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

Transitivity of interval and fuzzy-interval extensions of interval functions

Authors
Heriberto Román-Flores, Yurilev Chalco-Cano
Corresponding Author
Heriberto Román-Flores
Available Online June 2015.
DOI
10.2991/ifsa-eusflat-15.2015.203How to use a DOI?
Keywords
Transitivity, Zadeh's extensions.
Abstract

Let I = [a, b] be a real compact interval and ƒ : I I a continuous function. De ne Kc([a, b]) the class of all non empty compact subinterval of [a, b] and let the natural extension of ƒ to Kc([a, b]) , that is to say, (J) = ƒ(J) for all J ([a, b]). Also, let c([a, b]) the class of all fuzzy-intervals with support contained in [a, b] and consider ^ƒ the Zadeh's extension of ƒ to c([a, b]). The aim of this paper is to show that and ^ƒ are not transitive for any arbitrary self continuous function ƒ de ned on I.

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
10.2991/ifsa-eusflat-15.2015.203How 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  - Heriberto Román-Flores
AU  - Yurilev Chalco-Cano
PY  - 2015/06
DA  - 2015/06
TI  - Transitivity of interval and fuzzy-interval extensions of interval functions
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  - 1435
EP  - 1437
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.203
DO  - 10.2991/ifsa-eusflat-15.2015.203
ID  - Román-Flores2015/06
ER  -