Rough Cluster Research Articles

Rough lacunary statistical convergence in neutrosophic normed spaces

In this paper, we address some imprecisions in the definition of neutrosophic normed space proposed by Kirişçi and Şimşek [16], Definition 4. We propose a modification to the definition and introduce the notion of rough lacunary statistical convergence in the neutrosophic normed space. Furthermore, we present the idea of rough lacunary statistical cluster points in neutrosophic normed spaces and investigate the relationship between the set of these cluster points and the set of rough lacunary statistical limit points of the aforementioned convergence.

Rough statistical convergence in neutrosophic normed spaces

Neutrosophic normed spaces, one of the recent hot issues in mathematics, are covered in this paper. The Neutrosophic approach is based on the idea that the degree of uncertainty should be taken into consideration and that it is insufficient to categorise problems in daily life as either right or wrong. This paper proposes double sequences’ rough statistical convergence in Neutrosophic Normed Spaces. It then specifies the rough statistical limit points and cluster points of a double sequence in these spaces. This paper then looks at some of their fundamental characteristics. The necessity for more research is finally covered.

Rough statistical convergence of double sequences in intuitionistic fuzzy normed spaces

This paper proposes rough convergence and rough statistical convergence of a double sequence in intuitionistic fuzzy normed spaces. It then defines the rough statistical limit points and rough statistical cluster points of a double sequence in these spaces. Afterwards, this paper examines some of their basic properties. Finally, it discusses the need for further research.

Investigation on the characteristics and kinetics of isothermal reduction of hematite under simulated coke oven gas atmosphere in rotary bed reactor

The effect of H2–CO ratio, reduction temperature and time on the reduction degree, mineral phase, and morphology of the reduced production was investigated in this study by reducing hematite with coke oven gas (COG) as the reducing agent to alleviate the pressure from the increasing demand of iron ore. The kinetics analysis, reduction mechanism, and deposited carbon behavior were proposed. The results revealed that the reduction degree reached the maximum value of 94.69% at the temperature of 900 °C for 10 min in a simulated COG atmosphere. At 800 °C, the pores and cracks on the surface of the particle became more and wider as the reaction time increased. When the reaction time reached 30 min, massive Fe3C was attached to the surface, and the newly formed spherical metallic irons were bonded to each other and randomly distributed on the surface of the product particles. Besides, the deposited carbon mainly existed in two forms of a rough porous structure and cluster structure when the temperature increased to 900 °C. The hematite reduction process was mixed-controlled by one-dimensional diffusion reaction and three-dimensional interfacial reaction, and the activation energy decreased to 50.79 kJ/mol.

On rough convergence in amenable semigroups and some properties

The authors of the present paper, firstly, investigated relations between the notions of rough convergence and classical convergence, and studied on some properties of the rough convergence notion which the set of rough limit points and rough cluster points of a sequence of functions defined on amenable semigroups. Then, they examined the dependence of r-limit LIMrf of a fixed function f ∈ G on varying parameter r.

Cryokinetics and spin quenching in the N2 adsorption onto rhodium cluster cations

ABSTRACT The kinetics of N2 adsorption onto gas phase Rh i + clusters (i = 5–15) within 26 K He buffer gas have been investigated by Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometry, with particular focus to clusters i = 5,6,7,9. The adsorption limits m = mmax of [Rh i (N2) m ]+ clusters strongly depend on the size of the clusters. Some Rh i + clusters reveal an intermittent adsorption limit mx , which implies a rough cluster surface. Most of the clusters reveal smooth surfaces, which consist of Rh atoms with similar next neighbour coordination. The kinetic fits and relative rate constants reveal the sequential adsorption of N2 as the only significant reaction channel. In some cases, we find N2 desorption steps at high N2 loads indicating adsorption–desorption equilibria. For these steps, we determined Gibbs energies from the relative rate constants. We observed a significant reluctance towards N2 adsorption for the Rh5 + cluster, indicated by significant desorption at low N2 coverage. Our DFT calculations model the energetics of the N2 adsorption onto Rh5 + in terms of coverage dependent ‘spin valley’ curves, and we conclude that an adsorption induced spin quenching takes place upon considerable N2 coverage, m > 4.

Two-Stage Model with Rough Cluster and Salp Optimization Technique for Epistasis Detection

The discovery of gene-gene interactions to identify complex diseases is one of the primary challenges in genome-wide association studies (GWAS). Genetic interactions (Epistasis) are typically seen as interactions between various single nucleotide polymorphisms (SNPs). Genetic interactions discovery can assist the researchers in identifying gene pathways, recognizing gene activity, and discovering potential drug targets. Rough Cluster based Salp Optimization for Epistasis detection (RCSalp-Epi) is a two-stage epistasis model that has been evaluated on a variety of simulated disease models. In the screening stage, the rough clustering algorithm is employed to partition the genotype data into different clusters. The selection stage presents Salp optimization with a single objective function (SalpEpi-SO) and multiple objective functions (SalpEpi-MO) over the clusters to find disease-related SNP combinations. RCSalp-performance Epi's is evaluated in comparison with SalpEpi-SO and SalpEpi-MO. The outcome of the experimental analysis revealed that RCSalp-Epi-MO is superior to SalpEpi-SO and SalpEpi-MO in terms of power and execution time.

