Fuzzy similarity measure

1. “fuzzy Similarity Measure
For Classification”

2. Introduction:
• Definition:
The fuzzy similarity measure (distance measure) is a measure that depicts the
closeness (difference) among fuzzy sets.
• Where are similarity measures used:
In data science, the similarity measure is a way of measuring how data
samples are related or closed to each other.

3. Similarity Measure Formula:
𝑆𝐴𝐵 = 1 −
1
𝑛
𝑖=1
𝑛
| 𝐴(𝑥) 𝑖 − 𝐵 𝑥 𝑖 |
Where,
𝑆𝐴𝐵 = Normalized Hamming Similarity Measure
𝐴(𝑥) 𝑖 = Value of Expert Fuzzy Set
𝐵 𝑥 𝑖 = Value of Sample Fuzzy set

4. Example:
Expert Sets
Diagnosis
Temperature Headache Stomach Pain Cough Chest Pain
s1 s2 s3 s4 s5
D1 (Viral Fever) 0.4 0.3 0.1 0.4 0.1
D2 (Maleria) 0.7 0.2 0 0.7 0.1
D3 (Thyphoid) 0.3 0.6 0.2 0.2 0.1
D4 (Stomach Problem) 0.1 0.2 0.8 0.2 0.2
D5 (Chest Problem) 0.1 0 0.2 0.2 0.8
P (Patient) 0.8 0.6 0.2 0.6 0.1

5. Calculation by 𝑆𝐴𝐵 = 1 −
1
𝑛 𝑖=1
𝑛
| 𝐴(𝑥) 𝑖 − 𝐵 𝑥 𝑖 |
• 𝑆𝐷1,𝑝 = 1 − { 0.4 − (0.8) + 0.3 − (0.6)| + 0.1 − 0.2 + | 0.4 − 0.6 |+|(0.1) −(0.1)|}/5] = 0.2
• 𝑆𝐷2,𝑝 = 1−[{|(0.7)−(0.8)|+ |(0.2)−(0.6)|+|(0.0)−(0.2)|+|(0.7)−(0.6)|+|(0.1) −(0.1)|}/5] = 0.16
• 𝑆𝐷3,𝑝 = 1 − { 0.3 − 0.8 + 0.6 − (0.6)| + 0.2 − 0.2 + | 0.2 − 0.6 |+|(0.1 −(0.1)|}/5] = 0.18
• 𝑆𝐷4,𝑝 = 1 − { 0.1 − 0.8 + 0.2 − (0.6)| + 0.8 − 0.2 + | 0.2 − 0.6 |+|(0.2) −(0.1)|}/5]= 0.44
• 𝑆𝐷5,𝑝 = 1 − { 0.1 − 0.8 + 0.0 − (0.6)| + 0.2 − 0.2 + | 0.2 − 0.6 |+|(0.8) −(0.1)|}/5]= 0.48

6. Results:
Similarity Measures for medical Diagnosis
D1,P D2,P D3,P D4,P D5,P
0.2 0.16 0.18 0.44 0.48
• Hence, from the above table 1, It is clearly found that, the value of D5,P is
greater than the rest of the values so the patient is suffering from the D5 disease
which is Chest Problem
Table 1.