Fuzzy arithmetic with product t-norm

SOYLU G., ASLAN M.

IRANIAN JOURNAL OF FUZZY SYSTEMS, cilt.18, sa.6, ss.185-197, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 6
  • Basım Tarihi: 2021
  • Dergi Adı: IRANIAN JOURNAL OF FUZZY SYSTEMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.185-197
  • Anahtar Kelimeler: Fuzzy arithmetic, product t-norm, fuzzy number, SUM
  • Akdeniz Üniversitesi Adresli: Evet

Özet

Fuzzy arithmetic performed with the product t-norm is the focus of this paper. The subject is handled from both practical and theoretical perspectives. Explicit formulas for pro duct-sum and product-multiplication of triangular fuzzy numbers are obtained. These formulas can effectively replace the computational methods proposed so far. The issue that these operations are not shape preserving is solved by the presentation of appropriate approximations. Finally, the product arithmetic is compared in detail to the arithmetic performed with the boundary t-norms, namely the minimum and drastic sum.