A Characterization for Generalized Hukuhara Differentiable Interval-Valued Functions and Some Rules of Calculus

Juan Carlos Blanche-Alcócer; Yurilev Chalco-Cano

doi:10.1007/978-3-031-08971-8_25

A Characterization for Generalized Hukuhara Differentiable Interval-Valued Functions and Some Rules of Calculus

Juan Carlos Blanche-Alcócer
, Yurilev Chalco-Cano

Department of Mathematics

Universidad de Tarapacá

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this article we show a characterization for a gH-differentiable interval-valued function through of properties of the (lateral) differentiability of its length function. Then, we give a procedure to classify a gH-differentiable interval-valued function according to their four types of gH-differentiability. Furthermore, using this classification, we propose a procedure to determine the points at which the sum of two gH-differentiable functions is gH-differentiable as well as to determine their type of gH-differentiability.

Original language	English
Title of host publication	Information Processing and Management of Uncertainty in Knowledge-Based Systems - 19th International Conference, IPMU 2022, Proceedings
Editors	Davide Ciucci, Inés Couso, Jesús Medina, Dominik Ślęzak, Davide Petturiti, Bernadette Bouchon-Meunier, Ronald R. Yager
Publisher	Springer Nature
Pages	294-303
Number of pages	10
ISBN (Print)	9783031089701
DOIs	https://doi.org/10.1007/978-3-031-08971-8_25
State	Published - 2022
Event	19th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2022 - Milan, Italy Duration: 11 Jul 2022 → 15 Jul 2022

Publication series

Name	Communications in Computer and Information Science
Volume	1601 CCIS
ISSN (Print)	1865-0929
ISSN (Electronic)	1865-0937

Conference

Conference	19th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2022
Country/Territory	Italy
City	Milan
Period	11/07/22 → 15/07/22

Keywords

Interval-valued functions
algebra of interval-valued functions
generalized Hukuhara derivative

Access to Document

10.1007/978-3-031-08971-8_25

Cite this

Blanche-Alcócer, J. C., & Chalco-Cano, Y. (2022). A Characterization for Generalized Hukuhara Differentiable Interval-Valued Functions and Some Rules of Calculus. In D. Ciucci, I. Couso, J. Medina, D. Ślęzak, D. Petturiti, B. Bouchon-Meunier, & R. R. Yager (Eds.), Information Processing and Management of Uncertainty in Knowledge-Based Systems - 19th International Conference, IPMU 2022, Proceedings (pp. 294-303). (Communications in Computer and Information Science; Vol. 1601 CCIS). Springer Nature. https://doi.org/10.1007/978-3-031-08971-8_25

Blanche-Alcócer, Juan Carlos ; Chalco-Cano, Yurilev. / A Characterization for Generalized Hukuhara Differentiable Interval-Valued Functions and Some Rules of Calculus. Information Processing and Management of Uncertainty in Knowledge-Based Systems - 19th International Conference, IPMU 2022, Proceedings. editor / Davide Ciucci ; Inés Couso ; Jesús Medina ; Dominik Ślęzak ; Davide Petturiti ; Bernadette Bouchon-Meunier ; Ronald R. Yager. Springer Nature, 2022. pp. 294-303 (Communications in Computer and Information Science).

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abstract = "In this article we show a characterization for a gH-differentiable interval-valued function through of properties of the (lateral) differentiability of its length function. Then, we give a procedure to classify a gH-differentiable interval-valued function according to their four types of gH-differentiability. Furthermore, using this classification, we propose a procedure to determine the points at which the sum of two gH-differentiable functions is gH-differentiable as well as to determine their type of gH-differentiability.",

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Blanche-Alcócer, JC & Chalco-Cano, Y 2022, A Characterization for Generalized Hukuhara Differentiable Interval-Valued Functions and Some Rules of Calculus. in D Ciucci, I Couso, J Medina, D Ślęzak, D Petturiti, B Bouchon-Meunier & RR Yager (eds), Information Processing and Management of Uncertainty in Knowledge-Based Systems - 19th International Conference, IPMU 2022, Proceedings. Communications in Computer and Information Science, vol. 1601 CCIS, Springer Nature, pp. 294-303, 19th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2022, Milan, Italy, 11/07/22. https://doi.org/10.1007/978-3-031-08971-8_25

A Characterization for Generalized Hukuhara Differentiable Interval-Valued Functions and Some Rules of Calculus. / Blanche-Alcócer, Juan Carlos; Chalco-Cano, Yurilev.
Information Processing and Management of Uncertainty in Knowledge-Based Systems - 19th International Conference, IPMU 2022, Proceedings. ed. / Davide Ciucci; Inés Couso; Jesús Medina; Dominik Ślęzak; Davide Petturiti; Bernadette Bouchon-Meunier; Ronald R. Yager. Springer Nature, 2022. p. 294-303 (Communications in Computer and Information Science; Vol. 1601 CCIS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Blanche-Alcócer JC, Chalco-Cano Y. A Characterization for Generalized Hukuhara Differentiable Interval-Valued Functions and Some Rules of Calculus. In Ciucci D, Couso I, Medina J, Ślęzak D, Petturiti D, Bouchon-Meunier B, Yager RR, editors, Information Processing and Management of Uncertainty in Knowledge-Based Systems - 19th International Conference, IPMU 2022, Proceedings. Springer Nature. 2022. p. 294-303. (Communications in Computer and Information Science). doi: 10.1007/978-3-031-08971-8_25