Merging Hazy Sets with m-Schemes: A geometric approach to data visualization
Abstract
We introduce a general framework for aggregating dissimilarity functions. Such functions may arise from locally adjusting a metric to meet specific criteria, such as those employed in dimensionality reduction methods like UMAP and IsUMap, or from differing modalities of data representation. We formalize these approaches as m-schemes, a class of methods closely related to t-norms and t-conorms in probabilistic metrics, as well as to composition laws in information theory. These m-schemes provide a flexible and theoretically grounded approach to refining distance-based embeddings. We apply this method to consistency tests for multi-expert judgments, generalizing the Aczél-Saaty [1] ratio synthesis model for decision making.
Fields of Study & Subjects
Data Visualization and Analytics
Data Management and Algorithms
Image Retrieval and Classification Techniques
Publication details
- Journal / source
- Advances in Theoretical and Mathematical Physics
- Volume
- 29
- Issue
- 8
- Pages
- 2251–2284
- Publication date
- 1 January 2026
- Language
- EN