Cited By
View all- Chen LDeng Y(2023)A new probability transformation approach of mass functionSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-023-08295-627:20(15123-15132)Online publication date: 1-Oct-2023
Abstract
In evidence theory, the generalized belief entropy model unifies Renyi entropy, Tsallis entropy, and Deng entropy. In order to further unify the maximum values of Renyi entropy, Tsallis entropy, and Deng entropy, this paper proposes a maximum model of generalized belief entropy by analyzing the generalized belief entropy model. This model shows that the size of the maximum generalized belief entropy is not related to the specific mass value, but is related to the size of each propositional space, and the maximum values of Renyi–Deng entropy and Tsallis–Deng entropy are obtained through this model. In addition, the applicability of the proposed model is obtained through verification tests and sensitivity analysis of the model.
References
[1]
Abellan J, Castellano JG (2017) Improving the naive bayes classifier via a quick variable selection method using maximum of entropy. Entropy 19(6).
[2]
An J, Hu M, Fu L, and Zhan J A novel fuzzy approach for combining uncertain conflict evidences in the dempster-shafer theory IEEE Access 2019 7 7481-7501
[3]
Anjaria K (2020) Negation and entropy: effectual knowledge management equipment for learning organizations. Expert Syst Appl 157.
[4]
Araújo GLA (2019) Entropy measures for early detection of bearing faults. Physica A 514:458–472.
[5]
Biró TS, Néda Z, and Telcs A Entropic divergence and entropy related to nonlinear master equations Entropy 2019 21 10 993
[6]
Buono F, Longobardi M (2020) A dual measure of uncertainty: The Deng extropy. Entropy 22(5).
[7]
Chen L, Deng Y, and Cheong KH Probability transformation of mass function: a weighted network method based on the ordered visibility graph Eng Appl Artif Intell 2021 105 104438
[8]
Cui H, Liu Q, Zhang J, and Kang B An improved Deng entropy and its application in pattern recognition IEEE Access 2019 7 18284-18292
[9]
Das J and Bag BC Bounds of the entropy production of the irreversible thermodynamics and its relation with the non-equilibrium temperature Physica A 2019 520 433-449
[10]
Dempster AP Upper and lower probabilities induced by a multivalued mapping Ann Math Stat 1967 38 2 325-000
[11]
Deng Y Generalized evidence theory Appl Intell 2015 43 3 530-543
[12]
Deng Y Deng entropy Chaos Solit Fract 2016 91 549-553
[13]
Deng Y Information volume of mass function Int J Comput Commun Control 2020 15 6 3983
[14]
Deng Y Uncertainty measure in evidence theory Sci China Inf Sci 2020 63 11 210201
[15]
Dimpfl T and Peter FJ Group transfer entropy with an application to cryptocurrencies Physica A 2019 516 543-551
[16]
Dobovišek A, Markovič R, Brumen M, and Fajmut A The maximum entropy production and maximum Shannon information entropy in enzyme kinetics Physica A 2018 496 220-232
[17]
Dragan IM and Isaic-Maniu A An innovative model of reliability-the pseudo-entropic model Entropy 2019 21 9 846
[18]
Fan X, Guo Y, Ju Y, Bao J, Lyu W (2020) Multisensor fusion method based on the belief entropy and DS evidence theory. J Sensors 2020.
[19]
Gholami A, Bonakdari H, and Mohammadian A A method based on the Tsallis entropy for characterizing threshold channel bank profiles Physica A 2019 526 121089
[20]
Ghoshal K, Kumbhakar M, and Singh VP Distribution of sediment concentration in debris flow using Rényi entropy Physica A 2019 521 267-281
[21]
Gunn LH, Gzyl H, ter Horst E, Ariza MJ, Molina G (2019) Maximum entropy in the mean methods in propensity score matching for interval and noisy data. Commun Stat Theory Methods 48(18):4581–4597.
[22]
Gzyl H (2020) Construction of contingency tables by maximum entropy in the mean. Commun Stat Theory Methods.
[23]
Hazan A A maximum entropy network reconstruction of macroeconomic models Physica A 2019 519 1-17
[24]
He Z and Jiang W An evidential Markov decision making model Inf Sci 2018 467 357-372
[25]
Höns R (2012) Using maximum entropy and generalized belief propagation in estimation of distribution algorithms. Adap Learn Optim 14
[26]
Jaunzemis AD, Holzinger MJ, Chan MW, and Shenoy PP Evidence gathering for hypothesis resolution using judicial evidential reasoning Inf Fus 2019 49 26-45
[27]
Jiang W, Wang S (2017) An uncertainty measure for interval-valued evidences. Int J Comput Commun Control 12(5):631–644.
