Publication detail

Different Conceptions of Distance between Fuzzy Sets and Fuzzy Metric

BEDNÁŘ, J.

English title

Different Conceptions of Distance between Fuzzy Sets and Fuzzy Metric

Type

conference paper

Language

en

Original abstract

We discuss different conception of a distance between fuzzy sets and a distance between fuzzy numbers. The definition of the distance between fuzzy sets appropriately generalises the classical definition of distance between subsets of a metric space, so the distance between fuzzy sets is not a metric on family of all fuzzy subsets of a universe. The fuzzy metric (fuzzy distance between fuzzy numbers) is a generalisation of a metric, so it can be considered as a metric on family of all fuzzy numbers on a universe. These two different conceptions of a distance have some common properties, which are described in this paper.

English abstract

We discuss different conception of a distance between fuzzy sets and a distance between fuzzy numbers. The definition of the distance between fuzzy sets appropriately generalises the classical definition of distance between subsets of a metric space, so the distance between fuzzy sets is not a metric on family of all fuzzy subsets of a universe. The fuzzy metric (fuzzy distance between fuzzy numbers) is a generalisation of a metric, so it can be considered as a metric on family of all fuzzy numbers on a universe. These two different conceptions of a distance have some common properties, which are described in this paper.

Keywords in English

fuzzy metric, fuzzy distance, fuzzy metric space, fuzzy number

RIV year

2003

Released

04.06.2003

Publisher

VUT v Brně

Location

Brno

ISBN

80-214-2411-7

Book

Proceedings of the 8th International Conference on Soft Computing MENDEL 2003

Pages count

4

BIBTEX


@inproceedings{BUT11086,
  author="Josef {Bednář},
  title="Different Conceptions of Distance between Fuzzy Sets and Fuzzy Metric",
  booktitle="Proceedings of the 8th International Conference on Soft Computing MENDEL 2003",
  year="2003",
  month="June",
  publisher="VUT v Brně",
  address="Brno",
  isbn="80-214-2411-7"
}