </li></ul></ul><ul><ul><li>IF DeltaV=Change-Med AND DeltaT=Low THEN Output = NC </li></ul></ul><ul><ul><li>IF DeltaV=Change-Slight AND DeltaT=High THEN OUTPUT=DM </li></ul></ul><ul><ul><li>IF DeltaV=Change-Low AND DeltaT=Med THEN Output = DM </li></ul></ul>
  9. 9. INFERENCING <ul><li>MAX-MIN: this method tests the magnitudes of each rule and selects the highest one. This method does not combine the effect of all applicable rules </li></ul><ul><li>MAX-DOT or MAX-PRODUCT. Method scales each member function to fit under its respective peak value and takes the horizontal coordinate of the fuzzy centroid as output </li></ul>
  10. 10. INFERENCING <ul><li>AVERAGING: works but fails with contradictory rules, because it might average zero. </li></ul><ul><li>Root Squares:it is very complicated mathematically. It combines all the applicable rules, scales the functions at their respective magnitudes and computes the fuzzy centroid of the composite area. </li></ul>
  11. 11. MAX-MIN method
  12. 12. MAX-DOT Pseudo-code float Output[]; Value[] = GetMembership(inputV, DeltaV[]); // returns a value for Value_chLow, Value_nochange, etc Timming[] = GetMembership(inputT, DeltaT[]); // returns a value for Timming_low, Timming_High, etc For each rule if rule[I] applies then // depending on the Rule Timming/Value applies // and are used in the array Output[] = MAX(Value[I]*Timming[I], Output[]); end; return Defuzzify(Output[])
  13. 13. Other Applications ATM Admission control and congestion control
  14. 14. FLC:ATM Switcher [1]
  15. 15. FLC : Rules and Membership functions
  16. 16. FLC: Rules for the Fuzzy Congestion Controller
  17. 17. FLC: Defuzzification Rules 1, 2, 4,5,6 apply for IM Tsukamoto’s defuzzification method
  18. 18. References/Related Work <ul><li>[1] R. Cheng, C. Chuang. &quot;Design of a Fuzzy Traffic Controller for ATM Networks&quot;, IEEE/ACM Transactions on Networking, vol 4, No3., pp 460-469, June 1996. </li></ul><ul><li>[2] V. Catania, G. Ficili, S. Palazzo, D. Panno. &quot;A Comparative Analysis of Fuzzy versus Conventional Policing Mechanisms for ATM networks&quot;, IEEE/ACM Transactions on Networking, vol. 4, No.3, June 1996. </li></ul><ul><li>[3] H. Li, V. Yen &quot;Fuzzy Sets and Fuzzy Decision Making&quot;, CRC-Press, 1995. </li></ul><ul><li>[4] A. Bonde and S. Ghosh. “A comparative Study of Fuzzy versus “fixed” thresholds for robust queue management in cell-switching networks”, IEEE/ACM Transactions on Networking Vol. 2, No. 4, August 1994, pp 337-344 </li></ul><ul><li>[5] R. Cheng, C. Chang, L. Ling. “A QoS Neural Fuzzy Connection Admission Controller for Multimedia High-Speed Networks”, IEEE/ACM Transactions on Networking”, Vo. 7, No. 1, February 1999. </li></ul><ul><li>[6] L. Maguire, B. Roche, T. McGinnity, et. Al. “Predicting a chaotic time series using a fuzzy neural network” Elsevier- Information Sciences, No. 112, January 1998, 125-136 </li></ul><ul><li>[7] WEB SITE : http://www.seattlerobotics.org/encoder/mar98/fuz/f1_part1.html </li></ul>
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