# Relative sets and rough sets

• Volume: 11, Issue: 3, page 637-653
• ISSN: 1641-876X

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## Abstract

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In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap's four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Like truth-values of Belnap's logic, relative sets have two orderings; one is an order of inclusion and the other is an order of knowledge or information. By defining a rough set as a pair of definable sets, an integrated approach to relative sets and rough sets is obtained. With this definition, we are able to define an approximation of a rough set in an approximation space, and so we can obtain sequential approximations of a set, which is a good model of communication among agents.

## How to cite

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Mousavi, Amin, and Jabedar-Maralani, Parviz. "Relative sets and rough sets." International Journal of Applied Mathematics and Computer Science 11.3 (2001): 637-653. <http://eudml.org/doc/207524>.

@article{Mousavi2001,
abstract = {In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap's four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Like truth-values of Belnap's logic, relative sets have two orderings; one is an order of inclusion and the other is an order of knowledge or information. By defining a rough set as a pair of definable sets, an integrated approach to relative sets and rough sets is obtained. With this definition, we are able to define an approximation of a rough set in an approximation space, and so we can obtain sequential approximations of a set, which is a good model of communication among agents.},
author = {Mousavi, Amin, Jabedar-Maralani, Parviz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {interval sets; multi-valued logic; knowledge representation; rough sets; set theory; data analysis; Belnap's four-valued logic; relative sets; approximation space; communication among agents},
language = {eng},
number = {3},
pages = {637-653},
title = {Relative sets and rough sets},
url = {http://eudml.org/doc/207524},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Mousavi, Amin
AU - Jabedar-Maralani, Parviz
TI - Relative sets and rough sets
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 3
SP - 637
EP - 653
AB - In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap's four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Like truth-values of Belnap's logic, relative sets have two orderings; one is an order of inclusion and the other is an order of knowledge or information. By defining a rough set as a pair of definable sets, an integrated approach to relative sets and rough sets is obtained. With this definition, we are able to define an approximation of a rough set in an approximation space, and so we can obtain sequential approximations of a set, which is a good model of communication among agents.
LA - eng
KW - interval sets; multi-valued logic; knowledge representation; rough sets; set theory; data analysis; Belnap's four-valued logic; relative sets; approximation space; communication among agents
UR - http://eudml.org/doc/207524
ER -

## References

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