A non-boolean lattice derived by double indiscernibility

Yukio Pegio Gunji, Taichi Haruna

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

The central notion of a rough set is the indiscernibility that is based on an equivalence relation. Because an equivalence relation shows strong bondage in an equivalence class, it forms a Galois connection and the difference between the upper and lower approximations is lost. Here, we introduce two different equivalence relations, one for the upper approximation and one for the lower approximation, and construct a composite approximation operator consisting of different equivalence relations. We show that a collection of fixed points with respect to the operator is a lattice and there exists a representation theorem for that construction.

Original languageEnglish
Title of host publicationTransactions on Rough Sets XII
Pages211-225
Number of pages15
DOIs
Publication statusPublished - 2010 Aug 26
Externally publishedYes
EventRough Set and Knowledge Technology Conference, RSKT 2008 - Chengdu, China
Duration: 2008 May 12008 May 1

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6190 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceRough Set and Knowledge Technology Conference, RSKT 2008
CountryChina
CityChengdu
Period08/5/108/5/1

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Gunji, Y. P., & Haruna, T. (2010). A non-boolean lattice derived by double indiscernibility. In Transactions on Rough Sets XII (pp. 211-225). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6190 LNCS). https://doi.org/10.1007/978-3-642-14467-7_11