A comparative study of fuzzy rough sets
type: Item
instance of: scholarly article
title: A comparative study of fuzzy rough sets
zbMATH Open document ID: 1004.03043
DOI: 10.1016/S0165-0114(01)00032-X
author: Anna Maria Radzikowska
author: E. E. Kerre
published in: Fuzzy Sets and Systems
publication date: 2002-06-24T00:00:00Z
review text: A new approach to the fuzzification of well-known Pawlak's rough sets is discussed. New sets, called \(({\mathcal I},{\mathcal T})\)-fuzzy sets, are introduced, where \({\mathcal I}\) is an implicator, i.e., a function \({\mathcal I}:[0,1]^2 \to[0,1]\) satisfying the conditions: \({\mathcal I}(1,0)=0\), \({\mathcal I}(0,0)={\mathcal I}(0,1)={\mathcal I}(1,1)=1\), and \({\mathcal T}\) is a triangular norm, i.e., an increasing, associative and commutative mapping \({\mathcal T}:[0,1]^2\to [0,1]\) that satisfies the boundary condition for all \(x\in[0,1]:{\mathcal T}(x,1)=x\). The basic properties of the new sets are given.
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1758519
zbMATH Keywords: fuzzification of rough sets
zbMATH Keywords: implicator
zbMATH Keywords: triangular norm
reviewed by: Krassimir Atanassov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1758519