Fuzzy arithmetic with product t-norm

Soylu G., Aslan M.

IRANIAN JOURNAL OF FUZZY SYSTEMS, vol.18, no.6, pp.185-197, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 6
  • Publication Date: 2021
  • Journal Name: IRANIAN JOURNAL OF FUZZY SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.185-197
  • Keywords: Fuzzy arithmetic, product t-norm, fuzzy number, SUM
  • Akdeniz University Affiliated: Yes

Abstract

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.