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1. Fuzzy Inference System
Written by:
Hisham Jamal Ali Faraj Saleh Al-deafi

2. Introduction
●AFuzzyInferenceSystem(FIS)isawayofmapping
aninputspacetoanoutputspaceusingfuzzylogic
●FISusesacollectionoffuzzymembershipfunctions
andrules,insteadofBooleanlogic
●TherulesinFIS(sometimesmaybecalledasfuzzy
expertsystem)arefuzzyproductionrulesoftheform:
−ifpthenq,wherepandqarefuzzystatements.
●Forexample,inafuzzyrule
−ifxislowandyishighthenzismedium.

3. Cont…
●Thefunctionaloperationsinfuzzyexpertsystem
proceedinthefollowingsteps.
−Fuzzification
−FuzzyInferencing(applyimplicationmethod)
−Aggregationofalloutputs
−Defuzzification

4. Structure of a Fuzzy Expert System

5. Fuzzification
•Definition:Fuzzification is the process of converting crisp input
values into fuzzy sets.
•Purpose:Allows handling of imprecise or vague inputs in fuzzy
logic systems.
•Example:For temperature = 25°C, determine membership in
fuzzy sets like "Cold," "Cool," "Warm," and "Hot."

6. Fuzzy Inferencing
•Definition:Fuzzy inferencing is a method used in fuzzy logic
systems to derive decisions or actions based on fuzzy logic rules and
fuzzy input data.
•Objective:It aims to process imprecise or vague inputs to produce
meaningful and actionable outputs.
•Components:Fuzzy inferencing typically involves fuzzification, rule
evaluation, aggregation of rules, and defuzzification.

7. Aggregation of all outputs
•Definition:Combines the outputs of individual rules to
generate a comprehensive fuzzy inference.
•Methods:Includes methods like Maximum, Minimum, and
Average for combining fuzzy outputs.
•Purpose:Integrates multiple rules' outputs to derive a
coherent response or action.
•Example:Aggregates outputs from rules like "Increase air
conditioning" and "Reduce heating" to determine overall HVAC
control.

8. Generic Method
●Mainstepsare
−Evaluatetheantecedentforeachrule
−Obtaineachrule'sconclusion
−Aggregateconclusions
−Defuzzification
●Wewillexplainthesestepsusinganexampleof
TippingProblem
●Two inputs: Quality of food and Service at a restaurant
rated at scale from 0-10
●One output: Amount of tip to be given
●Tip should reflect the quality of the food and service.
●The tip might be in the range 5-15% of total bill paid.

9. Rules for Tipping
●Letusconsiderthefollowingthreerules
−Ifserviceispoororfoodisbad,thentipischeap
−Ifserviceisgood,thentipisaverage
−Ifserviceisexcellentorfoodisdelicious,thentipis
generous
●Inputvariables
−Service:representedbypoor,good,excellent
−Food:representedbybad,delicious
●OutputVariable:
−Tip:representedbycheap,average,generous

10. Antecedent for each rule

11. Rule's Conclusion

12. Aggregate Conclusions

13. All Steps Together looks like

14. MatLab
Fuzzy Toolkit

15. Introduction
●MATLAB fuzzy logic toolbox provides facility for the
development of fuzzy-logic systems using
−graphical user interface (GUI) tools
−command line functionality
●There are five primary GUI tools
−Fuzzy Inference System (FIS) Editor
−Membership Function Editor
−Rule Editor
−Rule Viewer
−Surface Viewer

16. GUI Tools

17. Fuzzy Inference System (FIS)
Editor

18. Membership Function Editor
Display & edit
values of current
variable
Select & edit
attributes of
membership
function
Name & edit
parameters of
membership
function

19. Rule Editor
Create and edit
rules
Rules –
automatically
updated

20. Rule Viewer
Shows how output
variable is used in
rules; shows
output of fuzzy
system
Shows how input
variable is used in
rules

21. Tsukamoto inference

22. Introduction

23. Comparison between inference Methods

24. Comparison between inference Methods

25. Comparison between inference Methods

26. Work mechanism

27. Work mechanism

28. Work mechanism

29. Example:

30. Con..

31. Con..

32. Final Solution

33. Advantages & Disadvantages

34. For
listening