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Authors: Irina Perfilieva 1 and Alexandr Šostak 2

Affiliations: 1 University of Ostrava and University of Latia, Czech Republic ; 2 University of Ostrava, Latvia

Keyword(s): Fuzzy Function, Extensional Function, Fuzzy Equivalence, Extension Principle.

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

Abstract: The aim of this contribution is to develop a theory of such concepts as fuzzy point, fuzzy set and fuzzy function in a similar style as is common in classical mathematical analysis. We recall some known notions and propose new ones with the purpose to show that, similarly to the classical case, a (fuzzy) set is a collection of (fuzzy) points or singletons. We show a relationship between a fuzzy function and its ordinary “skeleton” that can be naturally associated with the original function. We show that any fuzzy function can be extended to the domain of fuzzy subsets and this extension is analogous to the Extension Principle of L. A. Zadeh.

CC BY-NC-ND 4.0

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Paper citation in several formats:
Perfilieva, I. and Šostak, A. (2014). Fuzzy Function and the Generalized Extension Principle. In Proceedings of the International Conference on Fuzzy Computation Theory and Applications (IJCCI 2014) - FCTA; ISBN 978-989-758-053-6, SciTePress, pages 169-174. DOI: 10.5220/0005132701690174

@conference{fcta14,
author={Irina Perfilieva. and Alexandr Šostak.},
title={Fuzzy Function and the Generalized Extension Principle},
booktitle={Proceedings of the International Conference on Fuzzy Computation Theory and Applications (IJCCI 2014) - FCTA},
year={2014},
pages={169-174},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005132701690174},
isbn={978-989-758-053-6},
}

TY - CONF

JO - Proceedings of the International Conference on Fuzzy Computation Theory and Applications (IJCCI 2014) - FCTA
TI - Fuzzy Function and the Generalized Extension Principle
SN - 978-989-758-053-6
AU - Perfilieva, I.
AU - Šostak, A.
PY - 2014
SP - 169
EP - 174
DO - 10.5220/0005132701690174
PB - SciTePress

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