A new pseudo-metric for fuzzy sets

Laszlo Kovacs, Joel Ratsaby

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A new distance function for fuzzy sets is introduced. It is based on the descriptive complexity, that is, the number of bits (on average) that are needed to describe an element in the symmetric difference of the two sets. The value of the distance gives the amount of additional information needed to describe either one of the two sets when the other is known. We prove that the distance function is a pseudo-metric, namely, it is non-negative, symmetric, it equals zero if the sets are identical and it satisfies the triangle inequality.

Original languageEnglish
Title of host publicationArtificial Intelligence and Soft Computing - 13th International Conference, ICAISC 2014, Proceedings
PublisherSpringer Verlag
Pages205-216
Number of pages12
EditionPART 1
ISBN (Print)9783319071725
DOIs
StatePublished - 1 Jan 2014
Externally publishedYes
Event13th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2014 - Zakopane, Poland
Duration: 1 Jun 20145 Jun 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8467 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2014
Country/TerritoryPoland
CityZakopane
Period1/06/145/06/14

Keywords

  • Fuzzy sets
  • descriptive complexity
  • distance
  • entropy
  • triangle-inequality

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