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Simulation Research on the Relationship between Selected Inconsistency Indices Used in AHP
1Departments of Mathematics, Czestochowa University of Technology, 42-200 Częstochowa, Poland.
Entropy (Basel, Switzerland)
|October 28, 2023
Summary
The Analytic Hierarchy Process (AHP), a multi-criteria decision-making method, uses inconsistency indices (ICIs) to detect errors in pairwise comparison matrices. Some ICIs are highly correlated, suggesting they can be used interchangeably in AHP analysis.
Area of Science:
- Operations Research
- Decision Science
- Applied Mathematics
Background:
- The Analytic Hierarchy Process (AHP) is a popular multi-criteria decision-making method (MCDM) relying on pairwise comparisons organized in a Pairwise Comparison Matrix (PCM).
- Errors within PCMs can significantly impact the derived priorities, necessitating methods to assess and control for inconsistency.
- Saaty introduced the inconsistency index (ICI) to identify and manage errors in AHP, but numerous definitions and variations exist.
Purpose of the Study:
- To investigate the relationships and dependencies between different inconsistency indices (ICIs) used in the Analytic Hierarchy Process (AHP).
- To determine if certain ICIs exhibit high correlations, suggesting potential interchangeability in practical AHP applications.
- To provide empirical evidence on the correlations between selected ICIs through simulation.
Main Methods:
- Utilizing Monte Carlo simulation to generate data and observe dependencies within the AHP framework.
- Selecting specific pairs of inconsistency indices (ICIs) for analysis.
- Calculating Pearson correlation coefficients to quantify the linear association between selected ICIs.
- Visualizing the dependencies between ICIs using scatter plots.
Main Results:
- The Monte Carlo simulations revealed significant dependencies between certain pairs of inconsistency indices (ICIs).
- High Pearson correlation coefficients were observed for specific pairs of ICIs, indicating strong linear relationships.
- Scatter plots visually confirmed the close correlation between these selected ICIs.
Conclusions:
- Some inconsistency indices (ICIs) within the Analytic Hierarchy Process (AHP) are highly correlated.
- These highly correlated ICIs can potentially be used interchangeably in AHP, simplifying the decision-making process.
- The findings contribute to a better understanding of the behavior and relationships of different ICIs in AHP.
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