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An improved approach for incomplete information modeling in the evidence theory and its application in classification

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Abstract

Incomplete information modeling and fusion under uncertain circumstances remain a significant open problem in practical engineering. In this study, the Dempster–Shafer evidence theory is extended to the generalized evidence theory, and the above problem is addressed from the perspective of open-world assumptions. An improved method is proposed to model incomplete information, where the generalized basic probability assignment (GBPA) is generated using the Gaussian distribution model. First, we constructed the Gaussian distribution based on the mean and variance calculated from the training set. Then, we modeled the potential incomplete information with the GBPA of the empty set by matching the test sample with the constructed Gaussian distribution model. Next, we identified and recognized the unknown object by fusing the data with the generalized combination rule. Finally, classification experiments and comparative studies were conducted to illustrate the superiority and effectiveness of the proposed method.

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Data Availability

All data are included in the manuscript.

References

  • Chakraborty S, Chattopadhyay R, Chakraborty S (2020) An integrated d-Marcos method for supplier selection in an iron and steel industry. Decis Mak Appl Manag Eng 3(2):49–69

    Article  Google Scholar 

  • Chao F, Dong-Ling X, Xue M (2018) Determining attribute weights for multiple attribute decision analysis with discriminating power in belief distributions. Knowl Based Syst 143:127–141

    Article  Google Scholar 

  • Chao F, Chang W, Yang S (2020) Multiple criteria group decision making based on group satisfaction. Inf Sci 518:309–329

    Article  MathSciNet  Google Scholar 

  • Chen Z, Cai R (2022) Updating incomplete framework of target recognition database based on fuzzy gap statistic. Eng Appl Artif Intell 107:104521

    Article  Google Scholar 

  • Dempster AP (1967) Upper and lower probabilities induced by a multi-valued map**. Ann Math Stat 38(2):325–339

    Article  Google Scholar 

  • Deng Y (2015) Generalized evidence theory. Appl Intell 43(3):530–543

    Article  Google Scholar 

  • Deng X, **ao F, Deng Y (2017) An improved distance-based total uncertainty measure in belief function theory. Appl Intell 46(4):898–915

    Article  Google Scholar 

  • Denoeux T (2019) Decision-making with belief functions: a review. Int J Approx Reas 109:87–110

    Article  MathSciNet  Google Scholar 

  • Fan Y, Ma T, **ao F (2021) An improved approach to generate generalized basic probability assignment based on fuzzy sets in the open world and its application in multi-source information fusion. Appl Intell 51(6):3718–3735

    Google Scholar 

  • Frikha A, Moalla H (2015) Analytic hierarchy process for multi-sensor data fusion based on belief function theory. Eur J Oper Res 241(1):133–147

    Article  MathSciNet  Google Scholar 

  • Fujita H, Gaeta A, Loia V, Orciuoli F (2019) Hypotheses analysis and assessment in counterterrorism activities: a method based on OWA and fuzzy probabilistic rough sets. IEEE Trans Fuzzy Syst 28(5):831–845

    Article  Google Scholar 

  • Gao X, Pan L, Deng Y (2021) Quantum pythagorean fuzzy evidence theory: a negation of quantum mass function view. IEEE Trans Fuzzy Syst 30(5):1313–1327

    Article  Google Scholar 

  • Gao X, Jiang P, **e W, Chen Y, Zhou S, Chen B (2021) Decision fusion method for fault diagnosis based on closeness and Dempster–Shafer theory. J Intell Fuzzy Syst (Preprint):1–10

  • Han Z, Zhang C, Fu H, Zhou JT (2020) Trusted multi-view classification. In:International conference on learning representations, 2020

  • He Z, Jiang W (2018) An evidential dynamical model to predict the interference effect of categorization on decision making results. Knowl-Based Syst 150:139–149

    Article  Google Scholar 

  • Huang ZL, Jiang C, Zhang Z, Zhang W, Yang TG (2019) Evidence-theory-based reliability design optimization with parametric correlations. Struct Multidiscip Optim 60(2):565–580

    Article  MathSciNet  Google Scholar 

  • Jiang W, Zhan J (2017) A modified combination rule in generalized evidence theory. Appl Intell 46(3):630–640

    Article  MathSciNet  Google Scholar 

  • Jiang W, Cao Y, Deng X (2019) A novel z-network model based on Bayesian network and z-number. IEEE Trans Fuzzy Syst 28(8):1585–1599

    Article  Google Scholar 

  • Kang B, Zhang P, Gao Z, Chhipi-Shrestha G, Hewage K, Sadiq R (2020) Environmental assessment under uncertainty using Dempster–Shafer theory and z-numbers. J Ambient Intell Hum Comput 11(5):2041–2060

    Article  Google Scholar 

  • Kowalski P, Zocholl M, Jousselme A-L (2022) Explaining the impact of source behaviour in evidential reasoning. Inf Fusion 81:41–58

