Measure of Roughness for Rough Approximation of Fuzzy Sets and Its Topological Interpretation

Alexander Šostak

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Paper

Measure of Roughness for Rough Approximation of Fuzzy Sets and Its Topological Interpretation

Topics: Mathematical Foundations: Fuzzy Set Theory and Fuzzy Logic

In Proceedings of the International Conference on Fuzzy Computation Theory and Applications - Volume 0IJCCI, 61-67, 2014 , Rome, Italy

Author: Alexander Šostak

Affiliation: Institute of Mathematics and Computer Science of the University of Latvia, Latvia

Keyword(s): L-fuzzy Set, L-relation, L-fuzzy Rough Set, cl-monoid, Measure of Inclusion, L-fuzzy Topology, L-fuzzy Co-topology.

Related Ontology Subjects/Areas/Topics: Artificial Intelligence ; Computational Intelligence ; Fuzzy Systems ; Mathematical Foundations: Fuzzy Set Theory and Fuzzy Logic ; Soft Computing

Abstract: We define the measure of upper and the measure of lower rough approximation for L-fuzzy subsets of a set equipped with a reflexive transitive fuzzy relation R. In case when the relation R is also symmetric, these measures coincide and we call their value by the measure of roughness of rough approximation. Basic properties of such measures are studied. A realization of measures of rough approximation in terms of L-fuzzy topologies is presented.

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Paper citation in several formats:

Šostak, A. (2014). Measure of Roughness for Rough Approximation of Fuzzy Sets and Its Topological Interpretation. In Proceedings of the International Conference on Fuzzy Computation Theory and Applications (IJCCI 2014) - FCTA; ISBN 978-989-758-053-6, SciTePress, pages 61-67. DOI: 10.5220/0005080400610067

@conference{fcta14,
author={Alexander Šostak.},
title={Measure of Roughness for Rough Approximation of Fuzzy Sets and Its Topological Interpretation},
booktitle={Proceedings of the International Conference on Fuzzy Computation Theory and Applications (IJCCI 2014) - FCTA},
year={2014},
pages={61-67},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005080400610067},
isbn={978-989-758-053-6},
}

TY - CONF

JO - Proceedings of the International Conference on Fuzzy Computation Theory and Applications (IJCCI 2014) - FCTA
TI - Measure of Roughness for Rough Approximation of Fuzzy Sets and Its Topological Interpretation
SN - 978-989-758-053-6
AU - Šostak, A.
PY - 2014
SP - 61
EP - 67
DO - 10.5220/0005080400610067
PB - SciTePress