# CS607 Artificial Intelligence Assignment 4 Solution Fall 2013

Assignment

This assignment is about Fuzzy Inference Systems (FIS. You have studied in this course that FIS maps input to output using fuzzy logic. When there are multiple antecedents in if-conditions then we need to combine their fuzzy values to get a single effective value. Let’s say our if-condition has two part connected via OR operator e.g. IF food is good OR service is excellent…

In above, first we need to calculate fuzzy value (fuzzification) for both food and service quality and then combine these two fuzzy values with an OR operator. Fuzzy OR returns simply max among the two, thus we get fuzzy value for antecedent.

Once we get resultant fuzzy value for antecedent then we need to apply implication to calculate the fuzzy value of consequent for the given input value using a particular function. Two functions are commonly used i.e. min and product. Then we aggregate consequent values of multiple rules and apply defuzzification at the end.

In this assignment, you have to explore and understand Mamdani’s Fuzzy Inference method which is nicely discussed on below link…in a very comprehensive manner.

http://www.dma.fi.upm.es/java/fuzzy/fuzzyinf/main_en.htm

Your job is to explore the four steps of Mamdani’s Method as explained on http://www.dma.fi.upm.es/java/fuzzy/fuzzyinf/main_en.htm

1: Evaluate antecedent
2: Obtain conclusion
3: Aggregate conclusions
4: Defuzzify

After exploration, you need to apply your understanding on Example 1: Traffic with the following parameter settings at different steps.

 Step 1: Evaluate antecedent Step 2: Obtain conclusion Step 3: Aggregate conclusions Step 4: Defuzzification Parameters Membership Function for Arrival Membership Function for Arrival OR Operator Implication Method Consequent Membership function As per previous steps setting As per previous steps setting Set as Triangular(0,4,8) Triangular(0,2,7) Max Min Triangular (5,10,15)

With above settings for given parameters at each step, you need to calculate the value of output variable TimeG for the following input values.

 S. No. Input value for Arrival Input value for Line Output value for TimeG i.e. seconds the green light will last 1 6 6 ? 2 2 4 ? 3 1 7 ? 4 5 2 ?

Solution:

 S. No. Input value for Arrival Input value for Line Membership Function for Arrival Membership Function for Arrival Output value for TimeG i.e. seconds the green light will last 1 6 6 0.5 0.2 2 2 4 0.5 0.6 3 1 7 0.25 0 4 5 2 0.75 1

just put these values and when u get the result remebr this skip 2 nd 3rd step go to step no 4 and put the result value which you get in the first step then click at draw graph is drwan automatically then click at show calcultation