Abstract
Under the circumstance of the complete frame of discernment, There are quantities sufficient researches applying the Dempster-Shafer evidence theory (D-S theory) to process uncertain information. However, in most real cases, the frame of discernment is not complete, and the classic evidence theory is not applicable in some degree, including the basic probability assignment (BPA) generation method. In this paper, under the assumption of the open world, the BPA determination issue is focused originally, and a new method based on triangular fuzzy member is proposed to determine BPA. First, the mean value, standard deviation, extreme values as well as the triangular membership function of each attribute can be determined. Then, a nested structure BPA function with an assignment for the null set can be constructed, using the intersection point of one test sample and the models above. Experiments are conducted with the proposed method to determine BPA, through which the classification accuracy rates are computed, analyzed and compared with those generated by other BPA determination methods, which demonstrates the efficiency of the proposed method both in the open world and in the closed world.
Similar content being viewed by others
References
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
Dempster A (1967) Upper and lower probabilities induced by multivalued mapping. Annual Mathmatics Statistics 38(2):325–339
Shafer G (1976) A Mathematical theory of evidence. Princeton University Press, New Jersey
Jones RW, Lowe A, Harrison MJ (2002) A framework for intelligent medical diagnosis using the theory of evidence. Knowl-Based Syst 15(1-2):77–84
Ma J, Liu W, Miller P, Zhou H (2016) An evidential fusion approach for gender profiling. Inf Sci 333:10–20
Lin P-C, Gu J-C, Yang M-T (2014) Intelligent maintenance model for condition assessment of circuit breakers using fuzzy set theory and evidential reasoning. IET Generation Transmission & Distribution 8(7):1244–1253
Deng Y, Liu Y, Zhou D (2015) An improved genetic algorithm with initial population strategy for symmetric TSP. Mathematical Problems in Engineering 2015, Article ID 212794
Guo J (2016) A risk assessment approach for failure mode and effects analysis based on intuitionistic fuzzy sets and evidence theory. J Int Fuzzy Syst 30(2):869–881
Deng Y, Mahadevan S, Zhou D (2015) Vulnerability assessment of physical protection systems: a bio-inspired approach. Int J Unconv Comput 11(3,4):227–243
Liu HC, You JX, You XY, Shan MM (2015) A novel approach for failure mode and effects analysis using combination weighting and fuzzy vikor method. Appl Soft Comput 28:579–588
Jiang W, Xie C, Wei B, Zhou D (2016) A modified method for risk evaluation in failure modes and effects analysis of aircraft turbine rotor blades. Adv Mech Eng 8(4):1–16. doi:10.1177/1687814016644579
Yang Y, Han D (2016) A new distance-based total uncertainty measure in the theory of belief functions. Knowl-Based Syst 94:114–123
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 mapping employing evidential reasoning and fuzzy logic. Pattern Recogn Lett 48:24–33
Liu Z-G, Pan Q, Dezert J, Martin A (2016) Adaptive imputation of missing values for incomplete pattern classification. Pattern Recogn 52:85–95
Liu Z-G, Liu Y, Dezert J, Pan Q (2015) Classification of incomplete data based on belief functions and K-nearest neighbors. Knowl-Based Syst 89:113–125
Xu P, Deng Y, Su X, Mahadevan S (2013) A new method to determine basic probability assignment from training data. Knowl-Based Syst 46(1):69–80
Denoeux T (1995) A k-nearest neighbor classification rule based on dempster-shafer theory. IEEE Trans Syst Man Cybern 25(5):804–813
Rogova G (1994) Combining the results of several neural network classifiers. Neural Netw 7(5):777–781
Ph S, Kennes R (1994) The transferable belief model. Artif Intel 1(2):PS21–PS33
Deng Y (2015) A threat assessment model under uncertain environment. Math Probl Eng 2015:878024
