# REPRESENTATION THEOREM FOR FUZZY FUNCTIONS - Graded Form

### Martina Daňková

#### Abstract

In this contribution, we will extend results relating to representability of a fuzzy function using a crisp function. And additionally, we show for which functions there exist fuzzy function of a specific form. Our notion of fuzzy function has a graded character. More precisely, any fuzzy relation has a property of being a fuzzy function that is expressed by a truth degree. And it consists of two natural properties: extensionality and functionality. We will also provide a separate study of these two properties.

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#### Paper Citation

#### in Harvard Style

Daňková M. (2010). **REPRESENTATION THEOREM FOR FUZZY FUNCTIONS
- Graded Form** . In *Proceedings of the International Conference on Fuzzy Computation and 2nd International Conference on Neural Computation - Volume 1: ICFC, (IJCCI 2010)* ISBN 978-989-8425-32-4, pages 56-64. DOI: 10.5220/0003080900560064

#### in Bibtex Style

@conference{icfc10,

author={Martina Daňková},

title={REPRESENTATION THEOREM FOR FUZZY FUNCTIONS
- Graded Form},

booktitle={Proceedings of the International Conference on Fuzzy Computation and 2nd International Conference on Neural Computation - Volume 1: ICFC, (IJCCI 2010)},

year={2010},

pages={56-64},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003080900560064},

isbn={978-989-8425-32-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Fuzzy Computation and 2nd International Conference on Neural Computation - Volume 1: ICFC, (IJCCI 2010)

TI - REPRESENTATION THEOREM FOR FUZZY FUNCTIONS
- Graded Form

SN - 978-989-8425-32-4

AU - Daňková M.

PY - 2010

SP - 56

EP - 64

DO - 10.5220/0003080900560064