Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003 Association of Mizar Users

## Basic Properties of Rough Sets and Rough Membership Function

University of Bialystok

### Summary.

We present basic concepts concerning rough set theory. We define tolerance and approximation spaces and rough membership function. Different rough inclusions as well as the predicate of rough equality of sets are also introduced.

This work has been partially supported by CALCULEMUS grant HPRN-CT-2000-00102.

#### MML Identifier: ROUGHS_1

The terminology and notation used in this paper have been introduced in the following articles [20] [8] [25] [21] [1] [13] [22] [11] [19] [26] [28] [5] [2] [10] [9] [27] [7] [3] [14] [15] [6] [4] [16] [24] [23] [17] [18] [12]

#### Contents (PDF format)

1. Preliminaries
2. Tolerance and Approximation Spaces
3. Membership Function
4. Rough Inclusion
5. Rough Equality of Sets

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