TY - CHAP
T1 - A Note on Generalized Convexity for Fuzzy Mappings Through a Linear Ordering
AU - Rufián-Lizana, Antonio
AU - Chalco-Cano, Yurilev
AU - Ruiz-Garzón, Gabriel
AU - Jiménez-Gamero, M. Dolores
N1 - Publisher Copyright:
© 2018, Springer International Publishing AG.
PY - 2018
Y1 - 2018
N2 - In De Campos Ibáñez and González-Muñoz (Fuzzy Sets Syst 29:145–154, 1989, [6]), Goestschel and Voxman (Fuzzy Sets Syst 18:31–43, 1986, [7]) the authors considered a linear ordering on the space of fuzzy intervals. For each fuzzy mapping (fuzzy interval-valued mapping) F, based on the aforementioned linear ordering, they introduced a real-valued function TF on the domain of the fuzzy mapping F. Recently, Chalco-Cano et al. (Fuzzy Sets Syst 231:70–83, 2013, [4]) have studied the relationship between the generalized Hukuhara differentiability of a fuzzy mapping F (G-differentiability, for short) and the differentiability of TF, and some properties of local-global minima. This paper studies such properties for fuzzy mappings, using new concepts which generalize the existing ones.
AB - In De Campos Ibáñez and González-Muñoz (Fuzzy Sets Syst 29:145–154, 1989, [6]), Goestschel and Voxman (Fuzzy Sets Syst 18:31–43, 1986, [7]) the authors considered a linear ordering on the space of fuzzy intervals. For each fuzzy mapping (fuzzy interval-valued mapping) F, based on the aforementioned linear ordering, they introduced a real-valued function TF on the domain of the fuzzy mapping F. Recently, Chalco-Cano et al. (Fuzzy Sets Syst 231:70–83, 2013, [4]) have studied the relationship between the generalized Hukuhara differentiability of a fuzzy mapping F (G-differentiability, for short) and the differentiability of TF, and some properties of local-global minima. This paper studies such properties for fuzzy mappings, using new concepts which generalize the existing ones.
UR - https://www.scopus.com/pages/publications/85042942544
U2 - 10.1007/978-3-319-73848-2_66
DO - 10.1007/978-3-319-73848-2_66
M3 - Chapter
AN - SCOPUS:85042942544
T3 - Studies in Systems, Decision and Control
SP - 721
EP - 731
BT - Studies in Systems, Decision and Control
PB - Springer Nature
ER -