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## Analytic Hierarchy Process

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A technique for organizing and analyzing complex multi-objective decisions

Updated 21 Apr 2021

Analytic Hierarchy Process (AHP) is a simple technique, developed by Thomas L. Saaty in the 1970s, for organizing and analyzing complex multi-objective decisions. It combines both quantitative and qualitative analysis elements and it has particular application in group decision making. The philosophy of the technique is to decompose problem into a hierarchy of more easily understood sub-problems, each of which can be analyzed independently. Once the hierarchy is built, the decision makers systematically evaluate its various elements by comparing them to one another two at a time, with respect to their impact on an element above them in the hierarchy. The AHP converts these evaluations to numerical values that can be processed and compared over the entire range of the problem. A numerical weight is derived for each element of the hierarchy, allowing diverse and often incommensurable elements to be compared to one another in a rational and consistent way. In the final step of the process, numerical weights are calculated for each of the decision alternatives. These weights represent the alternatives' relative ability to achieve the goal.

The function facilitates the following:

• Simple AHP implementation

• Multiple decision makers option

• Simulation: An Monte-Carlo simulation-base extension of the Fuzzy AHP. The later is a special version of the simple AHP, which finds application in fuzzy environments, where the relative importance of the decision criteria and the alternatives is uncertain.

• Analytic Network Process: The generalization of the AHP, which incorporates dependences and feedbacks between decision criteria and options.

• Cost-Benefit analysis: The benefit (AHP weights) in relationship with the cost of the respective option.

• Optimization: In case of a resource allocation problem, the function estimates the optimal feasible combination of alternatives subject to the resources constraints.

• Prediction combination: In case this is a forecasting combination problem, the function generates a weighted averaged forecast, using the combination weights and the individual forecasts as inputs.

• Combination of all the above

### Cite As

Apostolos Panagiotopoulos (2021). Analytic Hierarchy Process (https://www.mathworks.com/matlabcentral/fileexchange/79643-analytic-hierarchy-process), MATLAB Central File Exchange. Retrieved .

Ashwin

Thank you

##### MATLAB Release Compatibility
Created with R2018b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux