Measure Identification for the Choquet Integral: A Python Module

Türkarslan E., Torra V.

International Journal of Computational Intelligence Systems, cilt.15, sa.1, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s44196-022-00146-w
  • Dergi Adı: International Journal of Computational Intelligence Systems
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, Directory of Open Access Journals
  • Anahtar Kelimeler: Fuzzy measure identification, k-additive fuzzy measure, Belief functions, Mobius transform, Python
  • TED Üniversitesi Adresli: Evet

Özet

© 2022, The Author(s).Fuzzy integrals are common concepts which are used to aggregate input values in practical applications. Aggregation of inputs using fuzzy integrals opens up numerous possibilities for modeling interaction, redundancy, and synergy of inputs. However, fuzzy integrals need a fuzzy measure to start this aggregation process. This situation pushes us into the fuzzy measure identification process. This process becomes difficult due to the monotony condition of the fuzzy measure and the exponential increase on the number of measure parameters. There are in the literature many ways to determine fuzzy measures. One of them is learning from data. In this paper, our aim is to introduce a new fuzzy measure identification tool to learn measures from empirical data. It is a Python module which finds the measure that minimizes the difference between the computed and expected outputs of the Choquet integral. In addition, we study some properties of the learning process. In particular, we consider k-additive fuzzy measures and belief functions as well as arbitrary fuzzy measures. Using these variety of measures we examine the effect of k and noisy data on the learning process.