Implication operators on bounded posets of closed intervals: A new approach

KARAÇAL F., KARACAİR K., ERTUĞRUL Ü., Mesiar R.

IRANIAN JOURNAL OF FUZZY SYSTEMS, cilt.23, sa.2, ss.141-156, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 2
  • Basım Tarihi: 2026
  • Doi Numarası: 10.22111/ijfs.2026.54178.9595
  • Dergi Adı: IRANIAN JOURNAL OF FUZZY SYSTEMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO)
  • Sayfa Sayıları: ss.141-156
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In this paper, under the inclusion order, we investigate fuzzy implication construction methods on P-S, the poset of closed intervals of a bounded poset P. We first propose some methods for constructing a fuzzy implication on P-S using pre-implications, up-sets, and down-sets on P. Next, we add two new construction methods based only on the relationship between elements of P-S. The methods are supported by propositions, examples, and related results.