1- I need the solution of each part of this lab and I need it in Word file,please.2- I need you to...

Question

1- I need the solution of each part of this lab and I need it in Word file,please.2- I need you to write for my in another file each steps in order to get the Matlab codes for this lab,please.Thanks, Best Wishes 
	
Document Preview: Lab: A Fuzzification Objective: Extend the Lab 1 exercise to return the membership in all fuzzy sets defined over a universe of discourse.Definitions: Fuzzy partition - Over the universe of discourse for input, the sum of the memberships of all fuzzy sets is exactly 1. Preparation: 1. For the triangular membership function, define the conditions for the center points and widths that create a fuzzy partition. How many fuzzy sets can have membership that is greater than zero? 2. Given the conditions in the previous step; mathematically prove that a fuzzy partition exists. 3. Given the requirements described in the lab, design an efficient algorithm for a fuzzification function that returns the memberships for the fuzzy sets over the input’s universe of discourse. 4. Design a test plan that exercises the fuzzification function. For example, calculate by hand membership values for specific input values and center points. Inputs for the extremes of the universe of discourse and center points are obvious test cases. Lab: 1. Write an m-file that implements a fuzzification scheme that assumes the input is crisp and the memberships are defined by triangular membership functions. The triangular membership functions form a fuzzy partition. The function returns the membership value in all the fuzzy sets in the vector form. The crisp value to be fuzzified and the centers of the membership functions are inputs. The function call should be in the form: [µ1, µ2, µ3,..., µn] = fuzzify (x, Centers) where µn is the membership value in the fuzzy set An. 2. Exercise the fuzzification function according the test plan designed in the preparation. Lab Report Include at a minimum: 1. Description of the assignment. 2. All work done for the preparation of the lab. This includes a description of your algorithm and how efficient it is. 3. Results of performing the tests described in your test plan. 4. Relevant observations and conclusions.

Robert · Accepted Answer

LAB REPORT
The assignment asks for developing a m-file program for a fuzzification function that returns the memberships for the fuzzy sets over the input’s universe of discourse. Triangular membership function being considered. The user would be required to define the number of different triangular membership functions which form the fuzzy partition, the centre of each of those MFs and the input variable x.
For simplicity, the width for each of the MFs is considered equal to 4 (can be changed through fuzzify.m) and spread evenly on both sides of each MF’s centre point (CP). The output of the function gives the membership value of the crisp input x for all the MFs defined by the user in vector form.
 For the MFs to cover the entire universe, the membership value for any input variable less than or greater than the two extreme centre points (CPs) is considered as 1. Figure below shows typical pictorial representation of the same.
For the triangular membership functions, if the center points and widths are such that a the family of fuzzy sets 
}
,.....,
{
1
n
A
A
 satisfies the conditions, 
U
A
A
n
i
i
i
¹
¹
=
"
,
,
,....,
1
f
 and 
å
=
=
Î
"
n
i
i
x
A
U
x
,...,
1
1
)
(
,
, it is a fuzzy partition with number of fuzzy sets that can have membership greater than zero as n.
PREPARATION
1. For the triangular membership function, define the conditions for the center points and widths that create a fuzzy partition. How many fuzzy sets can have membership that is greater than zero? 
With a triangular membership function conditions for the center points and widths that create a fuzzy partition are:
· The centre point of any membership function and the lower & upper boundary point of the membership functions on either side shall coincide. Typical figure is shown below. In other words, each membership function should overlaps only with the closest neighboring membership functions and not the next neighboring membership function. Also when a partition exists, for any possible input, its membership values in all relevant fuzzy sets should sum to 1.

1- I need the solution of each part of this lab and I need it in Word file,please. 2- I need you to write for my in another file each steps in order to get the Matlab codes for this lab,please....

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment