Đo lường độ không chắc chắn trong lý thuyết bằng chứng

Springer Science and Business Media LLC - Tập 63 - Trang 1-19 - 2020
Yong Deng1,2
1The Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, China
2School of Education, Shannxi Normal University, Xi’an, China

Tóm tắt

Là một sự mở rộng của lý thuyết xác suất, lý thuyết bằng chứng có khả năng xử lý tốt hơn thông tin không xác định và không chính xác. Nhờ vào những lợi thế của nó, lý thuyết bằng chứng có tính linh hoạt và hiệu quả hơn trong việc mô hình hóa và xử lý thông tin không chắc chắn. Đo lường độ không chắc chắn đóng một vai trò thiết yếu trong cả lý thuyết bằng chứng và lý thuyết xác suất. Trong lý thuyết xác suất, Entropy Shannon cung cấp một góc nhìn mới mẻ để đo lường độ không chắc chắn. Có nhiều loại entropy khác nhau tồn tại để đo lường độ không chắc chắn của sự phân bổ xác suất cơ bản (BPA) trong lý thuyết bằng chứng. Tuy nhiên, từ góc độ yêu cầu của việc đo lường độ không chắc chắn và vật lý, các entropy này vẫn còn gây tranh cãi. Do đó, quá trình đo lường độ không chắc chắn của BPA hiện vẫn là một vấn đề còn bỏ ngỏ trong tài liệu. Đầu tiên, bài báo này xem xét các biện pháp đo lường độ không chắc chắn trong lý thuyết bằng chứng, kèm theo phân tích về một số tranh cãi liên quan. Thứ hai, chúng tôi thảo luận về sự phát triển của entropy Deng như một cách hiệu quả để đo lường độ không chắc chắn, bao gồm việc giới thiệu định nghĩa của nó, phân tích các thuộc tính của nó và so sánh nó với các phương pháp khác. Chúng tôi cũng xem xét khái niệm entropy Deng lớn nhất, tam giác Pascal giả của entropy Deng lớn nhất, entropy niềm tin tổng quát và các biện pháp phân kỳ. Thêm vào đó, chúng tôi tiến hành phân tích ứng dụng của entropy Deng và tiếp tục xem xét các thách thức cho các nghiên cứu trong tương lai về đo lường độ không chắc chắn trong lý thuyết bằng chứng. Cuối cùng, bài viết sẽ cung cấp một kết luận để tóm tắt nghiên cứu này.

Từ khóa

#lý thuyết bằng chứng #đo lường độ không chắc chắn #entropy Shannon #entropy Deng #phân bố xác suất cơ bản #tranh cãi về độ không chắc chắn

Tài liệu tham khảo

Fu C, Chang W, Yang S. Multiple criteria group decision making based on group satisfaction. Inf Sci, 2020, 518: 309–329 Fu C, Chang W, Xue M, et al. Multiple criteria group decision making with belief distributions and distributed preference relations. Eur J Operational Res, 2019, 273: 623–633 He Y, Hu L F, Guan X, et al. New method for measuring the degree of conflict among general basic probability assignments. Sci China Inf Sci, 2012, 55: 312–321 Fei L, Feng Y, Liu L. Evidence combination using OWA-based soft likelihood functions. Int J Intell Syst, 2019, 34: 2269–2290 Liu Z, Pan Q, Dezert J, et al. Classifier fusion with contextual reliability evaluation. IEEE Trans Cybern, 2018, 48: 1605–1618 Wu B, Yan X, Wang Y, et al. An evidential reasoning-based CREAM to human reliability analysis in maritime accident process. Risk Anal, 2017, 37: 1936–1957 Wang Z, Gao J M, Wang R X, et al. Failure mode and effects analysis using Dempster-Shafer theory and TOPSIS method: application to the gas insulated metal enclosed transmission line (GIL). Appl Soft Comput, 2018, 70: 633–647 Liu Z G, Liu Y, Dezert J, et al. Evidence combination based on credal belief redistribution for pattern classification. IEEE Trans Fuzzy Syst, 2020, 28: 618–631 Pan Y, Zhang L, Wu X, et al. Multi-classifier information fusion in risk analysis. Inf Fusion, 2020, 60: 121–136 He Y, Jian T, Su F, et al. Two adaptive detectors for range-spread targets in non-Gaussian clutter. Sci China Inf Sci, 2011, 54: 386–395 Zadeh L A. Fuzzy sets. Inf Control, 1965, 8: 338–353 Pawlak Z. Rough sets. Int J Comput Inf Sci, 1982, 11: 341–356 Dempster A P. Upper and lower probabilities generated by a random closed interval. Ann Math Statist, 1968, 39: 957–966 Shafer G. A Mathematical Theory of Evidence. Princeton: Princeton University Press, 1976 Atanassov K T. Intuitionistic fuzzy sets. Fuzzy Sets Syst, 1986, 20: 87–96 Zadeh L A. A note on Z-numbers. Inf Sci, 2011, 181: 2923–2932 Yager R R. Pythagorean fuzzy subsets. In: Proceedings of 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013. 