An introduction to vague complemented ordered sets

Demirci M., Eken Z.

INFORMATION SCIENCES, vol.177, no.1, pp.150-160, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 177 Issue: 1
  • Publication Date: 2007
  • Doi Number: 10.1016/j.ins.2006.03.018
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.150-160
  • Keywords: fuzzy equivalence relation, fuzzy equality, many-valued equivalence relation, fuzzy ordering, fuzzy complement, fuzzy function, VALUED EQUIVALENCE-RELATIONS, GENERALIZED ASSOCIATIVE LAW, FUZZY FUNCTIONS, FOUNDATIONS, ALGEBRA, CONSTRUCTIONS, FUNDAMENTALS, LATTICES, AXIOMS
  • Akdeniz University Affiliated: Yes


The purpose of this paper is to introduce a theory of fuzzily defined complement operations on nonempty sets equipped with fuzzily defined ordering relations. Many-valued equivalence relation-based fuzzy ordering relations (also called vague ordering relations) provide a powerful and a comprehensive mathematical modelling of fuzzily defined partial ordering relations. For this reason, starting with a nonempty set X equipped with a many-valued equivalence relation and a vague ordering relation, a fuzzily defined complement operation (called a vague complement operation) on X will be formulated by means of the underling many-valued equivalence relation and vague ordering relation. Because of the fact that the practical implementations of vague complement operations basically depend on their representation properties, a considerable part of this paper is devoted to the representations of vague complement operations. In addition to this, the present paper provides various nontrivial examples for vague complements, and introduces a many-valued logical interpretation of quantum logic as a real application of vague complements. (c) 2006 Elsevier Inc. All rights reserved.