Day-ahead wind power forecasting based on the clustering of equivalent power curves

Wind power prediction (WPP) has developed in recent years into a way to solve the strong fluctuation problems that are caused by large-scale integration. Higher prediction accuracy is important to improve power grid security and economy. Wind turbine power curves, which describe the transformation between speed and power output, have been widely applied to WPP. In order to improve the accuracy of the prediction results and reduce the complexity of the model, this research proposes an improved Fuzzy C-means (FCM) Clustering Algorithm for day-ahead wind power prediction to resolve the difference in wind power output. By using the principle of minimum distance to select the relatively rough initial cluster centers of the samples, better clustering results can be obtained. The improved FCM method is used to classify turbines with similar power output characteristics into several categories, and a representative power curve is selected as the equivalent curve of the wind farm. And then capture the performance of the wind turbine. A day-ahead WPP model which utilizes numerical weather predictions (NWPs) as inputs for a subsequent equivalent power curve model is therefore established. The model proposed was validated using historical data taken from two different wind farms located in northeastern China.

When deviation happens between rough statistical convergence and rough weighted statistical convergence

AbstractIn this paper we introduce rough weighted statistical limit set and weighted statistical cluster points set which are natural generalizations of rough statistical limit set and statistical cluster points set of double sequences respectively. Some new examples are constructed to ensure the deviation of basic results. Both the sets don’t follow the usual extension properties which will be discussed here.

On rough convergence in 2-normed spaces and some properties

In this study, we investigated relationships between rough convergence and classical convergence and studied some properties about the notion of rough convergence, the set of rough limit points and rough cluster points of a sequence in 2-normed space. Also, we examined the dependence of r-limit LIMr 2xn of a fixed sequence (xn) on varying parameter r in 2-normed space

Dynamic Ensemble Selection Based on Rough Set Reduction and Cluster Matching

Dynamic Ensemble Selection Based on Rough Set Reduction and Cluster Matching

Characterization of rough weighted statistical limit set

Abstract Our focus is to generalize the definition of the weighted statistical convergence in a wider range of the weighted sequence {tn } n∈ℕ. We extend the concept of weighted statistical convergence and rough statistical convergence to renovate a new concept namely, rough weighted statistical convergence. On a continuation we also define rough weighted statistical limit set. In the year (2008) Aytar established the following results: The diameter of rough statistical limit set of a real sequence is ≤ 2r (where r is the degree of roughness) and in general it has no smaller bound. If the rough statistical limit set is non-empty then the sequence is statistically bounded. If x ∗ and c belong to rough statistical limit set and statistical cluster point set respectively, then |x ∗ − c| ≤ r. We investigate whether the above mentioned three results are satisfied for rough weighted statistical limit set or not? Answer is no. So our main objective is to interpret above mentioned different behaviors of the new convergence and characterize the rough weighted statistical limit set. Also we show that this set satisfies some topological properties like boundedness, compactness, path connectedness etc.

Rough statistical convergence on triple sequences

In this paper, using the concept of natural density, we introduce the notion of rough statistical convergence of triple sequences. We define the set of rough statistical limit points of a triple sequence and obtain rough statistical convergence criteria associated with this set. Later, we prove this set is closed and convex and also examine the relations between the set of rough statistical cluster points and the set of rough statistical limit points of a triple sequence.

Rough statistical cluster points

In this paper, we define the concepts of rough statistical cluster point and rough statistical limit point of a sequence in a finite dimensional normed space. Then we obtain an ordinary statistical convergence criteria associated with rough statistical cluster point of a sequence. Applying these definitions to the sequences of functions, we come across a new concept called statistical condensation point. Finally, we observe the relations between the sets of statistical condensation points, rough statistical cluster points and rough statistical limit points of a sequence of functions.

A classification approach based on variable precision rough sets and cluster validity index function

Purpose – The clustering/classification method proposed in this study, designated as the PFV-index method, provides the means to solve the following problems for a data set characterized by imprecision and uncertainty: first, discretizing the continuous values of all the individual attributes within a data set; second, evaluating the optimality of the discretization results; third, determining the optimal number of clusters per attribute; and fourth, improving the classification accuracy (CA) of data sets characterized by uncertainty. The paper aims to discuss these issues. Design/methodology/approach – The proposed method for the solution of the clustering/classifying problem, designated as PFV-index method, combines a particle swarm optimization algorithm, fuzzy C-means method, variable precision rough sets theory, and a new cluster validity index function. Findings – This method could cluster the values of the individual attributes within the data set and achieves both the optimal number of clusters and the optimal CA. Originality/value – The validity of the proposed approach is investigated by comparing the classification results obtained for UCI data sets with those obtained by supervised classification BPNN, decision-tree methods.

