Transitivity of interval and fuzzy-interval extensions of interval functions

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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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  -