[SOLVED] math matlab CSCI3154 Assignment 4: Fuzzy Inference

CSCI3154 Assignment 4: Fuzzy Inference
Instructor: Malcolm Heywood Due date: November 21st in class
Consider the input membership functions defined over a domain of discourse 6.5 x 6.5: (small) = 1 1 (1)
1 + exp((x + 2.5))
(medium) = 1 (2)
1+(x)4 2
1 (3) 1 + exp(x + 2.5)
(large) =
The partnering consequent functions for the fuzzy inference model are defined as follows:
z=1 (4) 1 + exp(15 C1 + 2.5)
z=1 1 (5) 1+exp(25C2 +15)
z=1 (6) 1+exp(15C3 +10)
All three consequents are defined on the same consequent domain of discourse, z. Finally, let the rule base have the form:
IFx smallTHENz isC1
IFx mediumTHENz isC2 IFx largeTHENz isC3
1

Questions
Use of a spreadsheet package to assist with answers to the following questions is recom- mended, but not strictly necessary.1
1. Provide a plot describing how the input membership operators vary as a function of x.
2. Provide a plot describing how the consequent membership operators vary as a function
of Ci.
3. Provide a plot describing how consequent membership varies as a function of x.
4. Provide a plot describing how z (the defuzzified output) varies as a function of x.
5. Is the relation between input and output monotonic or non-monotonic?
6. Now consider an input that characterizes the current state of the environment defined as a fuzzy measurement:
xs =max[min((x+4),(2x)),0] (7) What is the corresponding defuzzified output from the system?
1Matlab, Mathmatica, Maple would also do the job. 2