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 and 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