[28]
Jiang W, Wei B, Xie C, Zhou D (2016) An evidential sensor fusion method in fault diagnosis. Adv Mech Eng 8(3).
[29]
Jirousek R and Shenoy PP A new definition of entropy of belief functions in the Dempster-Shafer theory Int J Approx Reas 2018 92 49-65
[30]
Karci A (2018) Notes on the published article “fractional order entropy: new perspectives” by Ali Karci, Optik Int J Light Electron Opt 127(20):9172–9177 (Optik 171:107–108)
[31]
Karci A Fractional order entropy: new perspectives Optik 2016 127 20 9172-9177
[32]
Khalaj M, Tavakkoli-Moghaddam R, Khalaj F, Siadat A (2020) New definition of the cross entropy based on the Dempster-Shafer theory and its application in a decision-making process. Commun Stat Theory Methods 49(4):909–923.
[33]
Khan N and Anwar S Time-domain data fusion using weighted evidence and Dempster-Shafer combination rule: application in object classification Sensors 2019 19 23 5187
[34]
Khosravi Tanak A, Mohtashami Borzadaran GR, and Ahmadi J Maximum Tsallis entropy with generalized gini and gini mean difference indices constraints Physica A 2017 471 554-560
[35]
Khribi L, Fredette M, Macgibbon B (2016) The poisson maximum entropy model for homogeneous poisson processes. Commun Stat Simul Comput 45(9):3435–3456
[36]
Kuzemsky AL Temporal evolution, directionality of time and irreversibility Rivista Del Nuovo Cimento 2018 41 10 513-574
[37]
Liao H, Ren Z, and Fang R A Deng-entropy-based evidential reasoning approach for multi-expert multi-criterion decision-making with uncertainty Int J Comput Intell Syst 2020 13 1 1281-1294
[38]
Li Y, Deng Y (2018) Generalized ordered propositions fusion based on belief entropy. Int J Comput Commun Control 13(5):792–807
[39]
Liu F, Gao X, Zhao J, and Deng Y Generalized belief entropy and its application in identifying conflict evidence IEEE Access 2019 7 126625-126633
[40]
Luo C, Chen Y, Xiang H, et al. Evidence combination method in time domain based on reliability and importance J Syst Eng Electron 2018 29 6 1308-1316
[41]
Macedo P Ridge regression and generalized maximum entropy: An improved version of the ridge-gme parameter estimator Commun Stat Simul Comput 2017 46 5 3527-3539
[42]
Macedo P, Scotto M, and Silva E Regularization with maximum entropy and quantum electrodynamics: the merg(e) estimators Commun Stat Simul Comput 2016 45 3 1143-1157
[43]
Mambe MD, N’Takpe T, Anoh NG, Oumtanaga S (2018) A new uncertainty measure in belief entropy framework. Int J Adv Comput Sci Appl 9(11):600–606
[44]
Martyushev LM and Zubarev SN Entropy production and luminosity-effective temperature relation for main-sequence stars Physica A 2019 528 121403
[45]
Masi M A step beyond Tsallis and Renyi entropies Phys Lett A 2005 338 3–5 217-224
[46]
Mehri A, Agahi H, and Mehri-Dehnavi H A novel word ranking method based on distorted entropy Physica A 2019 521 484-492
[47]
Okada K (2018) Gyarmati’s principle and edelen representation of thermodynamic forces in the maximum entropy formalism. Physica A 489:40–46.
[48]
Pan Q, Zhou D, Tang Y, Li X, Huang J (2019) A novel belief entropy for measuring uncertainty in Dempster-Shafer evidence theory framework based on plausibility transformation and weighted Hartley entropy. Entropy 21(2).
[49]
Parkash O, Mukesh A (2016) Contribution of maximum entropy principle in the field of queueing theory. Commun Stat Theory Methods 45(12):3464–3472.