57–61 Fu C, Chang W, Xu D, et al. An evidential reasoning approach based on criterion reliability and solution reliability. Comput Industrial Eng, 2019, 128: 401–417 Xiao F. Generalization of Dempster-Shafer theory: a complex mass function. Appl Intell, 2020, 50: 3266–3275 Xiao F. Generalized belief function in complex evidence theory. J Intell Fuzzy Syst, 2020, 38: 3665–3673 Yang J B. Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties. Eur J Operational Res, 2001, 131: 31–61 Yang J B, Xu D L. On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty. IEEE Trans Syst Man Cybern A, 2002, 32: 289–304 Yang J B, Xu D L. Evidential reasoning rule for evidence combination. Artif Intell, 2013, 205: 1–29 Shannon C E. A mathematical theory of communication. Bell Syst Technical J, 1948, 27: 379–423 Deng Y. Deng entropy. Chaos Solitons Fractals, 2016, 91: 549–553 Xiao F. EFMCDM: evidential fuzzy multicriteria decision making based on belief entropy. IEEE Trans Fuzzy Syst, 2020, 28: 1477–1491 Xiao F. GIQ: a generalized intelligent quality-based approach for fusing multi-source information. IEEE Trans Fuzzy Syst, 2020. doi: https://doi.org/10.1109/TFUZZ.2020.2991296 Xiao F. Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy. Inf Fusion, 2019, 46: 23–32 Xiao F. A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems. IEEE Trans Syst Man Cybern Syst, 2020. doi: https://doi.org/10.1109/TSMC.2019.2958635 Xiao F. A new divergence measure for belief functions in D-S evidence theory for multisensor data fusion. Inf Sci, 2020, 514: 462–483 Xiao F. CED: a distance for complex mass functions. IEEE Trans Neural Netw Learning Syst, 2020. doi: https://doi.org/10.1109/TNNLS.2020.2984918 Höhle U. Entropy with respect to plausibility measures. In: Proceedings of the 12th IEEE International Symposium on Multiple Valued Logic, Paris, 1982 Smets P. Information content of an evidence. Int J Man-Machine Studies, 1983, 19: 33–43 Yager R R. Entropy and specificity in a mathematical theory of evidence. Int J General Syst, 1983, 9: 249–260 Dubois D, Prade H. Properties of measures of information in evidence and possibility theories. Fuzzy Sets Syst, 1987, 24: 161–182 Lamata M T, Moral S. Measures of entropy in the theory of evidence. Int J General Syst, 1988, 14: 297–305 Klir G J, Ramer A. Uncertainty in the Dempster-Shafer theory: a critical re-examination. Int J General Syst, 1990, 18: 155–166 Klir G J, Parviz B. A note on the measure of discord. In: Proceedings of the 8th Conference on Uncertainty in Artificial Intelligence, 1992. 138–141 Pal N R, Bezdek J C, Hemasinha R. Uncertainty measures for evidential reasoning I: a review. Int J Approximate Reasoning, 1992, 7: 165–183 Pal N R, Bezdek J C, Hemasinha R. Uncertainty measures for evidential reasoning II: a new measure of total uncertainty. Int J Approximate Reasoning, 1993, 8: 1–16 George T, Pal N R. Quantification of conflict in Dempster-Shafer framework: a new approach. Int J General Syst, 1996, 24: 407–423 Jousselme A L, Liu C S, Grenier D, et al. Measuring ambiguity in the evidence theory. IEEE Trans Syst Man Cybern A, 2006, 36: 890–903 Jiroušek R, Shenoy P P. A new definition of entropy of belief functions in the