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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2021
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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) |
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DOAJ |
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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 |
_version_ |
1718439578001473536 |