Information integration theory was proposed by Norman H. Anderson to describe and model how a person integrates information from a number of sources in order to make an overall judgment. The theory proposes three functions.

The valuation function ${\displaystyle V(S)}$ is an empirically derived mapping of stimuli to an interval scale. It is unique up to an interval exchange transformation (${\displaystyle y=ax+b}$).

The integration function ${\displaystyle r=I\{s_{1},s_{2},..,s_{n}\}}$ is an algebraic function combining the subjective values of the information. "Cognitive algebra" refers to the class of functions that are used to model the integration process. They may be adding, averaging, weighted averaging, multiplying, etc.

The response production function ${\displaystyle R=M(r)}$ is the process by which the internal impression is translated into an overt response.

Information integration theory differs from other theories in that it is not erected on a consistency principle such as balance or congruity but rather relies on algebraic models. The theory is also referred to as functional measurement, because it can provide validated scale values of the stimuli. An elementary treatment of the theory, along with a Microsoft Windows program for carrying out functional measurement analysis, is provided in the textbook by David J. Weiss.