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, vol.32, no.2, pp.157-175, 2003 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 2
  • Publication Date: 2003
  • Doi Number: 10.1080/0308107031000090774
  • Journal Name: INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.157-175
  • Keywords: fuzzy algebra, fuzzy group, vague group, fuzzy function, fuzzy arithmetic, fuzzy equivalence relation
  • Akdeniz University Affiliated: Yes

Abstract

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.