New fuzzy-interval inequalities in fuzzy-interval fractional calculus by means of fuzzy order relation
It is well-known that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis and fuzzy-interval analysis, t...
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| Published in | AIMS mathematics Vol. 6; no. 10; pp. 10964 - 10988 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
AIMS Press
2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2473-6988 2473-6988 |
| DOI | 10.3934/math.2021637 |
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| Abstract | It is well-known that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis and fuzzy-interval analysis, the inclusion relation (⊆) and fuzzy order relation $\left(\preccurlyeq \right)$ both are two different concepts, respectively. In this article, with the help of fuzzy order relation, we introduce fractional Hermite-Hadamard inequality ( HH -inequality) for h -convex fuzzy-interval-valued functions ( h -convex-IVFs). Moreover, we also establish a strong relationship between h -convex fuzzy-IVFs and Hermite-Hadamard Fejér inequality ( HH -Fejér inequality) via fuzzy Riemann Liouville fractional integral operator. It is also shown that our results include a wide class of new and known inequalities for h -convex fuzz-IVFs and their variant forms as special cases. Nontrivial examples are presented to illustrate the validity of the concept suggested in this review. This paper's techniques and approaches may serve as a springboard for further research in this field. |
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| AbstractList | It is well-known that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis and fuzzy-interval analysis, the inclusion relation (⊆) and fuzzy order relation (≼) both are two different concepts, respectively. In this article, with the help of fuzzy order relation, we introduce fractional Hermite-Hadamard inequality (HH-inequality) for h-convex fuzzy-interval-valued functions (h-convex-IVFs). Moreover, we also establish a strong relationship between h-convex fuzzy-IVFs and Hermite-Hadamard Fejér inequality (HH-Fejér inequality) via fuzzy Riemann Liouville fractional integral operator. It is also shown that our results include a wide class of new and known inequalities for h-convex fuzz-IVFs and their variant forms as special cases. Nontrivial examples are presented to illustrate the validity of the concept suggested in this review. This paper's techniques and approaches may serve as a springboard for further research in this field. It is well-known that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis and fuzzy-interval analysis, the inclusion relation (⊆) and fuzzy order relation $\left(\preccurlyeq \right)$ both are two different concepts, respectively. In this article, with the help of fuzzy order relation, we introduce fractional Hermite-Hadamard inequality ( HH -inequality) for h -convex fuzzy-interval-valued functions ( h -convex-IVFs). Moreover, we also establish a strong relationship between h -convex fuzzy-IVFs and Hermite-Hadamard Fejér inequality ( HH -Fejér inequality) via fuzzy Riemann Liouville fractional integral operator. It is also shown that our results include a wide class of new and known inequalities for h -convex fuzz-IVFs and their variant forms as special cases. Nontrivial examples are presented to illustrate the validity of the concept suggested in this review. This paper's techniques and approaches may serve as a springboard for further research in this field. |
| Author | Noor, Muhammad Aslam Noor, Khalida Inayat Khan, Muhammad Bilal Mohammed, Pshtiwan Othman Alsharif, Abdullah M. |
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| SubjectTerms | fuzzy-interval riemann liouville fractional integral operator h-convex fuzzy-interval-valued function hermite-hadamard fejér inequality hermite-hadamard inequality |
| Title | New fuzzy-interval inequalities in fuzzy-interval fractional calculus by means of fuzzy order relation |
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