WISP - Weighted Ideal Solution Point

Overview

W_i ∈ [0,1]. Higher W means better. WISP combines four different aggregation paradigms (additive, benefit-multiplicative, cost-multiplicative, fully multiplicative) through a geometric mean, making it robust to any single aggregation failure. The best alternative always receives W_max ≈ 1.

Output

utility, higher is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Alternative selection, Supplier evaluation

How it works

1. 1

   Max-normalisation r_ij = x_ij / max_i x_ij (direction-aware).

   $$r_{ij}=\frac{x_{ij}}{{\max }_i{x}_{ij}}$$

   Stanujkic 2021, p.4 Eq.(1)

2. 2

   Weighted matrix v_ij = w_j r_ij.

   $$v_{ij}=w_j{r}_{ij}$$

   Stanujkic 2021, p.4 Eq.(2)

3. 3

   Four utility variants: u_sd, u_pd, u_sr, u_pr (sum/product, diff/ratio).

   $$u_{sd}=\sum _{J^{+}}v-\sum _{J^{-}}v;u_{pd}=\prod _{J^{+}}v-\prod _{J^{-}}v;u_{sr}=\sum _{J^{+}}v/\sum _{J^{-}}v;u_{pr}=\prod _{J^{+}}v/\prod _{J^{-}}v$$

   Stanujkic 2021, p.5 Eqs.(3)-(6)

4. 4

   Final WISP score U_i = mean of normalised u_{sd},u_{pd},u_{sr},u_{pr}.

   $$U_i=\frac{1}{4}\sum _{k\in \{sd,pd,sr,pr\}}{\bar{u}}_i^{(k)}$$

   Stanujkic 2021, p.5 Eq.(7)

Look elsewhere when

Assumptions to verify

• Criteria preferences are independent (no synergistic interactions)
• Compensation is acceptable: high score on one criterion can offset low on another
• Decision matrix is complete (no missing values)

Edge cases and pitfalls

• S2 or S3 = 0: if any normalised value is 0 for benefit (or 1 for cost after inversion), the product becomes 0 - handle degenerate case.

Works with

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