Contradiction Matrix (TRIZ)

Overview

TRIZ (Russian: ТРИЗ — "Theory of Inventive Problem Solving") is a systematic methodology for solving technical problems by identifying underlying contradictions and applying proven solution patterns. The contradiction matrix is its best-known tool.

Starting in 1946, Genrich Altschuller analysed tens of thousands of patents and found that most inventions follow one of 40 recurring "inventive principles". He arranged these principles in a 39×39 matrix indexed by 39 generic engineering parameters — one axis is the parameter you want to improve, the other is the parameter that consequently worsens.

Technical contradiction: Improving one parameter (e.g. higher strength) makes another worsen (e.g. higher weight). The matrix provides candidate solutions for exactly these contradictions.

Inventive principle: An abstract solution strategy validated by many patents — e.g. "Segmentation", "Preliminary action", "Dynamics". 40 principles total, numbered as in Altschuller's catalogue.

The matrix does not replace brainstorming — it provides concrete prompts when the solution space is unclear. The standard output is three to four principles per cell, which serve as starting points for concrete ideas.

Approach

• Frame the problem as a technical contradiction: "If I improve X, then Y gets worse."
• Map X to one of the 39 standard parameters (improving).
• Map Y to one of the 39 standard parameters (worsening).
• Pick both parameters in the module — the matrix returns 0–4 recommended principles.
• For each principle, develop at least one concrete idea applicable to your problem.
• Develop the most promising ideas further or combine with other TRIZ tools (e.g. Substance-Field analysis, ARIZ).

Mapping a concrete problem onto the abstract parameters is the hardest step. Helpful: read the parameter description shown by the module after a selection, and check whether your case fits.

Interpreting the result

The matrix rarely gives exactly one answer — it opens a corridor of possible solution strategies. The recommended principles are statistically the most frequent solution paths for that specific contradiction in Altschuller's patent analysis.

An empty cell does not mean "no solution exists" — only that Altschuller's patent corpus showed no strong clustering. Re-mapping the parameters or rephrasing the contradiction can help.

Important: the recommended principles are prompts, not recipes. Only the transfer to the concrete case creates a solution — that is where the creative work happens.

When the matrix recommends conflicting principles or the cell stays empty, the underlying problem is often a **physical contradiction** (the same parameter must take two opposite values). The "Physical Contradiction (TRIZ)" module addresses exactly that case via the four separation principles.

To widen the solution space further, formulate an **Ideal Final Result** (module "Ideal Final Result (TRIZ)") before running the matrix and inventory available resources via the **Resources Checklist**. Quite often the matrix becomes unnecessary — an existing resource performs the job directly.

References & further reading

• G. S. Altshuller: "Creativity as an Exact Science" (1984).
• D. Mann: "Hands-On Systematic Innovation" — modern reformulation of the matrix.
• oxfordcreativity.co.uk — open TRIZ resources.
• Note: matrix data in this module is drawn from the standard literature. For critical applications, individual cells should be cross-checked against an authoritative source.

Examples

This module ships with the following example datasets — load any of them in the app with a single click.

Available in the following cycles

• No fixed phase in cycle DMAIC (lives in the "More" tile).
• No fixed phase in cycle DMADV (lives in the "More" tile).
• 8D: D5 — Corrective Actions