The Analytical Hierarchy Process

                         

The Analytical Hierarchy Process

The Analytic Hierarchy process (AHP) is a structured technique for establish and analyzing complex decisions, based on mathematics and psychology. It was developed by Thomas L.Saaty (1970).It represents an accurate approach for quantifying the weights of decision criteria. Individual expert’s experiences are utilized to estimate the relative magnitudes of factors through pair-wise comparisons.

        It is a technique for organizing and analyzing complex decisions, using a pairwise comparison approach to allow a more accurate ordering of priorities for decision making.

  The Analytic Hierarchy Process (AHP) is a powerful and flexible decision making process which helps people to set priorities and make the best decision when both qualitative and quantitative aspects of decisions need to be considered. Tighes (2005) stated that the AHP is a decision making tool that incorporates both qualitative and quantitative factors. By reducing complex decisions to a series of one-on-one comparisons, then synthesizing the results, AHP not only helps decision makers to arrive at the best decision, but also provides a clear rationale that it is the best. The AHP technique allows the calculation and evaluation of relative weights (Duc, 2006). The main framework of AHP is a hierarchical model. It comprises goal, criteria, perhaps sub-criteria and alternatives to each problem or decision. Pair wise comparison matrix is most important procedure of AHP. The criterion pairwise comparison matrix takes the pair wise comparisons as an input and produces the relative weights as output and the AHP provides a mathematical method of translating this matrix into a vector of relative weights for the criteria (Malczewski, 1996).In addition, one of the most important benefits of using the AHP is that experts from different backgrounds can provide their opinions, thus helping to evaluate the diverse dimensions of the problem being considered. Based on the criterion weights derived from the pair-wise comparison matrix, scores for group attributes in the hierarchy are calculated as a weighted average of elements in the group.

 The most frequently raised problem in MCDM is how to establish weights for a set of activities according to importance. Location decisions such as the ranking of alternative communities are representative multi-criteria decisions that require prioritizing multiple criteria. The AHP method commonly used in multi-criteria decision making experiences was found to be a useful method to determine the weights, compared with other methods used for determining weights. When applying AHP, constraints are compared with each other to determine the relative importance of each variable in accomplishing the overall goal. The AHP allows decision-makers to model a complex problem in a hierarchical structure showing the relationship of the goal, objectives, sub-objectives, and alternatives.

            To make a decision in an organized way to generate priorities we need to make comparisons and need a scale of numbers that indicates how many times more important or dominant one element is over another element with respect to the criterion or property they are compare. Saaty (1977) suggested a scale for comparison consisting of value ranging from 1 to 9 which described the intensity.

Table 1: Nine-Point AHP Scale (1980)

Description  of Preference	Scale
Equal  importance	1
Equal to Moderate importance	2
Moderate importance	3
Moderate to Strong importance	4
Strong importance	5
Strong to Very strong importance	6
Very strong importance	7
Very to Extremely strong importance	8
Extremely importance	9

 

AHP is divided into three stages:-

                  I. Decomposition - Identify and structure the criteria.

                 II. Comparative Judgement-through pairwise comparison.

                III. Aggregating the priorities-calculate suitability index and produce suitable map.

The analyzed of land use, suitability zone based on multi-criteria decision making (MCDA) system using GIS technique. Fourteen parameters are utilized for land suitability zones in the study area (LSZ). Comprehensive literature review and asking local expert opinions is help for weights assigned to various parameters. Then, AHP used to calculate weights often feature maps for LSZ. Consistency Index and Consistency Ratio both are equally play the very important role in AHP.

In the AHP, the quotient of this difference divided by (n-1) is defined as the Consistency index (CI), which is the index of the consistency of judgements across all pairwise comparisons (Lootsma12, 1991).

A Consistence Ratio (CR) is calculated by dividing the consistency index for the set of judgements by the index for the corresponding random matrix. Saaty suggests that if that ratio exceeds 0.1 the set of judgements may be too inconsistent to be reliable.

Others Applications of AHP

AHP has particular application in group decision making and is used around the world in a wide variety of decision situations, in fields such as government, business, industry, healthcare, shipbuilding and education. The applications of AHP to complex decision situations have numbered in the thousands, and have produced extensive results in problems involving planning, resource allocation, priority setting, and selection among alternatives. Others areas have included forecasting, total quality management, business process reengineering, quality function deployment, and the balanced scorecard.

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