Fuzzy Function and the Generalized Extension Principle

Irina Perfilieva, Alexandr Šostak

2014

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.

Paper Citation

in Harvard Style

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 - Volume 1: FCTA, (IJCCI 2014) ISBN 978-989-758-053-6, pages 169-174. DOI: 10.5220/0005132701690174

in Bibtex Style

@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 - Volume 1: FCTA, (IJCCI 2014)},
year={2014},
pages={169-174},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005132701690174},
isbn={978-989-758-053-6},
}

in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Fuzzy Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2014)
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