In recent years, due to the growing demand for computational resources, particularly in cloud computing systems, the data centers’ energy consumption is continually increasing, which directly causes price rise and reductions of resources’ productivity. Although many energy‐aware approaches attempt to minimize the consumption of energy, they cannot minimize the violation of service‐level agreements at the same time. In this paper, we propose a method using a granular neural network, which is used to model data processing. This method identifies the physical hosts’ workloads before the overflow and can improve energy consumption while also reducing violation of service‐level agreements. Unlike the other techniques that use a single criterion, namely, worked on the basis of the history of using the processor, we simultaneously use all the productivity rates criteria, that is, processor productivity rates, main memory, and bandwidth. Extensive real‐world simulations using the CloudSim simulator show the high efficiency of the proposed algorithm.
Multigranularity data analysis has recently become an active research topic in the intelligent computing and data mining fields. Feature selection via multigranularity data analysis is an effective tool for characterizing hierarchical data and enhancing the accuracy of the results. Although the multigranularity data analysis method has been widely adopted for feature selection, existing studies still present one prevalent disadvantage: multigranularity data analysis mostly focuses on information presented at a single granularity while ignoring the hierarchical structure of multigranularity data, which is contrary to the nature of multigranularity. Hence, this article proposes a multigranularity data analysis with a zentropy uncertainty measure for efficient and robust feature selection. Specifically, a consistent degree is first introduced to obtain optimal granularity combinations and establish an efficient neighborhood model for multigranularity information processing. Then, a novel and robust uncertainty measure is developed by integrating the multigranularity information, namely the zentropy-based measure. Considering its accuracy among uncertainty measures, two important measures are further designed and applied to feature selection. Extensive experiments demonstrate that the proposed method can achieve better robustness and classification performance than other state-of-the-art methods.
A problem of handling fuzzy quantities in a process of knowledge acquisition and deriving an inference mechanism by means of fuzzy relation equations is studied in extensive way. It is clearly pointed out that both of them are closely related and correspond to various types of fuzzy relation equations that are considered. Their relevance to the form of knowledge collected is also indicated. A problem of dimension reduction of a knowledge base is considered as well. Two modes of the use of the knowledge base (goal‐, and data‐driven) are also studied.
An important issue to bear in mind in Group Decision Making situations is that of consistency. However, the expression of consistent preferences is often a very difficult task for the decision makers, specially in decision problems with a high number of alternatives and when decision makers use fuzzy preference relations to provide their opinions. It leads to situations where a decision maker may not be able to express all his/her preferences properly and without contradiction. To overcome this problem, we propose the concept of the information granularity being regarded as an important and useful asset supporting the goal to reach consistent fuzzy preference relations. To do so, we develop a concept of granular fuzzy preference relation where each pairwise comparison is formed as a certain information granule instead of a single numeric value. As being more abstract, the granular format of the preference model offers the required flexibility to increase the level of consistency.
Big data with a large number of observations (samples) have posed genuine challenges for fuzzy clustering algorithms and fuzzy C-means (FCM), in particular. In this article, we propose an original algorithm referred to as a hyperplane division method to split the entire data set into disjoint subsets. By disjoint subsets, we mean that the data subspaces (parts of the entire data space), each of which is supported or spanned by the data points in the corresponding subset, do not overlap each other. The disjoint subsets turned out to be beneficial to the improvement of the quality of the clusters formed by the clustering algorithms. Moreover, considering that either a large number (say, thousands) or a small number (say, a few) of clusters may be pursued in the clustering task, we propose corresponding strategies (based on the hyperplane division method) to make clustering processes feasible, efficient, and effective. By validating the proposed strategies on both synthetic and publicly available data, we show their superiority (in terms of both efficiency and effectiveness) manifested in a visible way over the method of clustering the entire data and over some representative big data clustering methods.
Shadowed sets provide a meaningful description of information granules by abstracting the corresponding fuzzy sets into three categories: full acceptance, full rejection, and uncertain (represented by shadows). One of the main motivating points to derive shadowed sets from fuzzy sets is the determination and explanation of the separation thresholds based on a specific optimization mechanism. The available optimization objective functions are mainly discussed on semantic interpretations and their mathematical properties; constructive algorithms for optimal solutions have rarely been reported. In this paper, the continuous and convex properties of Pedrycz's optimization objective function to construct shadowed sets, as well as the existence and uniqueness of solution points, are analyzed in detail. It is demonstrated that different approximation region partitions would be generated even under the same optimization model, which requires further criteria to make the constructed shadowed sets well-defined. To address this limitation, the notions of passive and active constrained shadowed sets are introduced. A fast algorithm to obtain the proposed constrained shadowed sets is also designed based on the analyzed mathematical properties. Its performance is then illustrated by some typical fuzzy sets and some real data from the UCI repository.
In this paper we deal with fuzzy numbers that modelize uncertain quantities present in many fields of applications, such as man‐machine systems. Main attention is paid to inverse operations for fuzzy numbers which allow one to solve equations or systems of equations with fuzzy numbers. The relevance of the method proposed for the determination of parameters of fuzzy models is also stressed.