Dempster-Shafer theory. Int J Approximate Reasoning, 2018, 92: 49–65 Pan Q, Zhou D, Tang Y, et al. A novel belief entropy for measuring uncertainty in Dempster-Shafer evidence theory framework based on plausibility transformation and weighted hartley entropy. Entropy, 2019, 21: 163 Wen K, Song Y, Wu C, et al. A novel measure of uncertainty in the Dempster-Shafer theory. IEEE Access, 2020, 8: 51550–51559 Wang X, Song Y. Uncertainty measure in evidence theory with its applications. Appl Intell, 2018, 48: 1672–1688 Yang Y, Han D. A new distance-based total uncertainty measure in the theory of belief functions. Knowledge-Based Syst, 2016, 94: 114–123 Deng X, Xiao F, Deng Y. An improved distance-based total uncertainty measure in belief function theory. Appl Intell, 2017, 46: 898–915 Deng X. Analyzing the monotonicity of belief interval based uncertainty measures in belief function theory. Int J Intell Syst, 2018, 33: 1869–1879 Deng X, Jiang W. A total uncertainty measure for D numbers based on belief intervals. Int J Intell Syst, 2019, 34: 3302–3316 Xia J, Feng Y, Liu L, et al. On entropy function and reliability indicator for D numbers. Appl Intell, 2019, 49: 3248–3266 Yager R R. Interval valued entropies for Dempster-Shafer structures. Knowledge-Based Syst, 2018, 161: 390–397 Klir G J, Wierman M J. Uncertainty-based Information: Elements of Generalized Information Theory. Berlin: Springer, 1999 Klir G J. Uncertainty and Information: Foundations of Generalized Information Theory. Piscataway: Wiley-IEEE Press, 2006 Abe S, Okamoto Y. Nonextensive Statistical Mechanics and Its Applications. Berlin: Springer, 2001 Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys, 1988, 52: 479–487 Wang D, Gao J, Wei D. A new belief entropy based on Deng entropy. Entropy, 2019, 21: 987 Ozkan K. Comparing Shannon entropy with Deng entropy and improved Deng entropy for measuring biodiversity when a priori data is not clear. J Faculty Forestry-Istanbul Univ, 2018, 68: 136–140 Li J, Pan Q. A new belief entropy in Dempster-Shafer theory based on basic probability assignment and the frame of discernment. Entropy, 2020, 22: 691 Zhou Q, Mo H, Deng Y. A new divergence measure of pythagorean fuzzy sets based on belief function and its application in medical diagnosis. Mathematics, 2020, 8: 142 Kuzemsky A. Temporal evolution, directionality of time and irreversibility. La Rivista del Nuovo Cimento, 2018, 41: 513–574 Jiang W, Wang S. An uncertainty measure for interval-valued evidences. Int J Comput Commun, 2017, 12: 631–644 Mambe M D, N’Takp’e T, Georges N, et al. A new uncertainty measure in belief entropy framework. Int J Adv Comput Sci Appl, 2018, 9: 600–606 Xie K, Xiao F. Negation of belief function based on the total uncertainty measure. Entropy, 2019, 21: 73 Zhao Y, Ji D, Yang X, et al. An improved belief entropy to measure uncertainty of basic probability assignments based on Deng entropy and belief interval. Entropy, 2019, 21: 1122 Luo C K, Chen Y X, Xiang H C, et al. Evidence combination method in time domain based on reliability and importance. J Syst Eng Electron, 2018, 29: 1308–1316 Vandoni J, Aldea E, 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 Khan M N, Anwar S. Time-domain data fusion using weighted evidence and Dempster-Shafer combination rule: application in object classification. Sensors, 2019, 19: 5187 Pan L, Deng Y. Probability transform based on the ordered weighted averaging and entropy difference. Int J Comput Commun, 2020, 15: 4 Wang Y, Liu F, Zhu A. Bearing fault diagnosis based on a hybrid classifier ensemble approach and the improved Dempster-Shafer theory. Sensors, 2019, 19: 2097 Zhang Y, Liu Y, Zhang Z, et al. A weighted evidence combination approach for target identification in wireless sensor networks. IEEE Access, 2017, 5: 21585–21596 Abellan J. Analyzing properties of Deng entropy in the theory of evidence. Chaos Solitons Fractals, 2017, 95: 195–199 Kang B, Deng Y. The maximum Deng entropy. IEEE Access, 2019, 7: 120758–120765 Deng Y. The information volume of uncertain informaion: (1) mass function. 