Ensemble Decision Support System
Our system uses an ensemble approach that combines the strengths of multiple multi-criteria decision-making algorithms to produce more accurate and reliable recommendations.
Why These Algorithms?
Problem Context
- Choosing a concentration involves many factors (interest, talent, career goals)
- Each factor has a different level of importance
- Answers are subjective and not always certain (fuzzy)
- The system must determine the best alternative among several options
Applied Solution
- AHP to weight criteria based on importance
- TOPSIS to rank alternatives by ideal distance
- Fuzzy Logic to handle uncertainty in responses
- Ensemble to combine all methods for optimal output
Analytic Hierarchy Process (AHP)
What is AHP?
AHP (Analytic Hierarchy Process) is a decision-making method developed by Thomas L. Saaty in the 1970s. It helps decision-making by breaking complex problems into a simpler hierarchy.
How It Works in Our System
- 1 Questions are grouped into 5 main criteria
- 2 Each criterion is assigned a weight based on its importance
- 3 Scores are calculated by multiplying answers by criterion weights
- 4 Consistency Ratio is calculated to validate the result
Criteria & Weights
AHP Formula
Consistency Index (CI):
CI = (λmax - n) / (n - 1)
Consistency Ratio (CR):
CR = CI / RI
Where: lmax = maximum eigenvalue, n = number of criteria, RI = Random Index
If CR < 0.1, the judgment is considered consistent.
TOPSIS
What is TOPSIS?
TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) is a multi-criteria decision-making method developed by Hwang and Yoon in 1981.
Core idea: the best alternative is the one closest to the positive ideal solution and farthest from the negative ideal solution.
TOPSIS Steps
- 1 Build a normalized decision matrix
- 2 Compute the weighted matrix
- 3 Determine positive ideal (A+) and negative ideal (A-) solutions
- 4 Compute each alternative distance to A+ and A-
- 5 Compute preference value (closeness coefficient)
Concept Visualization
Best alternative = closest to A+ and farthest from A-
TOPSIS Formula
Normalization:
rij = xij / √(Σxij²)
Closeness Coefficient:
Ci = Di- / (Di+ + Di-)
Fuzzy Logic
What is Fuzzy Logic?
Fuzzy Logic is a computational approach introduced by Lotfi Zadeh in 1965. Unlike Boolean logic that only knows true/false (0/1), fuzzy logic allows partial truth values between 0 and 1.
Why Use Fuzzy?
- Handles uncertainty in subjective responses
- Measures confidence level of recommendation results
- Provides more natural and human-like outcomes
Membership Function
Triangular membership function for confidence level
Ensemble Decision
Final score is computed by combining outputs from all three algorithms using predefined weights. This ensemble approach produces recommendations that are more robust and accurate.
Ensemble Formula
Final Score = (TOPSIS × 0.40) + (AHP × 0.30) + (Weighted Sum × 0.30)
TOPSIS
Highest weight because it considers ideal solution distance
AHP
Ensures criteria are weighted by importance
Weighted Sum
Direct score from answers as baseline
Scientific References
Saaty, T. L. (1980). The Analytic Hierarchy Process. McGraw-Hill, New York.
Hwang, C. L., & Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag, Berlin.
Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8(3), 338-353.