# Relative sets and rough sets

Amin Mousavi; Parviz Jabedar-Maralani

International Journal of Applied Mathematics and Computer Science (2001)

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

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topMousavi, 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 -

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