Genuine sets, various kinds of fuzzy sets and fuzzy rough sets

Demirci M.

INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, cilt.11, sa.4, ss.467-494, 2003 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 4
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1142/s0218488503002193
  • Dergi Adı: INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.467-494
  • Anahtar Kelimeler: genuine sets, type-m fuzzy sets, type-2 fuzzy sets, fuzzy rough sets, intuitionistic fuzzy sets, possibility measures, TYPE-2
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, deriving the type-m fuzzy sets, intuitionistic fuzzy sets, Phi-fuzzy sets, rough sets, fuzzy rough sets and rough fuzzy sets as particular genuine sets, and establishing their connections with genuine sets, it is demonstrated that the theory of genuine sets provides a powerful tool to model various different kinds of uncertainty in a mathematical way. Furthermore, it is also shown that the genuine set theoretic descriptions of type-m fuzzy sets, intuitionistic fuzzy sets and fuzzy rough sets point out new features of these set notations, originated from the peculiar characteristics of genuine sets.