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Analytic Hierarchy Process (AHP)

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The Analytic Hierarchy Process (AHP) is a structured technique used for organizing and analyzing complex decisions, based on mathematics and psychology. In the context of requirements prioritization, AHP helps decision-makers weigh the relative importance of different requirements by comparing them pairwise relative to their impact on the overall project goals. This method breaks down the decision-making process into a hierarchy, allowing for a more comprehensive evaluation of each requirement's contribution to the project's success. The AHP process begins by defining the problem and determining the goal of the project. The requirements are then structured into a hierarchical model, typically consisting of the goal at the top, followed by criteria and sub-criteria, and finally the list of requirements at the lowest level. Decision-makers perform pairwise comparisons of the requirements at each level of the hierarchy, using a scale of relative importance (e.g., from 1 to 9). These comparisons produce a set of matrices from which priority weights are derived through mathematical calculations, often involving eigenvectors and eigenvalues. One of the key advantages of AHP is its ability to handle both qualitative and quantitative data, enabling a comprehensive assessment of factors such as cost, benefit, risk, and stakeholder preferences. It also provides a consistency ratio that helps in checking the consistency of the judgments made during pairwise comparisons. If the consistency ratio is too high, it indicates that the judgments may be unreliable, prompting a review of the comparisons. However, AHP can be time-consuming and complex, especially when dealing with a large number of requirements, as the number of pairwise comparisons increases exponentially. It requires careful facilitation to ensure accurate and consistent inputs from stakeholders. Despite these challenges, AHP is a powerful tool for prioritizing requirements in a systematic, logical, and justifiable manner, supporting decision-makers in focusing on the most critical requirements that align with the project's strategic objectives.

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Question 1

In the Analytic Hierarchy Process (AHP), what is the primary purpose of calculating the Consistency Ratio (CR)?

Correct Answer: To validate the logical consistency of pairwise comparisons

The Consistency Ratio (CR) in AHP serves as a crucial measure to check if decision makers have been consistent in their pairwise comparisons of criteria and alternatives. When making multiple pairwise comparisons, there's a possibility of inconsistency. For example, if A is preferred twice as much as B, and B is preferred twice as much as C, then logically A should be preferred four times as much as C. The CR helps identify if such logical relationships are maintained. A CR value of 0.10 or less is considered acceptable, indicating that the judgments are sufficiently consistent. If CR exceeds 0.10, the pairwise comparisons should be revisited and revised. The other answers describe different aspects of AHP: - Determining final weighted scores is a later step in the process after consistency is confirmed - Establishing relative importance is the purpose of pairwise comparisons themselves - Normalizing the matrix and generating priority vectors are mathematical steps in the process, but not the purpose of CR calculation

Question 2

In Analytic Hierarchy Process (AHP), when conducting pairwise comparisons of alternatives, what should be the maximum inconsistency level allowed to ensure reliable results?

Correct Answer: 10% or 0.10 on the Consistency Index

In Analytic Hierarchy Process (AHP), a consistency ratio of 10% (0.10) is the standard maximum acceptable threshold for ensuring reliable results. This threshold was established by Thomas Saaty, the creator of AHP, and is widely accepted in academic and professional practice. It represents an optimal balance between human judgment variation and decision-making accuracy. A consistency ratio above 0.10 suggests that the pairwise comparisons may be too random or inconsistent to be reliable. In such cases, the decision-maker should review and revise their judgments. The other suggested thresholds are incorrect because: - 25% is too high and would allow excessive inconsistency in the decision-making process - 5% is overly strict and would be impractical for most real-world applications - 15% exceeds the established standard and could lead to unreliable results

Question 3

In the Analytic Hierarchy Process (AHP), what is the recommended approach when comparing criteria that have vastly different scales of measurement?

Correct Answer: Normalize the measurement scales to create a common basis for comparison

Normalizing measurement scales to create a common basis for comparison is the correct approach in AHP when dealing with different scales of measurement. Here's why: Normalization is a fundamental principle in AHP that: - Converts different scales into comparable units (0-1 or percentages) - Preserves the relative relationships between alternatives - Enables consistent and meaningful pairwise comparisons - Maintains the mathematical validity of the AHP process Why other options are not optimal: Logarithmic transformation would distort the relative relationships between criteria and complicate interpretation. Multiplying by weighted factors before comparison would introduce bias and double-count importance, as weighting is already part of the AHP process. Converting to monetary values is: - Not always possible for qualitative criteria - May introduce additional assumptions and errors - Could lose important non-monetary aspects of the criteria

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