    Article  Google Scholar 

  • Li R, Chen Z, Li H, Tang Y (2022) A new distance-based total uncertainty measure in Dempster–Shafer evidence theory. Appl Intell 52(2):1209–1237

    Article  Google Scholar 

  • Liu Y-T, Pal NR, Marathe AR, Lin C-T (2017) Weighted fuzzy Dempster–Shafer framework for multimodal information integration. IEEE Trans Fuzzy Syst 26(1):338–352

    Article  Google Scholar 

  • Liu Z, Zhang X, Niu J, Dezert J (2020) Combination of classifiers with different frames of discernment based on belief functions. IEEE Trans Fuzzy Syst 29(7):1764–1774

    Article  Google Scholar 

  • Liu Z-G, Huang L-Q, Zhou K, Denoeux T (2020) Combination of transferable classification with multisource domain adaptation based on evidential reasoning. IEEE Trans Neural Netw Learn Syst 32(5):2015–2029

    Article  MathSciNet  Google Scholar 

  • Liu Z, Zhang X, Niu J, Dezert J (2021) Combination of classifiers with different frames of discernment based on belief functions. IEEE Trans Fuzzy Syst 29(7):1764–1774

    Article  Google Scholar 

  • Luo J, Shi L, Ni Y (2017) Uncertain power flow analysis based on evidence theory and affine arithmetic. IEEE Trans Power Syst 33(1):1113–1115

    Article  Google Scholar 

  • Meng J, Dongmei F, Tang Y (2020) Belief-peaks clustering based on fuzzy label propagation. Appl Intell 50(4):1259–1271

    Article  Google Scholar 

  • Pan Y, Zhang L, Li ZW, Ding L (2019) Improved fuzzy Bayesian network-based risk analysis with interval-valued fuzzy sets and D–S evidence theory. IEEE Trans Fuzzy Syst 28(9):2063–2077

    Article  Google Scholar 

  • Petrou ZI, Kosmidou V, Manakos I, Stathaki T, Adamo M, Tarantino C, Tomaselli V, Blonda P, Petrou M (2014) A rule-based classification methodology to handle uncertainty in habitat map** employing evidential reasoning and fuzzy logic. Pattern Recognit Lett 48:24–33

    Article  Google Scholar 

  • Sachan S, Almaghrabi F, Yang J-B, Dong-Ling X (2021) Evidential reasoning for preprocessing uncertain categorical data for trustworthy decisions: an application on healthcare and finance. Expert Syst Appl 185:115597

    Article  Google Scholar 

  • Schlickeiser R, Schlickeiser F (2020) A gaussian model for the time development of the SARS-COV-2 corona pandemic disease. predictions for Germany made on 30 March 2020. Physics 2(2):164–170

    Article  MathSciNet  Google Scholar 

  • Sezer SI, Akyuz E, Arslan O (2022) An extended heart Dempster–Shafer evidence theory approach to assess human reliability for the gas freeing process on chemical tankers. Reliab Eng Syst Saf 220:108275

    Article  Google Scholar 

  • Shafer G (1976) A mathematical theory of evidence. In: A mathematical theory of evidence. Princeton University Press, Princeton

  • Smets P, Kennes R (1994) The transferable belief model. Artif Intell 66(2):191–234

    Article  MathSciNet  Google Scholar 

  • Song Y, Wang X, Zhu J, Lei L (2018) Sensor dynamic reliability evaluation based on evidence theory and intuitionistic fuzzy sets. Appl Intell 48(11):3950–3962

    Article  Google Scholar 

  • Sun L, Chang Y, Jiexin P, Haofang Yu, Yang Z (2020) A weighted evidence combination method based on the pignistic probability distance and Deng entropy. J Aerosp Technol Manag 12:33

    Google Scholar 

  • Tang Y, Dongdong W, Liu Z (2021) A new approach for generation of generalized basic probability assignment in the evidence theory. Pattern Anal Appl 24(3):1007–1023

    Article  Google Scholar 

  • Tang Y, Chen Y, Zhou D (2022) Measuring uncertainty in the negation evidence for multi-source information fusion. Entropy 24(11):1596

    Article  MathSciNet  Google Scholar 

  • Tang Y, Sun Z, Zhou D, Huang Y (2023) Failure mode and effects analysis using an improved pignistic probability transformation function and grey relational projection method. Complex Intell Syst 3:1–15

    Google Scholar 

  • Tang Y, Dai G, Zhou Y, Huang Y, Zhou D (2023) Conflicting evidence fusion using a correlation coefficient-based approach in complex network. Chaos Solitons Fractals 176:114087

    Article  Google Scholar 

  • Tang Y, Wu L, Huang Y, Zhou D (2023) A new classification method using the generalized basic probability assignment. In: 2023 European control conference (ECC), pp 1–6. IEEE, New York

