Maximum entropy of random permutation set

Deng, Jixiang; Deng, Yong

doi:10.1007/s00500-022-07351-x

Cited by 53 publications

(8 citation statements)

References 53 publications

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“…Though the entropy of RPS is introduced, there is a lack of in-depth analysis regarding its maximum entropy. Therefore, Deng and Deng (Deng and Deng, 2022) presented an analytical expression for the maximum entropy of RPS as well as its PMF condition. Theorem 2 (Maximum RPS entropy (Deng and Deng, 2022)).…”

Section: Rps Entropymentioning

confidence: 99%

“…Therefore, Deng and Deng (Deng and Deng, 2022) presented an analytical expression for the maximum entropy of RPS as well as its PMF condition. Theorem 2 (Maximum RPS entropy (Deng and Deng, 2022)). Given a PES:…”

Section: Rps Entropymentioning

confidence: 99%

“…1, for a sample space whose cardinality is N , the envelope of Shannon entropy of a probability distribution is N , while in a power set whose maximum cardinality of its subsets is N , the envelope of Deng entropy is 3 N − 2 N . Although the analytical expression of the envelope of RPS entropy is given by Deng and Deng (Deng and Deng, 2022), its computational and expression complexity makes it difficult and inconvenient to discuss the properties and its physical meaning of maximum RPS entropy.…”

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confidence: 99%

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International Comparison on the Application of Information Technology in High School Mathematics Textbooks

Zhou

2021

School Mathematics Textbooks in China

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Ultra-dense networks are widely regarded as a promising solution to explosively growing applications of Internet-of-Things (IoT) mobile devices (IMDs). However, complicated and severe interferences need to be tackled properly in such networks. To this end, both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) are utilized at first. Then, in order to attain a goal of green and secure computation offloading, under the proportional allocation of computational resources and the constraints of latency and security cost, joint device association, channel selection, security service assignment, power control and computation offloading are done for minimizing the overall energy consumed by all IMDs. It is noteworthy that multi-step computation offloading is concentrated to balance the network loads and utilize computing resources fully. Since the finally formulated problem is in a nonlinear mixed-integer form, it may be very difficult to find its closed-form solution. To solve it, an improved whale optimization algorithm (IWOA) is designed. As for this algorithm, the convergence, computational complexity and parallel implementation are analyzed in detail. Simulation results show that the designed algorithm may achieve lower energy consumption than other existing algorithms under the constraints of latency and security cost.

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Section: Rps Entropymentioning

confidence: 99%

Section: Rps Entropymentioning

confidence: 99%

mentioning

confidence: 99%

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International Comparison on the Application of Information Technology in High School Mathematics Textbooks

Zhou

2021

School Mathematics Textbooks in China

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“…And uncertainty are universal in reality and vital for fusion systems 2 . Therefore, various theories have been established to handle uncertainty, including Z number, 3 rough sets, 4,5 random permutation set, 6–8 intuitionistic fuzzy set, 9–11 and so on 12,13 . Moreover, these theories have been applied in various fields, including data fusion, 14,15 decision making, 16–19 casual inference 20 community detection, 21,22 risk assessment, 23,24 reliability analysis, 25,26 social network analysis, 27 classification, 28,29 fault diagnosis, 30 medical diagnosis, 31,32 and so on.…”

Section: Introductionmentioning

confidence: 99%

Complex interval number‐based uncertainty modeling method with its application in decision fusion

Zheng

Xiao

2022

Int J of Intelligent Sys

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Complex evidence theory, a generalization of Dempster–Shafer evidence theory, is an effective uncertainty reasoning for decision fusion in complex‐valued domain. In particular, the generation of complex basic belief assignment (CBBA) is a key issue for uncertainty modeling in complex evidence theory. In this paper, we first construct complex interval number (CIN) model. In this context, we propose a novel CBBA generation method to model uncertainty in the framework of complex planes. Furthermore, we propose a novel decision‐making algorithm on the basis of the CIN‐based CBBA generation method. Through an application in pattern recognition on several real‐world data sets, the efficiency of the proposed decision‐making algorithm is verified.

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“…To address this issue, the definition of "negation permutation mass function" is proposed in this paper, which is a new approach to represent and process the knowledge based on random permutation sets theory. In addition, based on Chen [31] and Deng's [32]work, the change of entropy and dissimilarity of permutation mass function after each iteration of the negation process is presented.…”

Section: Introductionmentioning

confidence: 99%

Fine-Grained Allocation Algorithm for Sharing Heterogeneous Resources in Data Center

Xiao-chun

Fan

2020

西北工业大学学报

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Data in a data center are stored dispersively. The data-oriented task computing disperses big data analysis tasks to different computing nodes. The extensive use of graphics processing unit (GPU) makes it urgent and important to study how to reasonably assign heterogeneous resources to different computing frameworks. We investigate the existing big data computing framework and the GPU computing. Based on the existing cluster resource management model and the GPU management model, we propose a hybrid heterogeneous resource management model that combines CPU resources with GPU resources. The computing nodes manage local resources and implement tasks; the resource management center concertedly manage various computing frameworks. We design and implement a hybrid domain resource sharing and allocation algorithm, which allocates the hybrid domain resources to computing frameworks according to the coordinated use of them so as to fairly share the hybrid domain resources among various computing frameworks and prevent the CPU from too many tasks but the GPU or CPU from resource "hunger". The experimental results show that the allocation algorithm can increase the use of heterogeneous resources and the number of completed tasks by around 15%.

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Maximum entropy of random permutation set

Cited by 53 publications

References 53 publications

International Comparison on the Application of Information Technology in High School Mathematics Textbooks

International Comparison on the Application of Information Technology in High School Mathematics Textbooks

Complex interval number‐based uncertainty modeling method with its application in decision fusion

Fine-Grained Allocation Algorithm for Sharing Heterogeneous Resources in Data Center

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