[50]
Prajapati GL and Saha R Reeds: Relevance and enhanced entropy based Dempster Shafer approach for next word prediction using language model J Comput Sci 2019 35 1-11
[51]
Reny A (1961) On measures of entropy and information. In: Symposium on mathematics statistics and probabilities, pp 547–561
[52]
Seiti H and Hafezalkotob A Developing pessimistic-optimistic risk-based methods for multi-sensor fusion: an interval-valued evidence theory approach Appl Soft Comput 2018 72 609-623
[53]
Shannon CE A mathematical theory of communication Bell Syst Tech J 1948 27 3 379-423
[54]
Shen J, Zhou J (2019) Calculation formulas and simulation algorithms for entropy of function of LR fuzzy intervals. Entropy 21(3).
[55]
Song Y and Deng Y Entropic explanation of power set Int. J. Comput. Commun. Control 2021 16 4 4413
[56]
Swendsen RH The definition of the thermodynamic entropy in statistical mechanics Physica A 2017 467 67-73
[57]
Swendsen RH and Wang JS Negative temperatures and the definition of entropy Physica A 2016 453 24-34
[58]
Tabass MS and Borzadaran GRM The generalized maximum Tsallis entropy estimators and applications to the portland cement dataset Commun Stat Simul Comput 2017 46 4 3284-3293
[59]
Tang Y, Zhou D, Chan FTS (2018) An extension to Deng’s entropy in the open world assumption with an application in sensor data fusion. Sensors 18(6).
[60]
Tang Y, Zhou D, Xu S, He Z (2017) A weighted belief entropy-based uncertainty measure for multi-sensor data fusion. Sensors 17(4).
[61]
Tsallis C Possible generalization of Boltzman-Gibbs statistics J Stat Phys 1988 52 1–2 479-487
[62]
Tuğal Ihsan and Karci Ali Comparisons of Karci and Shannon entropies and their effects on centrality of social networks Physica A 2019 523 352-363
[63]
Vandoni J, Aldea E, and Le Hégarat-Mascle S Evidential query-by-committee active learning for pedestrian detection in high-density crowds Int J Approx Reason 2019 104 166-184
[64]
Viaggiu S Entropy, temperature and internal energy of trapped gravitons and corrections to the black hole entropy Physica A 2017 488 72-84
[65]
Wang X and Song Y Uncertainty measure in evidence theory with its applications Appl Intell 2018 48 7 1672-1688
[66]
Wang J, Qiao K, and Zhang Z An improvement for combination rule in evidence theory Futur Gener Comput Syst 2019 91 1-9
[67]
Wang Y, Liu F, and Zhu A Bearing fault diagnosis based on a hybrid classifier ensemble approach and the improved Dempster-Shafer theory Sensors 2019 19 9 2097
[68]
Wang D, Gao J, Wei D (2019a) A new belief entropy based on Deng entropy. Entropy 21(10).
[69]
Xue Y and Deng Y Interval-valued belief entropies for Dempster Shafer structures Soft Comput 2021 25 8063-8071
[70]
Xue Y, Deng Y (2021b) Tsallis extropy. Commun Stat Theory Methods.
[71]
Zhang Y, Liu Y, Zhang Z, Chao HC, Zhang J, and Liu Q A weighted evidence combination approach for target identification in wireless sensor networks IEEE Access 2017 5 21585-21596
[72]
Zhang Y, Liu Y, Zhang Z, and Zhao N Collaborative fusion for distributed target classification using evidence theory in iot environment IEEE Access 2018 6 62314-62323
[73]
Zhao Y, Ji D, Yang X, Fei L, Zhai C (2019) An improved belief entropy to measure uncertainty of basic probability assignments based on Deng entropy and belief interval. Entropy 21(11).
[74]
Zhou Q, Deng Y (2021) Belief extropy: measure uncertainty from negation. Commun Stat Theory Methods.
[75]
Zhou D, Tang Y, Jiang W (2017a) An improved belief entropy and its application in decision-making. Complexity.
[76]
Zhou D, Tang Y, Jiang W (2017b) A modified belief entropy in Dempster-Shafer framework. Plos One 12(5).
[77]
Zhu W, Yang H, Jin Y, Liu B (2017) A method for recognizing fatigue driving based on Dempster-Shafer theory and fuzzy neural network. Math Probl Eng
[78]
Zu T, Kang R, Wen M, and Zhang Q Belief reliability distribution based on maximum entropy principle IEEE Access 2018 6 1577-1582
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Published: 01 May 2022
Accepted: 09 February 2022
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View all- Chen LDeng Y(2023)A new probability transformation approach of mass functionSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-023-08295-627:20(15123-15132)Online publication date: 1-Oct-2023