MPSI - Modified PSI method for objective weighting (Modified Preference Selection Index weighting)

Overview

MPSI extracts criterion weights from PSI's Preference Variation Values. Criteria with LOWER Φ_j (less variance, more consistent discrimination) get HIGHER weight. This is counterintuitive - it differs from ENTROPY and CRITIC which give higher weight to higher-variance criteria.

Output

Weight, higher is better

Data

Crisp, complete numeric matrix

Weights

Derived internally, no weight source needed

Size

2+ alternatives, 3-12 criteria works best

Used for

Any (objective weighting)

How it works

1. 1

   Linear-max normalisation: for benefit x_ij / max_k(x_kj); for cost min_k(x_kj) / x_ij.

   $${\bar{x}}_{ij}=\frac{x_{ij}}{{\max }_k{x}_{kj}}\text{ (benefit)};{\bar{x}}_{ij}=\frac{{\min }_k{x}_{kj}}{x_{ij}}\text{ (cost)}$$

   Maniya & Bhatt 2010, p.1786 Eqs.(1)-(2)

2. 2

   Compute mean x̄_j and Preference Variation Value Φ_j = Σ_i (x̄_ij − x̄_j)² for each criterion.

   $${\bar{x}}_j=\frac{1}{m}\sum _i{\bar{x}}_{ij};{\Phi }_j=\sum _i({\bar{x}}_{ij}-{\bar{x}}_j{)}^2$$

   Maniya & Bhatt 2010, p.1786 Eqs.(3)-(4)

3. 3

   Compute weights from deviation from maximum variance: Ω_j = (1 − Φ_j) / Σ_k (1 − Φ_k). This is the MPSI weight extraction (distinct from PSI's I_i which ranks alternatives).

   $${\Omega }_j=\frac{1-{\Phi }_j}{{\sum }_k(1-{\Phi }_k)}$$

   Maniya & Bhatt 2010, p.1786 Eq.(5)

Look elsewhere when

Assumptions to verify

• Decision matrix exists with measurable criteria
• Sufficient inter-alternative variation per criterion

Edge cases and pitfalls

• Constant criterion column: Φ_j = 0, so (1 − Φ_j) = 1 - the criterion receives the average weight, not zero.

Works with

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