  • Tong Z, Philippe X, Denoeux T (2021) An evidential classifier based on Dempster–Shafer theory and deep learning. Neurocomputing 450:275–293

    Article  Google Scholar 

  • Wang S, Tang Y (2022) An improved approach for generation of a basic probability assignment in the evidence theory based on gaussian distribution. Arab J Sci Eng 47(2):1595–1607

    Article  Google Scholar 

  • Wang Z, Gao J-M, Wang R-X, Chen K, Gao Z-Y, Jiang Y (2018) 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 70:633–647

    Article  Google Scholar 

  • Wei F, Shuang Yu, Wang X (2021) A novel method to determine basic probability assignment based on adaboost and its application in classification. Entropy 23(7):812

    Article  MathSciNet  Google Scholar 

  • **ao F (2020) Generalized belief function in complex evidence theory. J Intell Fuzzy Syst 38(4):3665–3673

    Article  Google Scholar 

  • **aoyan S, Li L, Qian H, Mahadevan S, Deng Y (2019) A new rule to combine dependent bodies of evidence. Soft Comput 23(20):9793–9799

    Article  Google Scholar 

  • Xue Y, Deng Y (2021) Möbius transformation in generalized evidence theory. Appl Intell 31:1–14

    Google Scholar 

  • Yager RR (1987) On the Dempster–Shafer framework and new combination rules. Inf Sci 41(2):93–137

    Article  MathSciNet  Google Scholar 

  • Yang J-B, Dong-Ling X (2013) Evidential reasoning rule for evidence combination. Artif Intell 205:1–29

    Article  MathSciNet  Google Scholar 

  • Yin L, Deng X, Deng Y (2018) The negation of a basic probability assignment. IEEE Trans Fuzzy Syst 27(1):135–143

    Article  Google Scholar 

  • Yuan-Wei D, Zhong J-J (2021) Generalized combination rule for evidential reasoning approach and Dempster–Shafer theory of evidence. Inf Sci 547:1201–1232

    Article  MathSciNet  Google Scholar 

  • Zeshui X, Zhao N (2016) Information fusion for intuitionistic fuzzy decision making: an overview. Inf Fusion 28:10–23

    Article  Google Scholar 

  • Zhang J, Deng Y (2017) A method to determine basic probability assignment in the open world and its application in data fusion and classification. Appl Intell 46(4):934–951

  • Zhang Z, Han D, Dezert J, Yang Y (2017) Determination of basic belief assignment using fuzzy numbers. In: 2017 20th international conference on information fusion (fusion), pp 1–6. IEEE, New York

  • Zhi-gang S, Denoeux T (2018) BPEC: belief-peaks evidential clustering. IEEE Trans Fuzzy Syst 27(1):111–123

    Google Scholar 

  • Zhou L, Cui H, Huang C, Kang B, Zhang J (2022) Counter deception in belief functions using Shapley value methodology. Int J Fuzzy Syst 24(1):340–354

    Article  Google Scholar 

  • Zhun-Ga Liu Yu, Liu JD, Cuzzolin F (2020) Evidence combination based on credal belief redistribution for pattern classification. IEEE Trans Fuzzy Syst 28(4):618–631

    Article  Google Scholar 

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Funding

The work was supported by National Natural Science Foundation of China (Program No. 62301439), Natural Science Foundation of Chongqing, China (Program No. CSTB2023NSCQ-MSX0513), Natural Science Basic Research Program of Shaanxi (Program No. 2023-JC-QN-0689), and NWPU Research Fund for Young Scholars (Grant No. G2022WD01010).

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Authors and Affiliations

  1. School of Microelectronics, Northwestern Polytechnical University, **’an, 710072, Shaanxi, China

    Yongchuan Tang & Deyun Zhou

  2. Chongqing Innovation Center, Northwestern Polytechnical University, Chongqing, 401135, China

    Yongchuan Tang

  3. School of Information Science and Engineering, Zaozhuang University, Zaozhuang, 277160, Shandong, China

    Lei Wu

  4. School of Engineering, University of Warwick, Coventry, CV4 7AL, UK

    Yubo Huang

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  1. Yongchuan Tang
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Correspondence to Yongchuan Tang.

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The work was supported by National Natural Science Foundation of China (Program No. 62301439), Natural Science Foundation of Chongqing, China (Program No. CSTB2023NSCQ-MSX0513), Natural Science Basic Research Program of Shaanxi (Program No. 2023-JC-QN-0689), and NWPU Research Fund for Young Scholars (Grant No. G2022WD01010).

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Tang, Y., Wu, L., Huang, Y. et al. An improved approach for incomplete information modeling in the evidence theory and its application in classification. Soft Comput (2024). https://doi.org/10.1007/s00500-024-09740-w

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