In this paper, we proposed a new interval-valued approximation of interval-valued fuzzy numbers, which is the best one with respect to a certain measure of distance between interval-valued fuzzy numbers. Also, a set of criteria for interval-valued approximation operators is suggested.

Abstract In this article, the notion of interval-valued preinvex functions involving Riemann–Liouville fractional integral is described. By applying this, some new refinements Hermite–Hadamard inequality for operator are presented. Some novel special cases presented results discussed as well. Also, examples to validate our results. The established outcomes article may open another direction dif...

The main objective of this paper is to introduce a new class convexity called left-right–bi-convex fuzzy interval-valued functions. We study from the perspective fractional Hermite–Hadamard inequalities, involving integral left-right–AB integral. discuss several special cases that demonstrate our results are quite unifying. provide non-trivial numerical examples regarding means for positive rea...

In this article, the concepts of gH-subgradient and gH-subdifferential interval-valued functions are illustrated. Several important characteristics a convex function, e.g., closeness, boundedness, chain rule, etc. studied. Alongside, we prove that gH-differentiable function contains only gH-gradient. It is observed directional gH-derivative maximum all products between gH-subgradients direction...

In this paper, the notions of post-quantum integrals for two-variable interval-valued functions are presented. The newly described then used to prove some new Hermite–Hadamard inclusions co-ordinated convex functions. Many findings in paper important extensions previous literature. Finally, we present a few examples our findings. Analytic inequalities nature and especially techniques involved h...

In this paper, we shall discuss a newly introduced concept of center-radius total-ordered relations between two intervals. Here, address the Hermite–Hadamard-, Fejér- and Pachpatte-type inequalities by considering interval-valued Riemann–Liouville fractional integrals. Interval-valued for new class preinvexity, i.e., cr-h-preinvexity, are estimated. The operator is used first time to prove such...

Several extensions of Loewner’s theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalarto matrix-valued functions of an operator argument. A notion of κ-monotonicity is introduced and characterized in terms of classical ...