A grey rough set model for evaluation and selection of software cost estimation methods

Purpose – Due to the limitation of acknowledgment, the complexity of software system and the interference of noises, this paper aims to solve the traditional problem: traditional software cost estimation methods face the challenge of poor and uncertain inputs. Design/methodology/approach – Under such circumstances, different cost estimation methods vary greatly on estimation accuracy and effectiveness. Therefore, it is crucial to perform evaluation and selection on estimation methods against a poor information database. This paper presents a grey rough set model by introducing grey system theory into rough set based analysis, aiming for a better choice of software cost estimation method on accuracy and effectiveness. Findings – The results are very encouraging in the sense of comparison among four machine learning techniques and thus indicate it an effective approach to evaluate software cost estimation method where insufficient information is provided. Practical implications – Based on the grey rough set model, the decision targets can be classified approximately. Furthermore, the grey of information and the limitation of cognition can be overcome during the use of the grey rough interval correlation cluster method. Originality/value – This paper proposed the grey rough set model combining grey system theory with rough set for software cost estimation method evaluation and selection.

Rough Set based Attribute Clustering for Sample Classification of Gene Expression Data

Attribute clustering is one of the unsupervised data mining applications which have been previously used to identify statistical dependence between subsets of variables where the attributes within the same cluster have high similarity, but within different clusters have high dissimilarity. In this paper, we focus our discussion on the rough set theory for attribute clustering. Rough set theory is a theory adopted to deal with rough and uncertain knowledge, which analyzes the clusters and finds the data principles when previous knowledge is not available, providing a new method for data classification. Although there are numerous methods of rough set and cluster analysis, as the data objects are changing continuously, we have to improve these relevant technologies over time, and propose creative theory in response, meeting the demands of application. Lastly, the experimental result of our proposed algorithm Rough Set based attribute Clustering for Sample Classification (RSCSC) is compared with some of the traditional attribute clustering methods and it is proved to be efficient in finding the meaningful, feasible and compact patterns.

Rough C-means and Fuzzy Rough C-means for Colour Quantisation

Colour quantisation algorithms are essential for displaying true colour images using a limited palette of distinct colours. The choice of a good colour palette is crucial as it directly determines the quality of the resulting image. Colour quantisation can also be seen as a clustering problem where the task is to identify those clusters that best represent the colours in an image. In this paper we propose rough c-means and fuzzy rough c-means clustering algorithms for colour quantisation of images. Both approaches utilise the concept of lower and upper approximations of clusters to define palette colours. While in the rough c-means approach cluster centroids are refined iteratively through a linear combination of elements of the lower and upper approximations, the fuzzy rough c-means technique assigns variable membership values to the elements in the boundary region which in turn are incorporated into the calculation of cluster centres. Experimental results on a standard set of images show that these approaches performs significantly better than other, purpose built colour quantisation algorithms.

Rough clustering

AbstractTraditional clustering partitions a group of objects into a number of nonoverlapping sets based on a similarity measure. In real world, the boundaries of these sets or clusters may not be clearly defined. Some of the objects may be almost equidistant from the center of multiple clusters. Traditional set theory mandates that these objects be assigned to a single cluster. Rough set theory can be used to represent the overlapping clusters. Rough sets provide more flexible representation than conventional sets, at the same time they are less descriptive than the fuzzy sets. This paper describes the basic concept of rough clustering based on k‐means, genetic algorithms, Kohonen self‐organizing maps, and support vector clustering. The discussion also includes a review of rough cluster validity measures, and applications of rough clustering to such diverse areas as forestry, medicine, medical imaging, web mining, super markets, and traffic engineering. © 2011 John Wiley & Sons, Inc. WIREs Data Mining Knowl Discov 2011 1 64‐72 DOI: 10.1002/widm.16This article is categorized under: Technologies > Computational Intelligence Technologies > Machine Learning Technologies > Structure Discovery and Clustering

Methodology study of classification algorithm in traditional Chinese medicine syndrome study

Study of traditional Chinese medicine (TCM) syndromes is a key to the research of TCM modernization, and the core is the classification and diagnostic criteria of syndromes. The purpose of this article is to review the usage of classification algorithms of data mining in TCM syndrome researches, and comprehensively analyze the main features of algorithms and their applications. The appropriate classification algorithm should be chosen according to different research purposes. Rough sets and cluster analysis are suitable for exploratory research without requiring a prior knowledge. Fuzzy sets theory, neural networks and decision tree are suitable for syndrome diagnostic criteria research when the classification goal is clear, because they require a prior knowledge. Among them, fuzzy sets theory could be used in combination with other classification algorithms. Thus, some new methods such as fuzzy clustering, fuzzy rough sets or fuzzy decision tree might be more suitable for TCM algorithm classification research. It is suggested that some novel classification algorithms need to be developed to fit the condition of TCM syndrome, based on the interdisciplinary theories and technologies.