A non-boolean lattice derived by double indiscernibility

Yukio 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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages211-225
Number of pages15
Volume6190 LNCS
DOIs
Publication statusPublished - 2010
Externally publishedYes
EventRough Set and Knowledge Technology Conference, RSKT 2008 - Chengdu
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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Equivalence classes
Equivalence relation
Upper Approximation
Lower Approximation
Composite materials
Galois Connection
Approximation Operators
Representation Theorem
Equivalence class
Rough Set
Fixed point
Composite
Operator

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Gunji, Y., & Haruna, T. (2010). A non-boolean lattice derived by double indiscernibility. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6190 LNCS, 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

A non-boolean lattice derived by double indiscernibility. / Gunji, Yukio; Haruna, Taichi.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6190 LNCS 2010. p. 211-225 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6190 LNCS).

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

Gunji, Y & Haruna, T 2010, A non-boolean lattice derived by double indiscernibility. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 6190 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6190 LNCS, pp. 211-225, Rough Set and Knowledge Technology Conference, RSKT 2008, Chengdu, 08/5/1. https://doi.org/10.1007/978-3-642-14467-7_11
Gunji Y, Haruna T. A non-boolean lattice derived by double indiscernibility. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6190 LNCS. 2010. p. 211-225. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-14467-7_11
Gunji, Yukio ; Haruna, Taichi. / A non-boolean lattice derived by double indiscernibility. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6190 LNCS 2010. pp. 211-225 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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