Order relations, convexities, and Jensen’s integral inequalities in interval and fuzzy spaces

Tiago Mendonça da Costa; Yurilev Chalco-Cano; Laécio Carvalho de Barros; Geraldo Nunes Silva

doi:10.1007/978-3-319-95312-0_39

Order relations, convexities, and Jensen’s integral inequalities in interval and fuzzy spaces

Tiago Mendonça da Costa
, Yurilev Chalco-Cano
, Laécio Carvalho de Barros
, Geraldo Nunes Silva

Department of Mathematics

Universidade Federal do Pará
Universidade Estadual de Campinas
Universidade Estadual Paulista Júlio de Mesquita Filho

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

3 Scopus citations

Abstract

This study presents new interval and fuzzy versions of the Jensen’s integral inequality, which extend the classical Jensen’s integral inequality for real-valued functions, using Aumann and Kaleva integrals. The inequalities for interval-valued functions are interpreted through the preference order relations given by Ishibuchi and Tanaka, which are useful for dealing with interval optimization problems. The order relations adopted in the space of fuzzy intervals are extensions of those considered the interval spaces.

Original language	English
Title of host publication	Fuzzy Information Processing - 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018, Proceedings
Editors	Guilherme A. Barreto, Ricardo Coelho
Publisher	Springer Nature
Pages	450-463
Number of pages	14
ISBN (Print)	9783319953113
DOIs	https://doi.org/10.1007/978-3-319-95312-0_39
State	Published - 2018
Event	37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018 - Fortaleza, Brazil Duration: 4 Jul 2018 → 6 Jul 2018

Publication series

Name	Communications in Computer and Information Science
Volume	831
ISSN (Print)	1865-0929

Conference

Conference	37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018
Country/Territory	Brazil
City	Fortaleza
Period	4/07/18 → 6/07/18

Keywords

Fuzzy-interval-valued functions
Interval-valued functions
Jensen’s integral inequality

Access to Document

10.1007/978-3-319-95312-0_39

Cite this

da Costa, T. M., Chalco-Cano, Y., de Barros, L. C., & Silva, G. N. (2018). Order relations, convexities, and Jensen’s integral inequalities in interval and fuzzy spaces. In G. A. Barreto, & R. Coelho (Eds.), Fuzzy Information Processing - 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018, Proceedings (pp. 450-463). (Communications in Computer and Information Science; Vol. 831). Springer Nature. https://doi.org/10.1007/978-3-319-95312-0_39

da Costa, Tiago Mendonça ; Chalco-Cano, Yurilev ; de Barros, Laécio Carvalho et al. / Order relations, convexities, and Jensen’s integral inequalities in interval and fuzzy spaces. Fuzzy Information Processing - 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018, Proceedings. editor / Guilherme A. Barreto ; Ricardo Coelho. Springer Nature, 2018. pp. 450-463 (Communications in Computer and Information Science).

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abstract = "This study presents new interval and fuzzy versions of the Jensen{\textquoteright}s integral inequality, which extend the classical Jensen{\textquoteright}s integral inequality for real-valued functions, using Aumann and Kaleva integrals. The inequalities for interval-valued functions are interpreted through the preference order relations given by Ishibuchi and Tanaka, which are useful for dealing with interval optimization problems. The order relations adopted in the space of fuzzy intervals are extensions of those considered the interval spaces.",

keywords = "Fuzzy-interval-valued functions, Interval-valued functions, Jensen{\textquoteright}s integral inequality",

author = "\{da Costa\}, \{Tiago Mendon{\c c}a\} and Yurilev Chalco-Cano and \{de Barros\}, \{La{\'e}cio Carvalho\} and Silva, \{Geraldo Nunes\}",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018 ; Conference date: 04-07-2018 Through 06-07-2018",

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da Costa, TM, Chalco-Cano, Y, de Barros, LC & Silva, GN 2018, Order relations, convexities, and Jensen’s integral inequalities in interval and fuzzy spaces. in GA Barreto & R Coelho (eds), Fuzzy Information Processing - 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018, Proceedings. Communications in Computer and Information Science, vol. 831, Springer Nature, pp. 450-463, 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018, Fortaleza, Brazil, 4/07/18. https://doi.org/10.1007/978-3-319-95312-0_39

Order relations, convexities, and Jensen’s integral inequalities in interval and fuzzy spaces. / da Costa, Tiago Mendonça; Chalco-Cano, Yurilev; de Barros, Laécio Carvalho et al.
Fuzzy Information Processing - 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018, Proceedings. ed. / Guilherme A. Barreto; Ricardo Coelho. Springer Nature, 2018. p. 450-463 (Communications in Computer and Information Science; Vol. 831).

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

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AU - Chalco-Cano, Yurilev

AU - de Barros, Laécio Carvalho

AU - Silva, Geraldo Nunes

N1 - Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - This study presents new interval and fuzzy versions of the Jensen’s integral inequality, which extend the classical Jensen’s integral inequality for real-valued functions, using Aumann and Kaleva integrals. The inequalities for interval-valued functions are interpreted through the preference order relations given by Ishibuchi and Tanaka, which are useful for dealing with interval optimization problems. The order relations adopted in the space of fuzzy intervals are extensions of those considered the interval spaces.

AB - This study presents new interval and fuzzy versions of the Jensen’s integral inequality, which extend the classical Jensen’s integral inequality for real-valued functions, using Aumann and Kaleva integrals. The inequalities for interval-valued functions are interpreted through the preference order relations given by Ishibuchi and Tanaka, which are useful for dealing with interval optimization problems. The order relations adopted in the space of fuzzy intervals are extensions of those considered the interval spaces.

KW - Fuzzy-interval-valued functions

KW - Interval-valued functions

KW - Jensen’s integral inequality

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A2 - Barreto, Guilherme A.

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da Costa TM, Chalco-Cano Y, de Barros LC, Silva GN. Order relations, convexities, and Jensen’s integral inequalities in interval and fuzzy spaces. In Barreto GA, Coelho R, editors, Fuzzy Information Processing - 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018, Proceedings. Springer Nature. 2018. p. 450-463. (Communications in Computer and Information Science). doi: 10.1007/978-3-319-95312-0_39

Order relations, convexities, and Jensen’s integral inequalities in interval and fuzzy spaces

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