TY - GEN
T1 - A Review on Differentiability and Optimality Conditions in Fuzzy Environments
AU - Hernández-Jiménez, Beatriz
AU - Osuna-Gómez, Rafaela
AU - Chalco-Cano, Yurilev
AU - Costa, Tiago Mendoça da
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022
Y1 - 2022
N2 - In this paper we present a review of the most important notions and characterizations of differentiability and necessary optimality conditions for a fuzzy multiobjective problem. As basis of this review, we first study the fundamental aspects of the notions of differentiability for interval valued functions, since the fuzzy environment and the interval environment are closely related. Those aspects are related to the different definitions of difference for intervals and their drawbacks, the different definitions and characterizations of the differentiability for interval-valued functions and their drawbacks and how they have been solved in the literature. Based on the most important and meaning results on interval valued functions you can find in the literature, a review on notions of differentiability in fuzzy context is given, both in the case of functions of one variable, and several variables. And finally we present the review results of the necessary optimality conditions for fuzzy multiobjective problems and the main conclusions.
AB - In this paper we present a review of the most important notions and characterizations of differentiability and necessary optimality conditions for a fuzzy multiobjective problem. As basis of this review, we first study the fundamental aspects of the notions of differentiability for interval valued functions, since the fuzzy environment and the interval environment are closely related. Those aspects are related to the different definitions of difference for intervals and their drawbacks, the different definitions and characterizations of the differentiability for interval-valued functions and their drawbacks and how they have been solved in the literature. Based on the most important and meaning results on interval valued functions you can find in the literature, a review on notions of differentiability in fuzzy context is given, both in the case of functions of one variable, and several variables. And finally we present the review results of the necessary optimality conditions for fuzzy multiobjective problems and the main conclusions.
KW - Differentiability
KW - Fuzzy functions
KW - Optimality conditions
UR - https://www.scopus.com/pages/publications/85135091092
U2 - 10.1007/978-3-031-08971-8_21
DO - 10.1007/978-3-031-08971-8_21
M3 - Conference contribution
AN - SCOPUS:85135091092
SN - 9783031089701
T3 - Communications in Computer and Information Science
SP - 245
EP - 257
BT - Information Processing and Management of Uncertainty in Knowledge-Based Systems - 19th International Conference, IPMU 2022, Proceedings
A2 - Ciucci, Davide
A2 - Couso, Inés
A2 - Medina, Jesús
A2 - Ślęzak, Dominik
A2 - Petturiti, Davide
A2 - Bouchon-Meunier, Bernadette
A2 - Yager, Ronald R.
PB - Springer Nature
T2 - 19th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2022
Y2 - 11 July 2022 through 15 July 2022
ER -