2020. viXra:2006.0028 Tsallis C, Gell-Mann M, Sato Y. Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive. Proc Natl Acad Sci USA, 2005, 102: 15377–15382 Gao X, Deng Y. The Pseudo-Pascal triangle of maximum Deng entropy. Int J Comput Commun, 2020, 15: 1–10 Liu F, Gao X, Zhao J, et al. Generalized belief entropy and its application in identifying conflict evidence. IEEE Access, 2019, 7: 126625–126633 Song Y, Deng Y. Divergence measure of belief function and its application in data fusion. IEEE Access, 2019, 7: 107465–107472 Gao X, Liu F, Pan L, et al. Uncertainty measure based on Tsallis entropy in evidence theory. Int J Intell Syst, 2019, 34: 3105–3120 Pan L, Deng Y. A new belief entropy to measure uncertainty of basic probability assignments based on belief function and plausibility function. Entropy, 2018, 20: 842 Li Y, Deng Y. Generalized ordered propositions fusion based on belief entropy. Int J Comput Commun, 2018, 13: 792–807 Song Y, Deng Y. A new method to measure the divergence in evidential sensor data fusion. Int J Distributed Sens Networks, 2019, 15: 1–8 Xiao F. An improved method for combining conflicting evidences based on the similarity measure and belief function entropy. Int J Fuzzy Syst, 2018, 20: 1256–1266 Boulkaboul S, Djenouri D. DFIOT: data fusion for Internet of Things. J Netw Syst Manage, 2020, 54: 1–25 Xiao F, Qin B. A weighted combination method for conflicting evidence in multi-sensor data fusion. Sensors, 2018, 18: 1487 An J, Hu M, Fu L, et al. A novel fuzzy approach for combining uncertain conflict evidences in the Dempster-Shafer theory. IEEE Access, 2019, 7: 7481–7501 Wang J, Qiao K, Zhang Z. An improvement for combination rule in evidence theory. Future Generation Comput Syst, 2019, 91: 1–9 Tang Y, Zhou D, Chan F. An extension to Deng’s entropy in the open world assumption with an application in sensor data fusion. Sensors, 2018, 18: 1902 Hurley J, Johnson C, Dunham J, et al. Nonlinear algorithms for combining conflicting identification information in multisensor fusion. In: Proceedings of 2019 IEEE Aerospace Conference, 2019. 1–7 Liu Z, Xiao F. An evidential aggregation method of intuitionistic fuzzy sets based on belief entropy. IEEE Access, 2019, 7: 68905–68916 Wang Z, Xiao F. An improved multi-source data fusion method based on the belief entropy and divergence measure. Entropy, 2019, 21: 611 Fan X, Guo Y, Ju Y, et al. Multisensor fusion method based on the belief entropy and DS evidence theory. J Sens, 2020, 2020: 1–16 Tao R, Xiao F. Combine conflicting evidence based on the belief entropy and IOWA operator. IEEE Access, 2019, 7: 120724 Moral-Garcia S, Abellan J. Maximum of entropy for belief intervals under evidence theory. IEEE Access, 2020, 8: 118017 Dong Y, Zhang J, Li Z, et al. Combination of evidential sensor reports with distance function and belief entropy in fault diagnosis. Int J Comput Commun, 2019, 14: 329–343 Xiao F. A novel evidence theory and fuzzy preference approach-based multi-sensor data fusion technique for fault diagnosis. Sensors, 2017, 17: 2504 Wang Z, Xiao F. An improved multisensor data fusion method and its application in fault diagnosis. IEEE Access, 2019, 7: 3928–3937 Chen L, Diao L, Sang J. A novel weighted evidence combination rule based on improved entropy function with a diagnosis application. Int J Distributed Sens Netw, 2019, 15: 1–13 Liu F, Wang Y. A novel method of ds evidence theory for multi-sensor conflicting information. In: Proceedings of the 4th International Conference on Machinery, Materials and Computer (MACMC 2017). Paris: Atlantis Press, 2018. 