Analytic Hierarchy Process (AHP)

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

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

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