Repairing the inconsistent pairwise comparison matrix using a cosine distance and grey wolf optimiser-based framework...

Area of Science:

• Decision Sciences
• Operations Research
• Artificial Intelligence

Background:

• Inconsistent Pairwise Comparison Matrices (PCMs) hinder credible Multi-Criteria Decision-Making (MCDM).
• Optimizing PCMs requires minimizing deviation from original judgments while improving the Consistency Ratio (CR).

Purpose of the Study:

• To develop a novel framework for detecting and correcting inconsistencies in PCMs.
• To enhance the credibility of decision-making processes through consistent matrix generation.

Main Methods:

• Utilized a novel distance formula based on Cosine Distance to quantify PCM inconsistencies.
• Employed the Grey Wolf Optimizer (GWO), a swarm intelligence algorithm, for matrix repair.
• Introduced a maximum correction range (ε) to control the extent of matrix adjustments based on decision-maker preferences.

Main Results:

• Achieved a significant reduction in CR from 0.546487 to 0.073397 for a special case matrix.
• Demonstrated successful generation of a consistent matrix with minimal deviation from the original.
• Showcased superior performance compared to existing algorithms like ANTAHP and PSO.

Conclusions:

• The proposed framework effectively addresses PCM inconsistencies using Cosine Distance and GWO.
• The method preserves decision-maker preferences while achieving a high degree of consistency.
• This approach offers a robust solution for improving the reliability of MCDM.