Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology

Logic of prototypes and counterexamples: possibilities and limits

Authors
Thomas Vetterlein
Corresponding Author
Thomas Vetterlein
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.99How to use a DOI?
Keywords
Vague property, prototypical examples, counterexamples, logic of vagueness, Kleene logic.
Abstract

Fuzzy sets are a popular tool to model vague properties. It is, however, well-known that this model usually involves a good degree of arbitrariness. In this contribution we consider the possibility of standardising the construction of fuzzy sets at least withregard to the borderline cases. To this end, we identify a vague property with the sets of clearly positive cases and clearly negative cases and under the assumption that the universe of discourse is a metric space, we determine the fuzzy set by what can be described as a linear interpolation. Following this idea, we discuss a number of logic-based approaches to reasoning under vagueness.

Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
Series
Advances in Intelligent Systems Research
Publication Date
June 2015
ISBN
978-94-62520-77-6
ISSN
1951-6851
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.99How to use a DOI?
Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Thomas Vetterlein
PY  - 2015/06
DA  - 2015/06
TI  - Logic of prototypes and counterexamples: possibilities and limits
BT  - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 697
EP  - 704
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.99
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.99
ID  - Vetterlein2015/06
ER  -