---
title: "Decision-making matrix model"
source: "https://systems-analysis.info/eng/Decision-making_matrix_model"
wiki: "systems-analysis.info/eng"
article: "Decision-making_matrix_model"
language: "en"
categories:
  - "Category:Decision theory"
  - "Category:Decision-making"
  - "Category:English"
  - "Category:Modeling"
  - "Category:Science"
revision_id: 112
wiki_created_at: 2026-09-06T22:17:33Z
wiki_modified_at: 2026-09-06T22:17:33Z
downloaded_at: 2026-09-07T22:21:06Z
---

# Decision-making matrix model

# Decision-making matrix model

**Decision-making matrix model** is a formalized representation of a choice problem in the form of a table (matrix) that reflects the relationships between possible alternatives and the external conditions that influence the outcome. This model is used for analyzing decisions under conditions of **uncertainty**, **risk**, and **multiple criteria**.

## Matrix Structure

The model is built upon the following components:

- **Alternatives (courses of action)** — A₁, A₂, ..., Aₘ — the rows of the matrix.
- **States of nature (scenarios)** — E₁, E₂, ..., E_d — the columns of the matrix.
- **Payoff** — Yᵢⱼ = fⱼ(Aᵢ), the outcome for the combination of Aᵢ and Eⱼ.

Such a table is called a **payoff matrix** and has dimensions m × d, where each cell contains an evaluation of the outcome for the corresponding "alternative–state" pair.

## Interpretation of Payoffs

The Yᵢⱼ values are interpreted as:

- income or profit,
- degree of goal achievement,
- utility or preferability of the outcome.

If the evaluations are of different natures, they can be normalized to a common scale, for example, from 0 to 1.

## Purpose and Advantages of the Model

The matrix model serves as a basis for:

- applying choice criteria (Wald, Savage, Laplace, Hurwicz, etc.),
- analyzing the behavior of the Decision Maker (DM) without knowledge of probabilities,
- justifying robust solutions,
- transitioning to the construction of decision trees and scenarios.

**Advantages:**

- clarity and structure;
- suitability for computer processing;
- versatility.

## Example of a Matrix Structure

| Alternative | State E₁ | State E₂ | ... | State E_d |
|-------------|----------|----------|-----|-----------|
| A₁          | Y₁₁      | Y₁₂      | ... | Y₁d       |
| A₂          | Y₂₁      | Y₂₂      | ... | Y₂d       |
| ...         | ...      | ...      | ... | ...       |
| Aₘ          | Yₘ₁      | Yₘ₂      | ... | Yₘd       |

## Application in Decision Making

The matrix model is applied:

- under uncertainty — with deterministic criteria;
- under risk — with given probabilities;
- in multi-criteria analysis — as a basis for aggregation;
- in decision support systems.

## External links

- <a href="https://en.wikipedia.org/wiki/Decision-matrix_method" class="external text" rel="nofollow">Decision-matrix method — Wikipedia</a>

## See also

- [Decision-making under uncertainty](https://systems-analysis.info/eng/Decision-making_under_uncertainty "Decision-making under uncertainty")
- [Multi-criteria decision analysis](https://systems-analysis.info/eng/Multi-criteria_decision_analysis "Multi-criteria decision analysis")
- [Decision tree](https://systems-analysis.info/eng/Decision_tree "Decision tree")