Pseudo-ordering and $ \delta^{1} $-level mappings: A study in fuzzy interval convex analysis

Muhammad Zakria Javed; Muhammad Uzair Awan; Loredana Ciurdariu; Omar Mutab Alsalami; Muhammad Zakria Javed; Muhammad Uzair Awan; Loredana Ciurdariu; Omar Mutab Alsalami

doi:10.3934/math.2025327

AIMS Mathematics

2025, Volume 10, Issue 3: 7154-7190. doi: 10.3934/math.2025327

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Research article

Pseudo-ordering and $ \delta^{1} $-level mappings: A study in fuzzy interval convex analysis

1.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
2.
Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania
3.
Department of Electrical Engineering, College of Engineering, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 31 December 2024 Revised: 14 March 2025 Accepted: 20 March 2025 Published: 28 March 2025
MSC : 26A51, 26D07, 26D10, 26D15, 26D20

This work utilized the concepts of fuzzy interval analysis and convexity to explore some novel refinements of classical counterparts. The main goal was to look into a type of strong convexity that connected the ideas of pseudo-ordering, $ \delta^{1} $-level mappings, and the control function $ \hslash_{\circ} $. This type of mapping is called a fuzzy number-valued $ \hslash_{\circ} $-super-quadratic mapping. An interesting fact is that all the function classes extracted from this class were new and novel and quite useful in the optimization and approximation theory. We assessed this class of functions pertaining to essential properties, examples, and various integral inequalities such as Jensen's, reverse Jensen's, Jensen-Mercer, Hermite-Hadamard and Fejer's like inequalities in the classical, and fractional framework. Furthermore, we delivered the accuracy of our findings through graphical and tabular approaches, particularly a novel application for means.
- fuzzy convex mappings,
- Super-quadratic mappings,
- Jensen's inequality,
- Jensen-Mercer's inequality,
- Hermite-Hadamard's inequality,
- Fejer's inequality
Citation: Muhammad Zakria Javed, Muhammad Uzair Awan, Loredana Ciurdariu, Omar Mutab Alsalami. Pseudo-ordering and $ \delta^{1} $-level mappings: A study in fuzzy interval convex analysis[J]. AIMS Mathematics, 2025, 10(3): 7154-7190. doi: 10.3934/math.2025327

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Abstract

This work utilized the concepts of fuzzy interval analysis and convexity to explore some novel refinements of classical counterparts. The main goal was to look into a type of strong convexity that connected the ideas of pseudo-ordering, $ \delta^{1} $-level mappings, and the control function $ \hslash_{\circ} $. This type of mapping is called a fuzzy number-valued $ \hslash_{\circ} $-super-quadratic mapping. An interesting fact is that all the function classes extracted from this class were new and novel and quite useful in the optimization and approximation theory. We assessed this class of functions pertaining to essential properties, examples, and various integral inequalities such as Jensen's, reverse Jensen's, Jensen-Mercer, Hermite-Hadamard and Fejer's like inequalities in the classical, and fractional framework. Furthermore, we delivered the accuracy of our findings through graphical and tabular approaches, particularly a novel application for means.

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