On invariant arithmetic statistically convergence via weighted density

In this paper, our concern is to introduce the concepts of invariant arithmetic convergence, invariant arithmetic statistically convergence and lacunary invariant arithmetic statistically convergence using weighted density via Orlicz function φe. Finally, we give some relations between lacunary invariant arithmetic statistical φe-convergence and invariant arithmetic statistical φe-convergence via weighted density

On invariant arithmetic statistically convergence via weighted density

In this paper, our concern is to introduce the concepts of invariant arithmetic convergence, invariant arithmetic statistically convergence and lacunary invariant arithmetic statistically convergence using weighted density via Orlicz function φe. Finally, we give some relations between lacunary invariant arithmetic statistical φe-convergence and invariant arithmetic statistical φe-convergence via weighted density.

WEIGHTED STATISTICAL CONVERGENCE OF REAL VALUED SEQUENCES

Functions defined in the form ``$g:\mathbb{N}\to[0,\infty)$ such that $\lim_{n\to\infty}g(n)=\infty$ and $\lim_{n\to\infty}\frac{n}{g(n)}=0$'' are called weight functions. Using the weight function, the concept of weighted density, which is a generalization of natural density, was defined by Balcerzak, Das, Filipczak and Swaczyna in the paper ``Generalized kinsd of density and the associated ideals'', Acta Mathematica Hungarica 147(1) (2015), 97-115.In this study, the definitions of $g$-statistical convergence and $g$-statisticalCauchy sequence for any weight function $g$ are given and it is proved that these two concepts are equivalent. Also some inclusions of the sets of all weight $g_1$-statistical convergent and weight $g_2$-statistical convergent sequences for $g_1,g_2$ which have the initial conditions are given.

An Intuitionistic Fuzzy Approach With Rough Entropy Measure to Detect Outliers in Two Universal Sets

The process of recognizing patterns, collecting knowledge from massive databases is called data mining. An object which does not obey and deviates from other objects by their characteristics or behavior are known as outliers. Research works carried out so far on outlier detection were focused only on numerical data, categorical data, and in single universal sets. The main goal of this article is to detect outliers significant in two universal sets by applying the intuitionistic fuzzy cut relationship based on membership and non-membership values. The proposed method, weighted density outlier detection, is based on rough entropy, and is employed to detect outliers. Since it is unsupervised, without considering class labels of decision attributes, weighted density values for all conditional attributes and objects are calculated to detect outliers. For experimental analysis, the Iris dataset from the UCI repository is taken to detect outliers, and comparisons have been made with existing algorithms to prove its efficiency.