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 : </li></ul>