
## 3.1. Algorithm.

Name : FSP Input **: Set of cities and the factors deemed suitable for prediction.** Output **: Sorted list of cities with most probable location at the top.**
1. X ← {ψi
}
2. E ← {εi}
3. (Λ, Ξ) ←
nεi = Λ (εi) | Λ (εi) ∈ [0, 1]Xo∈ [^**X, E**]
4. FOR ψi
, ψj
∈ X2**calculate and store**
5. ρ ψi
, ψj
=
εi ∈ Ξ | Λ (ψi) ≥ Λ
ψj
	
6. χ ψi
, ψj
=
εi ∈ Ξ | Λ (ψi) ≤ Λ
ψj
	
7. **END FOR**
8. FOR ψi ∈ X **calculate and store**
9. ▽ (ψi) = X
ψj∈X
ρ ψi
, ψj 10. ∆ (ψi) = X

![0_image_0.png](0_image_0.png)

ψj∈X
χ ψi
, ψj 11. Ω (ψi) = X

![0_image_1.png](0_image_1.png)

.$ \big||\rho\left(\psi_i,\psi_j\right)\cap\chi\left(\psi_i,\psi_j\right)\big||_2$  . 

![0_image_2.png](0_image_2.png)

3.2. Explanation of FSP. FSP exploits comparison of a given city's total dominations vis-a-vis its subordinations and magnifying this quotient by the **number of equally** graded attributes. For given two cities, domination is an attribute and/or a decision factor in which one city has a higher grade of membership as compared to **the other one.**
Similarly, subjection is the factor where one city has a lesser membership grade than the other one. In FSP, ρ and χ **denote the dominations and subjections, respectively. A full** listing of ρ ψi
, ψj and χ ψi
, ψj
**looks like the discernibility matrix of Skowron [12, 10]**
in Rough Set Theory.