IDOCRIW - Integrated Determination of Objective CRIteria Weights

Overview

IDOCRIW combines two complementary objective weighting perspectives: ENTROPY captures inter-alternative variance (discrimination power) and CILOS captures inter-criterion conflict (loss when sacrificing one criterion for another). Their product amplifies criteria that score high on both dimensions.

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

   Compute Entropy weights w^E_j on the data.

   $$w_j^E=\text{Entropy}(X{)}_j$$

   Zavadskas-Podvezko 2016, p.10 Eq.(1)

2. 2

   Compute CILOS weights w^C_j on the data.

   $$w_j^C=\text{CILOS}(X{)}_j$$

   Zavadskas-Podvezko 2016, p.10 Eq.(2)

3. 3

   IDOCRIW weights w_j = (w^E_j · w^C_j) / Σ (w^E_k · w^C_k).

   $$w_j=\frac{w_j^E{w}_j^C}{{\sum }_{k=1}^n{w}_k^E{w}_k^C}$$

   Zavadskas-Podvezko 2016, p.10 Eq.(3)

Look elsewhere when

Assumptions to verify

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

Edge cases and pitfalls

• If any CILOS weight q^C_j = 0 (all losses for criterion j are zero), then w_j = 0 regardless of entropy - inspect the loss matrix for degenerate rows.

Works with

How to cite