SPOTIS - Stable Preference Ordering Towards Ideal Solution

Overview

p_i ∈ [0,1]. Lower p means the alternative is closer to the ideal solution. SPOTIS is designed to be rank-reversal free: adding or removing alternatives does not change the relative ranking of existing alternatives, because the normalisation is based on fixed user-defined bounds, not on the alternatives themselves. Bounds [x_min_j, x_max_j] define the decision space and must be set by the decision-maker before evaluation.

Output

utility, lower 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

   Define bounds S_j^{min}, S_j^{max} per criterion (Stable Preference).

   $$S_j=[S_j^{\min },S_j^{\max }],S_j^{\ast }=S_j^{\max }(J^{+})\text{or}{S}_j^{\min }(J^{-})$$

   Dezert 2020, p.3 Eq.(1)

2. 2

   Normalised distance from ideal δ_ij = |x_ij − S_j*| / (S_j^max − S_j^min).

   $${\delta }_{ij}=\frac{|x_{ij}-S_j^{\ast }|}{S_j^{\max }-S_j^{\min }}$$

   Dezert 2020, p.3 Eq.(2)

3. 3

   Weighted aggregated distance D_i = Σ w_j δ_ij; ASCENDING ranking (smaller is better).

   $$D_i=\sum _{j=1}^n{w}_j{\delta }_{ij},\text{rank ascending}$$

   Dezert 2020, p.3 Eq.(3)

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

• Ill-defined bounds (x_max_j = x_min_j): division by zero in distance formula - check E-4.

• Bounds too narrow: alternatives outside bounds produce distances > 1 - bounds should encompass the full feasible range.

Works with

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