Related papers: Expansion of Generalized Hukuhara Differentiable I…
In this paper we propose a new concept of differentiability for interval-valued functions. This concept is based on the properties of the Hausdorff-Pompeiu metric and avoids using the generalized Hukuhara difference.
This paper deals with the new concept of interval whose both the bounds themselves are also intervals. We name this new type of interval as Type-2 interval. Here we have introduced Type-2 interval-valued function and its properties. To…
In this article, the concepts of gH-subgradients and gH-subdifferentials of interval-valued functions are illustrated. Several important characteristics of the gH-subdifferential of a convex interval-valued function, e.g., closeness,…
In this paper, we provide a comprehensive investigation of the generalized Hukuhara nabla derivative for fuzzy functions on time scales. We establish some characterizations of generalized Hukuhara nabla differentiable fuzzy functions on…
In this paper, we discuss existence of Hukuhara differentiability of fuzzy-valued functions. Several examples are worked out to check that fuzzy-valued functions are one time, two times and n-times H-differentiable. We study the effects of…
This paper investigates the generalized Hukuhara differentiability of fuzzy number-valued functions on arbitrary time scales using delta calculus. By carefully examining and improving existing results, we develop a unified and complete…
In this paper, we define generalized Hukuhara diamond-alpha integral for fuzzy functions on time scales and obtain some of its fundamental properties and also we establish the relationship between diamond-alpha differentiation and…
In this article, the notion of gH-Clarke derivative for interval-valued functions is proposed. To define the concept of gH-Clarke derivatives, the concepts of limit superior, limit inferior, and sublinear interval-valued functions are…
In this paper, we show that generalized Hukuhara directional differentiability of an interval-valued function (IVF) defined on Riemannian manifolds is not equivalent to the directional differentiability of its center and half-width…
Gradual numbers have been introduced recently as a means of extending standard interval computation methods to fuzzy intervals. The literature treats monotonic functions of fuzzy intervals. In this paper, we combine the concepts of gradual…
We consider fuzzy valued functions from two parametric representations of $\alpha$-level sets. New concepts are introduced and compared with available notions. Following the two proposed approaches, we study fuzzy differential equations.…
In this paper, we obtain a version of Ekeland's variational principle for interval-value functions by means of the Dancs-Hegedus-Medvegyev theorem [14]. We also derive two versions of Ekeland's variational principle involving the…
We present some properties of the gradient of a mu-differentiable function. The Method of Lagrange Multipliers for mu-differentiable functions is then exemplified.
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…
This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…
In this paper, we first study the arithmetic properties of intuitionistic fuzzy number, the monotonicity of intuitionistic fuzzy function and the derivative of intuitionistic fuzzy functions and then we study the fundamental properties on…
We introduce and investigate the concept of harmonical $h$-convexity for interval-valued functions. Under this new concept, we prove some new Hermite-Hadamard type inequalities for the interval Riemann integral.
This paper introduces the extended set difference, a generalization of the Hukuhara and generalized Hukuhara differences, defined for compact convex sets in $\mathbb{R}^d$. The proposed difference guarantees existence for any pair of such…
In this paper we extend the refined second-order Poincar\'e inequality for Poisson functionals from a one-dimensional to a multi-dimensional setting. Its proof is based on a multivariate version of the Malliavin-Stein method for normal…
In this paper we develop the idea of abstract homogeneity in the context of interval-valued (IV) functions endowed with admissible orders and investigate some of its properties.