MAUT - Multi-Attribute Utility Theory

Overview

U(A_i) ∈ [0,1] with linear utility functions. Higher U means greater overall utility. MAUT requires that criteria satisfy preferential independence (stronger: additive independence) for the additive form to be valid. In practice, this is often assumed without formal verification. Non-linear utility functions (exponential, etc.) can be specified per criterion if the decision-maker's risk attitude warrants it.

Output

utility, higher is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Alternative selection, Supplier evaluation

How it works

1. 1

   Elicit single-attribute utility functions u_j(x).

   $$u_j(x_{ij}):\mathbb{R}\to [0,1],u_j(x_j^{\min })=0,u_j(x_j^{\max })=1$$

   Keeney-Raiffa 1976, Ch.3 Eq.(3.1)

2. 2

   Evaluate utilities u_ij = u_j(x_ij) for each alternative.

   $$u_{ij}=u_j(x_{ij})$$

   Keeney-Raiffa 1976, Ch.3 Eq.(3.4)

3. 3

   Multi-attribute utility via additive form U_i = Σ w_j u_ij (assuming preferential independence).

   $$U_i=\sum _{j=1}^n{w}_j{u}_{ij}$$

   Keeney-Raiffa 1976, Ch.6 Eq.(6.1)

4. 4

   Descending ranking by U_i.

   $$\text{rank}(A_i)\propto -U_i$$

   Keeney-Raiffa 1976, Ch.6

Look elsewhere when

Assumptions to verify

• Criteria preferences are independent (no synergistic interactions)
• Compensation is acceptable: high score on one criterion can offset low on another
• Decision matrix is complete (no missing values)

Edge cases and pitfalls

• •ties u_ij = u_j(x_ij) for each alternative.

• Additive independence assumption: if criteria are correlated in preferences (e.g. cost and quality are not independent), the additive form is invalid - use multiplicative or multilinear form instead.

Works with

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