Cradis Method

Multi-criteria decision making (MCDM) methods assist decision-makers in selecting the most suitable option among multiple alternatives based on various criteria. Among these methods, the CRADIS (Compromise Ranking of Alternatives from Distance to Ideal Solution) method, recently developed, provides a compromise ranking of alternatives based on their distances from the ideal solution. In complex decision-making processes, evaluation based on a single criterion is often insufficient. Therefore, MCDM methods have been developed and are now widely used across various fields. As one of these methods, CRADIS offers a more balanced decision support by primarily evaluating the distances of alternatives from the ideal solution.

The CRADIS method ranks alternatives in the decision matrix according to their distances from the positive and negative ideal solutions. The fundamental assumption is that the best alternative is the one closest to the ideal solution and farthest from the negative ideal. The method is applied through the following steps:

Alternatives and criteria are defined as follows:

A = {A₁, A₂, …, A_m}: Set of alternatives

C = {C₁, C₂, …, C_n}: Set of criteria

x_ij: Performance value of the i-th alternative on the j-th criterion

$\left|\begin{array}{ccc}x11& x12& x1n\\ x21& x22& x2n\\ xm1& xm2& xmn\end{array}\right|$

All criteria are normalized to make them comparable. Linear min-max normalization is commonly used:

r_ij = $\frac{xij-min(xj)}{max(xj)-min(xj)}$

r_ij = $\frac{max(xj)-xij}{max(xj)-min(xj)}$

Result: Normalized matrix R = [r_ij]

Multiply by weights w_j to reflect the importance of criteria:

v_ij = w_j ⋅ r_ij

Result: Weighted decision matrix V = [v_ij]

Positive ideal solution:

v_j⁺ = max_i(v_ij)

Negative ideal solution:

v_j⁻ = min_i(v_ij)

The distance of each alternative from both the positive and negative ideal solutions is calculated:

Distance to positive ideal solution (D⁺):

D_i⁺ = $\sum _{j=1}^n$ [v_ij − v_j⁺]

Distance to negative ideal solution (D⁻):

D_i⁻ = $\sum _{j=1}^n$ [v_ij − v_j⁻]

The CRADIS method calculates the compromise score for each alternative as follows:

S_i = $\frac{D{i}^{-}}{D{i}^{+}+D{i}^{-}}$

This score S_i lies in the range [0,1]. A higher score indicates that the alternative is closer to the ideal solution and farther from the negative ideal.

Alternatives are ranked in descending order according to their S_i scores. The alternative with the highest score is the best choice.

These formulas constitute the core mathematical structure of the CRADIS method. In practice, these steps can be easily implemented using Excel, Python, MATLAB, or specialized decision support systems.