Academic Background and Problem Introduction

In the field of Multi-Expert Multi-Criteria Decision-Making (MEMCDM), effectively handling uncertainty and imprecise information has always been a core challenge. Particularly in complex scenarios involving multiple experts and decision criteria, experts’ opinions often diverge, complicating the decision-making process. To address this issue, researchers have proposed decision methods based on Interval Sets, which can more comprehensively describe uncertain qualitative information through upper and lower bound sets. However, existing decision methods based on Interval Sets, especially the similarity and dissimilarity measures in the Alternative Queuing Method (AQM), still have certain limitations, particularly in the framework of Absolute Quantization, where the accuracy and comprehensiveness of information extraction need improvement.

This study aims to improve the similarity and dissimilarity measures of Interval Sets by introducing the concept of Relative Quantization and, on this basis, proposes an Improved Alternative Queuing Method (IAQM) to enhance the decision performance of MEMCDM. Specifically, the authors construct improved similarity and dissimilarity measures for Interval Sets through systematic structural analysis and statistical fusion, and propose improved Possibility Degrees, ultimately forming a more robust decision index for ranking alternatives.

Source and Author Information

This paper is co-authored by Xin Xie, Xianyong Zhang, Zhiying Lv, and Jiang Chen, affiliated with the School of Mathematical Sciences at Sichuan Normal University, the College of Artificial Intelligence at Chengdu University of Information Technology, and multiple laboratories at the Research Center of Sichuan Normal University. The paper was accepted on February 15, 2025, and published in the journal Cognitive Computation, with the DOI 10.1007/s12559-025-10426-0.

Research Process and Main Methods

1. Construction and Improvement of Interval-Set Information Tables

First, the authors review the basic concepts of Interval-Set Information Tables (ISITs) and point out the shortcomings of existing similarity and dissimilarity measures. Existing methods primarily rely on Absolute Quantization, measuring similarity and dissimilarity by calculating the ratio of the intersection to the union of the three regions (positive, negative, and boundary regions) of Interval Sets. However, this approach has limitations in the depth and comprehensiveness of information extraction.

To address this issue, the authors propose the core formula of Relative Quantization, corereli, which provides a richer information description by arithmetically averaging two relative cardinality ratios. Specifically, corereli not only considers the relationship between the intersection and union but also introduces the structural division of Interval Sets, thereby more accurately reflecting the similarity and dissimilarity between Interval Sets.

2. Improved Similarity and Dissimilarity Measures

Based on corereli, the authors further propose Improved Similarity Measures (ISMs) and Improved Dissimilarity Measures (IDMs). These measures structurally simulate existing absolute measures but are essentially improved through Relative Quantization. For example, the Improved Normalized Hamming Similarity (ISNH) and Improved Euclidean Similarity (ISNE) are reconstructed using the relative core formula corereli.

Additionally, the authors propose the Generalized-Hybrid Similarity Measure (ISGHN), which further extends the application scope of similarity measures through parameterization. Through these improvements, the authors demonstrate the superiority of relative measures in information extraction and decision performance.

3. Improved Alternative Queuing Method (IAQM)

Based on the improved similarity and dissimilarity measures, the authors propose an Improved Alternative Queuing Method (IAQM) for handling MEMCDM problems based on Interval Sets. Specifically, IAQM is implemented through the following steps:

1. Information Transformation: Convert the evaluation information from multiple experts into Interval-Set Information Tables.
2. Weight Determination: Determine the weights of each criterion based on improved dissimilarity measures using the Maximum Deviation Method.
3. Possibility Degree Calculation: Use improved Possibility Degrees to perform pairwise comparisons of alternatives under each criterion.
4. Sorting Index Generation: Generate a robust sorting index through weighted arithmetic averaging for the final ranking of alternatives.

4. Algorithm Evaluation and Experimental Verification

To verify the effectiveness and superiority of IAQM, the authors design two types of data experiments: one based on a real case of e-commerce platform selection, and the other on simulated experiments using six public datasets. In the evaluation process, the authors propose two new decision evaluation metrics—Separability and Goodness—to quantify the quality of decision ranking.

4.1 E-commerce Platform Selection Case

In the case of e-commerce platform selection, the authors compare the decision effects of the existing AQM and the improved IAQM on four e-commerce platforms. The results show that IAQM outperforms the existing AQM in both the accuracy and stability of decision ranking, especially in handling divergent opinions from multiple experts, where IAQM demonstrates stronger robustness.

4.2 Public Dataset Simulation Experiments

In the simulated experiments using six public datasets, the authors further verify the universality and effectiveness of IAQM across different datasets. The experimental results indicate that IAQM outperforms the existing AQM in decision performance across all datasets, particularly in handling high-dimensional data and complex decision scenarios, where IAQM shows stronger adaptability.

Research Conclusions and Value

By introducing the concept of Relative Quantization, this paper improves the similarity and dissimilarity measures of Interval Sets and proposes an Improved Alternative Queuing Method (IAQM) for handling MEMCDM problems based on Interval Sets. The main contributions of the study include:

1. Proposal of Relative Similarity and Dissimilarity Measures: Through the core formula of Relative Quantization, corereli, the authors construct more precise similarity and dissimilarity measures, enhancing the depth and comprehensiveness of information extraction.
2. Improved Alternative Queuing Method (IAQM): Based on the improved measures, the authors propose IAQM, which outperforms the existing AQM in both the accuracy and robustness of decision ranking.
3. Proposal of Decision Evaluation Metrics: The authors design two new decision evaluation metrics—Separability and Goodness—to quantify the quality of decision ranking, providing new evaluation tools for future research.

This study not only theoretically deepens the uncertainty measures of Interval Sets but also provides more effective solutions for complex MEMCDM problems in practical applications, demonstrating significant scientific value and application prospects.

Research Highlights

1. Introduction of Relative Quantization: By introducing the concept of Relative Quantization, the authors improve existing similarity and dissimilarity measures, enhancing the accuracy and comprehensiveness of information extraction.
2. Improved Alternative Queuing Method (IAQM): IAQM demonstrates stronger robustness and adaptability in handling complex MEMCDM problems, especially in scenarios with divergent opinions from multiple experts.
3. New Decision Evaluation Metrics: The proposal of Separability and Goodness provides new quantitative tools for evaluating the quality of decision ranking, offering important methodological significance.

Other Valuable Information

The research framework and experimental design of this paper provide important references for future related studies, especially in handling high-dimensional data and complex decision scenarios, where the universality and effectiveness of IAQM offer new insights for the design of future decision algorithms. Additionally, the concept of Relative Quantization proposed by the authors provides a new perspective for uncertainty handling in other fields.