Interpretive Structural Model (ISM)

Interpretative Structural Modeling (ISM) is a system engineering research method used to analyze system structure relationships. It is located in SPSSAU -> Comprehensive Evaluation -> ISM.

SPSSAU Operations

Paste (or edit) the matrix data, then click 'Start'. SPSSAU involves two key parameters: Adjacency Matrix and Hierarchical Decomposition.

Adjacency Matrix: The default input is 'Adjacency Matrix'. If the input data is a reachability matrix, select 'Reachability Matrix'

Hierarchical Decomposition: The default setting is 'Outcome Priority - UP Type', but it can be changed to 'Cause Optimization - DOWN Type'.

SPSSAU Data Format

To input data, paste it directly into the table (or edit within the table). The ISM data format is as follows: The first row contains titles. Data begins from the second row. The data must form a square matrix (i.e., the number of rows and columns must be equal, excluding the title row). The data should contain only 0 and 1, and the lower-right triangular data must be 0.

Algorithm

1.Prepare the adjacency matrix

Denoted as A, an adjacency matrix of size n × n is constructed for n elements:

$$A=\left(\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ a_{n1}& a_{n2}& \cdots & a_{nn}\end{array}\right)$$ a_ij = 1,Element i directly affects element j.
a_ij = 0,Element i does not affect element j.

2.Compute the reachability matrix (M)

M is computed as follows:

$$\mathit{(}\mathit{A}\mathit{+}\mathit{1}{\mathit{)}}^{\mathit{k}\mathit{-}\mathit{1}}\ne \mathit{(}\mathit{A}\mathit{+}\mathit{1}{\mathit{)}}^{\mathit{k}}=\mathit{(}\mathit{A}\mathit{+}\mathit{1}{\mathit{)}}^{\mathit{k}\mathit{+}\mathit{1}}=M$$

I is the identity matrix and k is the iteration count.

3.Determine the reachability set (R) and antecedent set (Q)

Compute R and Q as follows:

$$R_i=\{j\mid m_{ij}=1\}$$ $$Q_i=\{j\mid m_{ji}=1\}$$

The intersection of R and Q is S, calculated as follows:

$$S_i=C_i\cap P_i$$

4.Hierarchical Extraction

Two extraction methods are available: Outcome Priority and Cause Priority.

Outcome Priority: The condition is R = S.

Cause Priority: The condition is Q = S.