m Polar Fuzzy Set
What is an m polar Fuzzy Set (m-PFS)?
An m polar Fuzzy Set is a powerful extension of the Bipolar Fuzzy Set. While a bipolar set only considers two poles (positive and negative), an m polar set allows us to monitor m-different properties or criteria simultaneously for a single object.
Here, each pi(x) is a value between 0 and 1, representing the “i-th” polar characteristic of the element.
Example: Evaluating a Candidate (m=3)
Imagine a company hiring a manager based on three poles: Technical Skill, Leadership, and Communication. Here, m = 3.
| Candidate | Technical (p1) | Leadership (p2) | Communication (p3) |
|---|---|---|---|
| John | 0.9 | 0.4 | 0.6 |
| Sarah | 0.7 | 0.8 | 0.9 |
In this case, Sarah’s m polar membership is (0.7, 0.8, 0.9). This provides a multi-dimensional view that a standard fuzzy set (a single number) cannot capture.
Operations on m polar Fuzzy Sets
Operations are performed component-wise. This means we compare the same “pole” across different sets.
1. m polar Intersection (AND)
Takes the minimum value for each corresponding pole.
2. m polar Union (OR)
Takes the maximum value for each corresponding pole.
3. m polar Complement (NOT)
Subtracts each component value from 1.
Comparison: Why m polar?
Common Applications:
- Selection Processes: Hiring, choosing a vendor, or selecting a project.
- Medical Diagnosis: Assessing multiple symptoms simultaneously.
- Risk Assessment: Evaluating financial, operational, and reputational risks.
Designed by: Dr. M.U. Mirza
Mathematical Researcher & Educator