Resemblance is a nearness

  • Authors:
  • Vladimír Janis

  • Affiliations:
  • Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovakia

  • Venue:
  • Fuzzy Sets and Systems - Theme: Basic notions
  • Year:
  • 2003

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Abstract

In (Fuzzy Sets and Systems 133 (2) (2003)) the authors claim that the transitivity condition usually used in the definition of a fuzzy equivalence of fuzzy equality is not suitable in a lot of real situations. The fuzzy relation of a resemblance in a metric space is defined in a different way in (Fuzzy Sets and Systems 133 (2) (2003)). The present paper shows that the same relation (called fuzzy nearness) as in (Fuzzy Sets and Systems 133 (2) (2003)) has been used by several authors in several works to study mainly properties of real function in more general context. A brief review of a variety of results achieved using the relation of a fuzzy nearness is provided.