Fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions

In this study, we introduce and study new fuzzy-interval integral is known as fuzzy-interval double integral, where the integrand is fuzzy-interval-valued functions (FIVFs). Also, some fundamental properties are also investigated. Moreover, we present a new class of convex fuzzy-interval-valued func...

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Autores principales: Muhammad Bilal Khan, Pshtiwan Othman Mohammed, Muhammad Aslam Noor, Khadijah M. Abualnaja
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Publicado: AIMS Press 2021
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Acceso en línea:https://doaj.org/article/41dc40edb30945a39869b587c8d7858a
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spelling oai:doaj.org-article:41dc40edb30945a39869b587c8d7858a2021-11-11T01:56:35ZFuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions10.3934/mbe.20213251551-0018https://doaj.org/article/41dc40edb30945a39869b587c8d7858a2021-07-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021325?viewType=HTMLhttps://doaj.org/toc/1551-0018In this study, we introduce and study new fuzzy-interval integral is known as fuzzy-interval double integral, where the integrand is fuzzy-interval-valued functions (FIVFs). Also, some fundamental properties are also investigated. Moreover, we present a new class of convex fuzzy-interval-valued functions is known as coordinated convex fuzzy-interval-valued functions (coordinated convex FIVFs) through fuzzy order relation (FOR). The FOR (≼) and fuzzy inclusion relation (⊇) are two different concepts. With the help of fuzzy-interval double integral and FOR, we have proved that coordinated convex fuzzy-IVF establish a strong relationship between Hermite-Hadamard (HH-) and Hermite-Hadamard-Fejér (HH-Fejér) inequalities. With the support of this relation, we also derive some related HH-inequalities for the product of coordinated convex FIVFs. Some special cases are also discussed. Useful examples that verify the applicability of the theory developed in this study are presented. The concepts and techniques of this paper may be a starting point for further research in this area.Muhammad Bilal KhanPshtiwan Othman Mohammed Muhammad Aslam NoorKhadijah M. Abualnaja AIMS Pressarticlefuzzy-interval-valued functionfuzzy double integralcoordinated convex fuzzy-interval-valued functionhermite-hadamard inequalityhermite-hadamard-fejér inequalityBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 6552-6580 (2021)
institution DOAJ
collection DOAJ
language EN
topic fuzzy-interval-valued function
fuzzy double integral
coordinated convex fuzzy-interval-valued function
hermite-hadamard inequality
hermite-hadamard-fejér inequality
Biotechnology
TP248.13-248.65
Mathematics
QA1-939
spellingShingle fuzzy-interval-valued function
fuzzy double integral
coordinated convex fuzzy-interval-valued function
hermite-hadamard inequality
hermite-hadamard-fejér inequality
Biotechnology
TP248.13-248.65
Mathematics
QA1-939
Muhammad Bilal Khan
Pshtiwan Othman Mohammed
Muhammad Aslam Noor
Khadijah M. Abualnaja
Fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions
description In this study, we introduce and study new fuzzy-interval integral is known as fuzzy-interval double integral, where the integrand is fuzzy-interval-valued functions (FIVFs). Also, some fundamental properties are also investigated. Moreover, we present a new class of convex fuzzy-interval-valued functions is known as coordinated convex fuzzy-interval-valued functions (coordinated convex FIVFs) through fuzzy order relation (FOR). The FOR (≼) and fuzzy inclusion relation (⊇) are two different concepts. With the help of fuzzy-interval double integral and FOR, we have proved that coordinated convex fuzzy-IVF establish a strong relationship between Hermite-Hadamard (HH-) and Hermite-Hadamard-Fejér (HH-Fejér) inequalities. With the support of this relation, we also derive some related HH-inequalities for the product of coordinated convex FIVFs. Some special cases are also discussed. Useful examples that verify the applicability of the theory developed in this study are presented. The concepts and techniques of this paper may be a starting point for further research in this area.
format article
author Muhammad Bilal Khan
Pshtiwan Othman Mohammed
Muhammad Aslam Noor
Khadijah M. Abualnaja
author_facet Muhammad Bilal Khan
Pshtiwan Othman Mohammed
Muhammad Aslam Noor
Khadijah M. Abualnaja
author_sort Muhammad Bilal Khan
title Fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions
title_short Fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions
title_full Fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions
title_fullStr Fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions
title_full_unstemmed Fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions
title_sort fuzzy integral inequalities on coordinates of convex fuzzy interval-valued functions
publisher AIMS Press
publishDate 2021
url https://doaj.org/article/41dc40edb30945a39869b587c8d7858a
work_keys_str_mv AT muhammadbilalkhan fuzzyintegralinequalitiesoncoordinatesofconvexfuzzyintervalvaluedfunctions
AT pshtiwanothmanmohammed fuzzyintegralinequalitiesoncoordinatesofconvexfuzzyintervalvaluedfunctions
AT muhammadaslamnoor fuzzyintegralinequalitiesoncoordinatesofconvexfuzzyintervalvaluedfunctions
AT khadijahmabualnaja fuzzyintegralinequalitiesoncoordinatesofconvexfuzzyintervalvaluedfunctions
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