Publication result detail

Fuzzy Metrics in Space of Fuzzy Points

BEDNÁŘ, J.

Original Title

Fuzzy Metrics in Space of Fuzzy Points

English Title

Fuzzy Metrics in Space of Fuzzy Points

Type

Paper in proceedings (conference paper)

Original Abstract

The main purpose of this paper is to conceive fuzzy metric spaces as generalisation of metric spaces. We define the distance between two fuzzy points in a fuzzy metric space as a normal fuzzy set in set of non-negative real numbers on the basis of Zadeh’s extension principle. Properties of these fuzzy distances as a suitable partial ordering or a triangle inequality we have formulated in several theorems and illustrated by examples. We have shown that, by fuzzifying a contractive mapping, we will obtain a fuzzy contractive mapping.

English abstract

The main purpose of this paper is to conceive fuzzy metric spaces as generalisation of metric spaces. We define the distance between two fuzzy points in a fuzzy metric space as a normal fuzzy set in set of non-negative real numbers on the basis of Zadeh’s extension principle. Properties of these fuzzy distances as a suitable partial ordering or a triangle inequality we have formulated in several theorems and illustrated by examples. We have shown that, by fuzzifying a contractive mapping, we will obtain a fuzzy contractive mapping.

Key words in English

fuzzy metric, fuzzy distance, fuzzy metric space, fuzzy contraction

Authors

BEDNÁŘ, J.

Released

12.08.2004

Publisher

HS Zittau/Gorlitz

Location

Zittau, Germany

ISBN

3-98080889-5-5

Book

Proceedings of East West Fuzzy Colloquium 2004

Pages from

91

Pages count

6

BibTex

@inproceedings{BUT17455,
  author="Josef {Bednář}",
  title="Fuzzy Metrics in Space of Fuzzy Points",
  booktitle="Proceedings of East West Fuzzy Colloquium 2004",
  year="2004",
  pages="6",
  publisher="HS Zittau/Gorlitz",
  address="Zittau, Germany",
  isbn="3-98080889-5-5"
}