Good evening. Can you check the problem below and provide me with a solution and steps and formula on how you arrived at the answers. Using fuzzy logic to predict college GPA A college admissions director wants to use High School GPA and ACT score to predict the final GPA when a student graduates from her institution. She divides GPAs into 5 fuzzy sets: Poor – student is at risk for being admitted because of risky HS GPA Marginal – student is marginally qualified due to his HS GPA Average – student has average HS GPA Good – student has a good HS GPA Very Good – student has a very good HS GPA She will use the same fuzzy sets for College GPAs and HS GPAs shown below. Fuzzy Sets for HS and College GPA Diagram here showing in the fig 1 image below From left, the fuzzy sets are: Poor. Poor intersects x axis when x = 1, and x=2. The apex is at (1.5,1) Marginal: Marginal intersects the x axis at x = 1.5 and x = 2.5. The apex is at (2,1.0) Fair: Fair intersects the x axis at 2, and 3.. The apex is at (2.5,1) Good: Good intersects the x axis at 2.5 and 3.5. The apex is at (3,1) Very Good: Very good intersects the x axis at 3 and 4. The apex is at (3.5,1) Fuzzy Sets for ACT Scores Diagram here showing in the fig 2 image below The admissions director divides ACT scores into 3 groups: Marginal – marginal intersects the x (ACT) axis at 0 and 24 Average – average intersects the x axis at 12 and 36 High – high intersects the x axis at 24 and 48. Note that ACT scores range from 0-36. Individual scores are determined each year. Admissions director predicts college GPAs The admissions director’s calculus is a bit rusty, so she decides to use 4 techniques for each student: a) Weighted average – for this method, she determines that the representative members in each of the GPA fuzzy sets will be the one with maximum membership. for poor, the max is 1.5; for marginal the max is 2;, for fair, the max is 2.5; for good, the max is 3; and for very good the max is 3.5 b)First of maximum c)Middle of maximum d)Largest of maximum Developing the Fuzzy Rules and Working Problems 1) Fuzzy rules set 1 and Problem 1 If HS GPA is marginal and ACT is average, then college GPA is average. If HS GPA is fair and ACT is High then college GPA is High Use the method of weighted averages and determine the college GPA for a student with HS GPA = 2.1 and ACT = 26. 2) Fuzzy Rules Set 2 Problem 2 If HS GPA is good and ACT is Average, then College GPA is Good If HS GPA is very good and ACT is High, then College GPA Use the methods of First of Max, Middle of Max, and Largest of Max to find the college GPA for a student whose HS GPA is 3.4 and whose ACT score is 32
Good evening. Can you check the problem below and provide me with a solution and steps and formula on how you arrived at the answers.
Using fuzzy logic to predict college GPA
A college admissions director wants to use High School GPA and ACT score to predict the final GPA when a student graduates from her institution. She divides GPAs into 5 fuzzy sets:
- Poor – student is at risk for being admitted because of risky HS GPA
- Marginal – student is marginally qualified due to his HS GPA
- Average – student has average HS GPA
- Good – student has a good HS GPA
- Very Good – student has a very good HS GPA
She will use the same fuzzy sets for College GPAs and HS GPAs shown below.
Fuzzy Sets for HS and College GPA Diagram here showing in the fig 1 image below
From left, the fuzzy sets are:
Poor. Poor intersects x axis when x = 1, and x=2. The apex is at (1.5,1)
Marginal: Marginal intersects the x axis at x = 1.5 and x = 2.5. The apex is at (2,1.0)
Fair: Fair intersects the x axis at 2, and 3.. The apex is at (2.5,1)
Good: Good intersects the x axis at 2.5 and 3.5. The apex is at (3,1)
Very Good: Very good intersects the x axis at 3 and 4. The apex is at (3.5,1)
Fuzzy Sets for ACT Scores Diagram here showing in the fig 2 image below
The admissions director divides ACT scores into 3 groups:
Marginal – marginal intersects the x (ACT) axis at 0 and 24
Average – average intersects the x axis at 12 and 36
High – high intersects the x axis at 24 and 48.
Note that ACT scores range from 0-36. Individual scores are determined each year.
Admissions director predicts college GPAs
The admissions director’s calculus is a bit rusty, so she decides to use 4 techniques for each student:
- a) Weighted average – for this method, she determines that the representative members in each of the GPA fuzzy sets will be the one with maximum membership.
- for poor, the max is 1.5; for marginal the max is 2;, for fair, the max is 2.5; for good, the max is 3; and for very good the max is 3.5
b)First of maximum
c)Middle of maximum
d)Largest of maximum
Developing the Fuzzy Rules and Working Problems
1) Fuzzy rules set 1 and Problem 1
- If HS GPA is marginal and ACT is average, then college GPA is average.
- If HS GPA is fair and ACT is High then college GPA is High
Use the method of weighted averages and determine the college GPA for a student with HS GPA = 2.1 and ACT = 26.
2) Fuzzy Rules Set 2 Problem 2
- If HS GPA is good and ACT is Average, then College GPA is Good
- If HS GPA is very good and ACT is High, then College GPA
Use the methods of First of Max, Middle of Max, and Largest of Max to find the college GPA for a student whose HS GPA is 3.4 and whose ACT score is 32.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 2 images
