COCOSO - Combined Compromise Solution

Overview

k_i > 0. Higher k_i means better. COCOSO combines three appraisal strategies (k_ia: proportional total, k_ib: ratio to minimum, k_ic: weighted λ-compromise) into a geometric-arithmetic mean. The three strategies check robustness - if all three agree, the ranking is stable.

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

   Compromise normalisation per criterion type.

   $$r_{ij}=\{\begin{array}{ll}\frac{x_{ij}-\min x_{ij}}{\max x_{ij}-\min x_{ij}}& j\in J^{+}\\ \frac{\max x_{ij}-x_{ij}}{\max x_{ij}-\min x_{ij}}& j\in J^{-}\end{array}$$

   Yazdani 2019, p.2506 Eq.(1)

2. 2

   Weighted Sum component S_i = Σ w_j r_ij.

   $$S_i=\sum _{j=1}^n{w}_j{r}_{ij}$$

   Yazdani 2019, p.2506 Eq.(2)

3. 3

   Weighted Product component P_i.

   $$P_i=\sum _{j=1}^n(r_{ij}{)}^{w_j}$$

   Yazdani 2019, p.2506 Eq.(3)

4. 4

   Three appraisal scores k_a (additive), k_b (sum of ratios), k_c (balanced).

   $$k_{a,i}=\frac{P_i+S_i}{{\sum }_k(P_k+S_k)},k_{b,i}=\frac{S_i}{{\min }_k{S}_k}+\frac{P_i}{{\min }_k{P}_k},k_{c,i}=\frac{\lambda S_i+(1-\lambda )P_i}{\lambda {\max }_k{S}_k+(1-\lambda ){\max }_k{P}_k}$$

   Yazdani 2019, p.2506 Eqs.(4)-(6)

5. 5

   Final compromise k_i and descending ranking.

   $$k_i=(k_{a,i}{k}_{b,i}{k}_{c,i}{)}^{1/3}+\frac{1}{3}(k_{a,i}+k_{b,i}+k_{c,i})$$

   Yazdani 2019, p.2507 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

• Constant criterion column (max = min): min-max normalisation denominator is zero - check E-2.

Works with

How to cite