TY - GEN
T1 - A note on dynamics of interval extensions of interval functions
AU - Roman-Flores, H.
AU - Chalco-Cano, Y.
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/9/29
Y1 - 2015/9/29
N2 - Let I = [a, b] a real compact interval and f : I → I a continuous function. Define Kc([a, b]) the class of all non empty compact subinterval of [a, b] and let fc the natural extension of f to Kc([a, b]), that is to say, fc(J) = f(J) for all J ∈ Kc([a, b]). Also, let Fc([a, b]) the class of all fuzzy-intervals with support contained in [a, b] and consider fcc the Zadeh's extension of f to Fc([a, b]). The aim of this paper is to show some dynamical properties of fc and fcc in relation to the Devaney's conditions for complexity of functions and, in particular, to show the surprising difference between the dynamics on the base space X = [a, b] compared with the dynamics of the interval extension Kc([a, b]) and fuzzy-interval extension Fc([a, b]), which could be useful in the mathematical modelling of real problems.
AB - Let I = [a, b] a real compact interval and f : I → I a continuous function. Define Kc([a, b]) the class of all non empty compact subinterval of [a, b] and let fc the natural extension of f to Kc([a, b]), that is to say, fc(J) = f(J) for all J ∈ Kc([a, b]). Also, let Fc([a, b]) the class of all fuzzy-intervals with support contained in [a, b] and consider fcc the Zadeh's extension of f to Fc([a, b]). The aim of this paper is to show some dynamical properties of fc and fcc in relation to the Devaney's conditions for complexity of functions and, in particular, to show the surprising difference between the dynamics on the base space X = [a, b] compared with the dynamics of the interval extension Kc([a, b]) and fuzzy-interval extension Fc([a, b]), which could be useful in the mathematical modelling of real problems.
KW - Complexity theory
KW - Entropy
KW - Extraterrestrial measurements
KW - Fractals
KW - Solitons
UR - https://www.scopus.com/pages/publications/84961917695
U2 - 10.1109/NAFIPS-WConSC.2015.7284178
DO - 10.1109/NAFIPS-WConSC.2015.7284178
M3 - Conference contribution
AN - SCOPUS:84961917695
T3 - Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS
BT - 2015 Annual Meeting of the North American Fuzzy Information Processing Society, NAFIPS 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - Annual Meeting of the North American Fuzzy Information Processing Society, NAFIPS 2015
Y2 - 17 August 2015 through 19 August 2015
ER -