Communicative approximations as rough sets

Authors:
Mohua Banerjee;Abhinav Pathak;Gopal Krishna;Amitabha Mukerjee
Affiliations:
Dept of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India;Dept of Computer Science & Engineering, Indian Institute of Technology, Kanpur, India;Dept of Computer Science & Engineering, Indian Institute of Technology, Kanpur, India;Dept of Computer Science & Engineering, Indian Institute of Technology, Kanpur, India
Venue:
RSCTC'10 Proceedings of the 7th international conference on Rough sets and current trends in computing
Year:
2010

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Abstract

Communicative approximations, as used in language, are equivalence relations that partition a continuum, as opposed to observational approximations on the continuum. While the latter can be addressed using tolerance interval approximations on interval algebra, new constructs are necessary for considering the former, including the notion of a "rough interval", which is the indiscernibility region for an event described in language, and "rough points" for quantities and moments. We develop the set of qualitative relations for points and intervals in this "communicative approximation space", and relate them to existing relations in exact and tolerance-interval formalisms. We also discuss the nature of the resulting algebra.