Hi guys can you check the given problem below and provide me with a solution and also the steps showing how you arrive at the answers. Thank you. 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 is showing in the 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 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 3.4and whose ACT score is 32.

Hi guys can you check the given problem below and provide me with a solution and also the steps showing how you arrive at the answers. Thank you. 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 is showing in the 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 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 3.4and whose ACT score is 32.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Hi guys can you check the given problem below and provide me with a solution and also the steps showing how you arrive at the answers. Thank you.

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 is showing in the 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 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 3.4and whose ACT score is 32.

**Title: Understanding Fuzzy Sets for ACT Scores and College GPA**

In this educational explanation, we explore two diagrams representing fuzzy sets, which are used to describe ambiguity and uncertainty in data.

### Diagram Descriptions

#### Figure 1: Fuzzy Set for High School and College GPA
- The diagram depicts a triangular fuzzy set with dashed lines.
- The vertical axis has labels "1", "0.5", and "0".
- The structure indicates varying degrees of membership of GPA scores within the fuzzy set.

#### Figure 2: Fuzzy Set for ACT Scores
- The diagram shows a similar triangular structure with a solid line.
- Labels on the horizontal axis indicate scores "24" and "36".
- The fuzzy set represents the likelihood of different ACT scores fitting into the defined category (e.g., qualifying scores for college admission).

### Explanation of Fuzzy Sets

Fuzzy sets allow for a range of values to have degrees of membership, rather than strict inclusion or exclusion. In educational assessment, such as ACT scores or GPA, fuzzy sets help model real-world scenarios where boundaries are not distinct, providing a more nuanced understanding of student performance.

Understanding these diagrams aids educators and students in appreciating how scores and academic results can be analyzed beyond conventional crisp boundaries.

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