in this paper, we propose a new method for fuzzy numbers. in this method, we assume that ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. so, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. then, mic and mis that are to be the convex combinations and the standard deviation respectively we acquire them from these components. finally,...

Recently, a general class of the Hermit--Hadamard-Fejer inequality on convex functions is studied in [H. Budak, March 2019, 74:29, textit{Results in Mathematics}]. In this paper, we establish a generalization of Hermit--Hadamard--Fejer inequality for fractional integral based on co-ordinated convex functions.Our results generalize and improve several inequalities obtained in earlier studies.

In this paper, we obtain Jensen’s inequality for GG-convex functions. Also, we get in- equalities alike to Hermite-Hadamard inequality for GG-convex functions. Some examples are given.

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

in this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. so the results in locally convex spaces can be translated in gradual normed linear spaces. finally, we give an examp...

this paper uses integrated data envelopment analysis (dea) models to rank all extreme and non-extreme efficient decision making units (dmus) and then applies integrated dea ranking method as a criterion to modify genetic algorithm (ga) for finding pareto optimal solutions of a multi objective programming (mop) problem. the researchers have used ranking method as a shortcut way to modify ga to d...

Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.

In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

In this paper, a local approach to the concept of Hudetz $g$-entropy is presented. The introduced concept is stated in terms of Hudetz $g$-entropy. This representation is based on the concept of $g$-ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.

In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...