Find & Rank Your Best Property

When you rate your priorities on a scale of 1 to 10, a linear translation often dilutes extreme preferences. To solve this, PGNest applies a quadratic power-scaling function to the user-defined ratings:

By squaring the ratings before normalization, a critical requirement (10/10) gets 4 times the weight of a moderate requirement (5/10). This ensures dominant criteria mathematically drive the rankings, matching realistic student trade-offs.

Since criteria have different units (Rent in ₹, Distance in km, Safety in stars), they must be normalized to a dimensionless range [0, 1]:

This maps the worst-performing property to 0.0 and the best-performing property to 1.0 for each specific criterion.

The Weighted Sum Model is a linear, additive multi-objective aggregation method. The overall rating score for a PG accommodation i is calculated as:

It is highly intuitive and linear: a high score in one criterion can compensate for a low score in another.

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a non-linear geometric MCDA algorithm. It ranks accommodations based on their distance to the ideal positive and negative bounds:

1. Vector Normalization: Renders criteria scale-independent.
   v_ij = x_ij ⁄ √(∑_k=1..m x_kj²)
2. Weighted Normalized Matrix: Multiplying weights: y_ij = w_j × v_ij.
3. Identify Ideal Best (A^*) & Negative-Ideal Worst (A^-):
   Considers best and worst achievable values across the cohort.
4. Compute Euclidean Distances:
   S_i^* = √(∑ (y_ij - y_j^*)²)   ,   S_i^- = √(∑ (y_ij - y_j^-)²)
5. Compute Closeness Coefficient:
   C_i = S_i^- ⁄ (S_i^* + S_i^-)

TOPSIS favors accommodations that are balanced and penalizes those with extreme weaknesses.