Why 1/(1+d) Is an Effective Distance-Based Similarity Measure: Two Explanations

Julio Urenda, The University of Texas at El Paso
Olga Kosheleva, The University of Texas at El Paso
Vladik Kreinovich, The University of Texas at El Paso

Technical Report: UTEP-CS-22-99a

To appear in Proceedings of the 11th IEEE International Conference on Intelligent Systems IS'22, Warsaw, Poland, October 12-14, 2022.


Most of our decisions are based on the notion of similarity: we use a decision that helped in similar situations. From this viewpoint, it is important to have, for each pair of situations or objects, a numerical value describing similarity between them. This is called a similarity measure. In some cases, the only information that we can use to estimate the similarity value is some natural distance measure d(a,b). In many such situations, empirical data shows that the similarity measure 1/(1+d) is very effective. In this paper, we provide two explanations for this effectiveness.