Analytic Hierarchy Process (AHP) developed by Thomas L. Saaty and is one of the methods that can be used in decision-making by taking into account factors of perception, preference, experience and intuition. AHP combines assessments and personal values into a logical way.
Analytic Hierarchy Process (AHP) is used to simplify complex problems and unstructured, strategic, and dynamic into parts, as well as make the variables in a hierarchical level. Complex problem consists of more than one (multicriteria) problem, the structure of the problem is not yet clear, the uncertainty of the opinion of decision-makers, and the inaccuracy of available data.
This method is a framework for making decisions effectively to the problem by simplifying and speeding up the decision process by solving the problem into parts, arranging parts or variables in a hierarchical arrangement, giving a numerical value to the subjective judgment of the importance of each variable and synthesize These considerations to specify which variable has the highest priority and act to affect the outcome of the situation. This method also incorporates the strength of feeling and logic on various issues, and synthesize diverse considerations into the match result we estimate intuitively as presented on the consideration that has been made.
Axiomatic grounding AHP
Analytic Hierarchy Process (AHP) has the axiomatic foundation consisting of:
1. Comparison Resiprocal, which implies that the pairwise comparison matrix is formed should be the opposite. For example, if A is f times more important than B then B is 1 / f times more important than A.
2. Homogenity, which implies similarity in doing comparisons. For example, it is not possible to compare oranges with tennis ball in terms of taste, but more relevant to compare in terms of weight.
3. Dependence, which means that each level has a link (complete hierarchy) although possible relationship imperfect (incomplete hierarchy).
4. Expectation, which means menonjolkon assessments are expectations and preferences of decision-making clan. Assessment can be quantitative data and qualitative.

Stages of Decision Making
Stages of decision-making in the AHP method is basically as follows:
1. Defining the problem and determine the desired solution.
2. Creating a hierarchical structure that begins with a general purpose, continued with criteria and alternaif-alternatives that wants are ranked.
3. Form a pairwise comparison matrix that describes the relative contribution or influence each element of each level objectives or criteria above. Comparisons were made based on the judgment of choice or decision-makers by assessing the level of the interest rate of an element compared to other elements.
4. Normalize the data is by dividing the value of each element in the matrix is ​​paired with a total value of each column.
5. Calculating the eigenvalues ​​vector and tested for consistency, if not consistent then the data retrieval (preference) should be repeated. Eigenvalues ​​vector in question is the maximum eigenvalue vector obtained by using matlab or with the manual.
6. Repeat steps 3, 4, and 5 for all levels of hierarchy.
7. Calculating eigen vector of each pairwise comparison matrix. Eigenvalues ​​vector is the weight of each element. This step is to synthesize option in the prioritization of the elements on the lowest hierarchy level to the achievement of objectives.
8. Test the consistency of the hierarchy. If it does not comply with CR < 0, 100, the assessment must be repeated.

Source : http://informatika.web.id/analytical-hierarchi-process-ahp.htm