343–349 Cui H, Liu Q, Zhang J, et al. An improved deng entropy and its application in pattern recognition. IEEE Access, 2019, 7: 18284–18292 Xia J, Feng Y, Liu L, et al. An evidential reliability indicator-based fusion rule for Dempster-Shafer theory and its applications in classification. IEEE Access, 2018, 6: 24912–24924 Zhang Y, Liu Y, Zhang Z, et al. Collaborative fusion for distributed target classification using evidence theory in IOT environment. IEEE Access, 2018, 6: 62314–62323 Buono F, Longobardi M. A dual measure of uncertainty: the Deng extropy. Entropy, 2020, 22: 1–10 Pan L, Deng Y. An association coefficient of a belief function and its application in a target recognition system. Int J Intell Syst, 2020, 35: 85–104 Huang Z, Jiang W, Tang Y. A new method to evaluate risk in failure mode and effects analysis under fuzzy information. 2018, 22: 4779–4787 Wang H, Deng X, Zhang Z, et al. A new failure mode and effects analysis method based on Dempster-Shafer theory by integrating evidential network. IEEE Access, 2019, 7: 79579–79591 Liu Z, Xiao F. An intuitionistic evidential method for weight determination in FMEA based on belief entropy. Entropy, 2019, 21: 211 Zheng H, Tang Y. Deng entropy weighted risk priority number model for failure mode and effects analysis. Entropy, 2020, 22: 280 Pan Q, Zhou D, Tang Y, et al. A novel antagonistic Weapon-Target assignment model considering uncertainty and its solution using decomposition co-evolution algorithm. IEEE Access, 2019, 7: 37498–37517 Li Y, Wang A, Yi X. Fire control system operation status assessment based on information fusion: case study. Sensors, 2019, 19: 2222 Liu H, Ma Z, Deng X, et al. A new method to air target threat evaluation based on Dempster-Shafer evidence theory. In: Proceedings of 2018 Chinese Control and Decision Conference (CCDC), 2018. 2504–2508 Fei L, Deng Y, Hu Y. DS-VIKOR: a new multi-criteria decision-making method for supplier selection. Int J Fuzzy Syst, 2019, 21: 157–175 Xiao F. A multiple-criteria decision-making method based on D numbers and belief entropy. Int J Fuzzy Syst, 2019, 21: 1144–1153 Li M, Xu H, Deng Y. Evidential decision tree based on belief entropy. Entropy, 2019, 21: 897 Yan H, Deng Y. An improved belief entropy in evidence theory. IEEE Access, 2020, 8: 57505–57516 Chen L, Li Z, Deng X. Emergency alternative evaluation under group decision makers: a new method based on entropy weight and DEMATEL. Int J Syst Sci, 2020, 51: 570–583 Shang X, Song M, Huang K, et al. An improved evidential DEMATEL identify critical success factors under uncertain environment. J Ambient Intell Humanized Comput, 2019 Huang Z, Yang L, Jiang W. Uncertainty measurement with belief entropy on the interference effect in the quantum-like Bayesian networks. Appl Math Comput, 2019, 347: 417–428 He Z, Jiang W. An evidential Markov decision making model. Inf Sci, 2018, 467: 357–372 Kang B. Construction of stable hierarchy organization from the perspective of the maximum deng entropy. In: Integrated Uncertainty in Knowledge Modelling and Decision Making. Berlin: Springer, 2019. 421–431 Mambe M D, Oumtanaga S, Anoh G N. A belief entropy-based approach for conflict resolution in IOT applications. In: Proceedings of 2018 1st International Conference on Smart Cities and Communities (SCCIC), 2018. 1–5 Prajapati G L, 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