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Paper details
Number 3 - September 2001
Volume 11 - 2001
Relative sets and rough sets
Amin Mousavi, Parviz Jabedar-Maralani
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.
Keywords
rough sets, set theory, data analysis, multi-valued logic, interval sets, knowledge representation