@INPROCEEDINGS { Rsds2493,
author = {Polkowski, Lech T.}, 
title = {A Set Theory for Rough Sets. Toward A Formal Calculus of Vague Statements}, 
booktitle = {Abstracts of TASC 2004: Theory and Applications of Soft Computing}, 
pages = {42--53}, 
publisher = {Polish-Japanese Institute of Information Technology}, 
address = {Warsaw, Poland}, 
year = 2004, 
editor = {Polkowski, Lech}, 
abstract = {Rough set theory is a paradigm for approximate reasoning based on a formal mathematical basis, viz., it assumes that concepts are divided into exact and non--exact (rough) ones by means of a topological structure induced by a representation of knowledge as a classification. A classification in its most simple form is an equivalence relation on a universe of objects; the classification induces a partition topology and concepts (subsets of the universe) that are clopen are exact whereas other concepts are rough. In consequence, rough sets are represented as pairs of exact sets of the form (interior, closure). In the paper, we propose a set theory that represents formally exact and rough sets as satisfying or not a certain dichotomy based on a new form of membership in a set; this membership acquires a mereological character as it is based on containment. As a result, we propose a new form of set theory suitable  as a set theory for rough sets. Models of this theory serve as of interpretation for a class of intensional logics, viz., rough mereological logics defined by means of rough inclusions - basic predicates of rough mereology. An application of these logics is proposed in semantic interpretation of vague statements forming the domain of Calculus of Perceptions proposed by  L.A. Zadeh.}, 
keywords = {rough set theory (RST), approximations, set theory, rough mereological logic (RML), information systems, decision logic, calculus of vague statements, }, 
}