Density estimates on the unit simplex and calculation of the mode of a sample

Maia Angelova, Gleb Beliakov, Sergiy Shelyag, Ye Zhu

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


This paper addresses reliable and efficient calculation of the mode of a multivariate sample, which is a classical fusion function. In particular, we focus on the inputs given on the unit simplex, when aggregating elements of Atanassov intuitionistic fuzzy sets, interval-valued fuzzy sets and their extensions, as well as compositional data. We outline the use of a specially designed 2-additive fuzzy measures and the Choquet integral for the purposes of reducing computational complexity in higher dimensions. We present computational analysis and benchmark four different methods of density-based mode estimation.

Original languageEnglish
Pages (from-to)850-868
Number of pages19
JournalInternational Journal of Intelligent Systems
Issue number5
Early online date20 Feb 2020
Publication statusPublished - May 2020
Externally publishedYes


  • aggregation functions
  • delaunay triangulation
  • density estimate
  • interval valued fuzzy sets
  • mode
  • nearest neighbours


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