What is the ISM method?

People constantly make judgments such as “good vs. bad” or “like vs. dislike” in daily life. Explaining the criteria behind those judgments, however, is often difficult. Real-world problems rarely hinge on a single factor—multiple elements interact inside a structure.

ISM (Interpretive Structural Modeling) is a methodology for organizing such complex interdependencies as a layered directed graph. It treats a system as “a set of elements and a relation defined over them” and models the structure in an interpretive manner.

Representative structural modeling (SM) approaches include:

• ISM (Interpretive Structural Modeling)
• DEMATEL (Decision Making Trial and Evaluation Laboratory)

This article focuses on ISM and walks through the procedure using the public web tool /tools/ism/.

Preconditions for ISM

To apply ISM, assume the following:

• The system consists of ( n ) elements [ S = { s_1, s_2, \dots, s_n } ]

• A binary relation ( R ) is defined over the elements. If “( s_i ) influences ( s_j )”, represent it as [ s_i R s_j ] which corresponds to an arrow ( s_i \to s_j ) in a directed graph.

• The relation is transitive. [ (s_i R s_j) \land (s_j R s_k) \implies (s_i R s_k) ]

Steps of the ISM method

The ISM workflow has four stages, which map to Step 1–Step 4 in the public tool.

1. Extract elements (Step 1)
2. Input relationships / build the SSIM (Step 2)
3. Compute reachability matrices and perform level decomposition (Step 3)
4. Draw the final directed graph (Step 4)

The sections below explain each stage.

Step 1. Extract elements

List the elements you want to analyze. The tool automatically assigns IDs (1..n) when you “enter one element per line”.

Example:

Clear goals
Executive sponsorship
Experienced team
Appropriate tools
Process standardization
Secured resources
Co-creation with customers

Step 2. Build the SSIM (Structural Self-Interaction Matrix)

Next, capture how the elements influence each other in the SSIM (Structural Self-Interaction Matrix).

Meaning of each symbol:

The tool provides pairwise selectors and an editor for the upper-triangular matrix.

Step 3. Matrix conversion and transitive closure

(1) Initial reachability matrix (IRM)

Convert the SSIM into numbers to obtain the initial reachability matrix (IRM).

• Diagonal elements: always 1 (reflexive law)
• If the SSIM entry is V, set (M_{ij} = 1)
• If the entry is A, set (M_{ji} = 1)
• If the entry is X, set both (M_{ij} = M_{ji} = 1)
• If the entry is O, set 0

(2) Boolean algebra operations

ISM uses Boolean algebra instead of ordinary arithmetic.

(3) Calculate the transitive closure

Starting from the IRM, iteratively compute powers to obtain the transitive closure matrix T.

[ T = (IRM)^* = I \lor IRM \lor IRM^2 \lor IRM^3 \dots ]

Because the element set is finite, the sequence stabilizes at some ( r ). Beyond that point, further powers do not change the matrix. This stable matrix is the final reachability matrix (transitive closure).

The tool can export the closure as JSON or CSV.

Step 3’. Level decomposition via reachability and antecedent sets

From the reachability matrix, define the following for each element:

• Reachability set R(i): elements reachable from i
• Antecedent set A(i): elements that can reach i

Compare them and find elements that satisfy [ R(i) \cap A(i) = R(i) ] These elements form the highest level.

Remove those elements from the sets and repeat the evaluation for the remaining elements. This yields the hierarchical structure. The tool presents the result as a “Level decomposition” list.

Step 4. Draw the final directed graph

Finally, render the Interpretive Structural Model (ISM hierarchical graph) based on the level decomposition.

• Each element appears as a rectangular node.
• Enabling transitive reduction removes redundant arrows that can be inferred via intermediate elements, improving readability.
• You can export the graph as SVG.

Summary

ISM is a powerful way to organize complex systems based on relationships between elements. Manual work or spreadsheets quickly become unwieldy, but the public tool /tools/ism/ lets you perform the entire flow—from input through computation to graph drawing—in the browser.

References

• Yoshikazu Sawaragi and Hitoshi Kawamura (eds.), Sankagata Systems Approach (Participatory Systems Approach), Nikkan Kogyo Shimbun, 1981. (Japanese-language reference)