Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, Part II: Vague algebraic notions

Demirci M.

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, cilt.32, sa.2, ss.157-175, 2003 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Sayı: 2
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1080/0308107031000090774
  • Dergi Adı: INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.157-175
  • Anahtar Kelimeler: fuzzy algebra, fuzzy group, vague group, fuzzy function, fuzzy arithmetic, fuzzy equivalence relation
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, accepting the paper [Demirci, M. (2003a) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part I: fuzzy functions and their applications", Int. J. Gen. Syst. 32, 123-155] as a starting point, the general theory of M-vague algebraic notions such as M-vague semigroup, M-vague monoid, M-vague group, M-vague ring and M-vague field is developed on the basis of many-valued equivalence relations, and the rudimentary tools of this theory are introduced. It is elicited how the separation condition on *-fuzzy equalities affects the formulation of results within the present context. Furthermore, M-vague arithmetic operations, introduced in Demirci [( 2002) "Fundamentals of M-vague algebra and M-vague arithmetic operations", Int. J. Uncertainty Fuzziness Knowledge-Based Syst. 10(1), 25-75] are extended to the case of many-valued equivalence relations. By stating some motivating examples, it is also shown how the M-vague algebraic notions and M-vague arithmetic operations can be applied in practice.