Some Certain Fuzzy Fractional Inequalities for Up and Down ℏ-Pre-Invex via Fuzzy-Number Valued Mappings
Muhammad Bilal Khan, Adriana Cătaş, Najla M. Aloraini, Mohamed S. Soliman
Abstract
In this study, we apply a recently developed idea of up and down fuzzy-ordered relations between two fuzzy numbers. Here, we consider fuzzy Riemann–Liouville fractional integrals to establish the Hermite–Hadamard-, Fejér-, and Pachpatte-type inequalities. We estimate fuzzy fractional inequalities for a newly introduced class of ℏ-preinvexity over fuzzy-number valued settings. For the first time, such inequalities involving up and down fuzzy-ordered functions are proven using the fuzzy fractional operator. The stated inequalities are supported by a few numerical examples that will be helpful to validate our main results.
Topics & Concepts
MathematicsFuzzy logicFuzzy measure theoryFuzzy numberHermite polynomialsClass (philosophy)InequalityOperator (biology)Fuzzy subalgebraApplied mathematicsPure mathematicsAlgebra over a fieldFuzzy setMathematical analysisComputer scienceArtificial intelligenceGeneRepressorChemistryBiochemistryTranscription factorMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsFuzzy Systems and Optimization