Deng Y (2015) Generalized evidence theory. Appl Intell 43(3):530–543
Jiang W, Wei B, Qin X, Zhan J, Tang Y (2016) Sensor data fusion based on a new conflict measure. Mathematical Problems in Engineering. 2016, Article ID 5769061. doi:10.1155/2016/5769061
Zavadskas EK, Antuchevicience J, Hajiagha SHR (2015) The interval-valued intuitionistic fuzzy multimoora method for group decision making in engineering. Math Probl Eng 2015:560690
Song Y, Wang X, Lei L, Yue S (2016) Uncertainty measure for interval-valued belief structures. Measurement 80:241– 250
Ning X, Yuan J, Yue X (2006) Uncertainty-based optimization algorithms in designing fractionated spacecraft. Scientific Reports 6:22979
Fan G, Zhong D, Yan F, Yue P (2016) A hybrid fuzzy evaluation method for curtain grouting efficiency assessment based on an AHP method extended by D numbers. Expert Syst Appl 44(1):289–303
Ning X, Yuan J, Yue X, Ramirez-Serrano A (2014) Induced generalized choquet aggregating operators with linguistic information and their application to multiple attribute decision making based on the intelligent computing. J Int Fuzzy Syst 27(3):1077–1085
Deng Y (2017) Fuzzy analytical hierarchy process based on canonical representation on fuzzy numbers. J Comput Anal Appl 22(2):201–228
Sabahi F, Akbarzadeh-t M-R (2013) A qualified description of extended fuzzy logic. Inf Sci 244:60–74
Sabahi F, Akbarzadeh-t M-R (2014) Introducing validity in fuzzy probability for judicial decision-making. Int J Approx Reason 55(6):1383–1403
Jiang W, Xie C, Luo Y, Tang Y Ranking z-numbers with an improved ranking method for generalized fuzzy numbers. J Int Fuzzy Syst (Preprint) 1–13. doi:10.3233/JIFS-16139
Su X, Mahadevan S, Han W, Deng Y (2016) Combining dependent bodies of evidence. Appl Intell 44(3):634–644
Fu C, Yang J-B, Yang S-L (2015) A group evidential reasoning approach based on expert reliability. Eur J Oper Res 246(3):886–893
Song Y, Wang X, Lei L, Xing Y (2015) Credibility decay model in temporal evidence combination. Inf Process Lett 115(2):248– 252
Liu HC, You JX, Fan XJ, Lin QL (2014) Failure mode and effects analysis using D numbers and grey relational projection method. Expert Syst Appl 41(10):4670–4679
Jiang W, Wei B, Xie C, Zhou D (2016) An evidential sensor fusion method in fault diagnosis. Advances in Mechanical Engineering 8(3):1–7
Li Y, Chen J, Ye F, Liu D (2016) The improvement of DS evidence theory and its application in IR/MMW target recognition. Journal of Sensors (1903792)
Liu Z-G, Pan Q, Dezert J (2014) A belief classification rule for imprecise data. Appl Intell 40(2):214–228
Yu C, Yang J, Yang D, Ma X, Min H (2015) An improved conflicting evidence combination approach based on a new supporting probability distance. Expert Syst Appl 42(12):5139– 5149
Du W, Gao Y, Liu C, Zheng Z, Wang Z (2015) Adequate is better: particle swarm optimization with limited-information. Appl Math Comput 268:832–838
Du W-B, Zhou X-L, Lordan O, Wang Z, Zhao C, Zhu Y-B (2016) Analysis of the chinese airline network as multi-layer networks. Transportation Research Part E: Logistics and Transportation Review 89:108–116
Cheng D, Hao R-X, Feng Y-Q (2015) Embedding even cycles on folded hypercubes with conditional faulty edges. Inf Process Lett 115(12):945–949
Ning X, Zhang T, Wu Y, Zhang P, Zhang J, Li S, Yue X, Yuan J (2016) Coordinated parameter identification technique for the inertial parameters of non-cooperative target. PloS One 11(4):e0153604
Jiang W, Zhan J, Zhou D, Li X (2016) A method to determine generalized basic probability assignment in the open world. Mathematical Problems in Engineering. 2016, Article ID 3878634. doi:10.1155/2016/3878634
Chou CC (2016) A generalized similarity measure for fuzzy numbers. J Int Fuzzy Syst 30(2):1147–1155
Goyal RK, Kaushal S (2016) A constrained non-linear optimization model for fuzzy pairwise comparison matrices using teaching learning based optimization. Appl Intell:1–10. doi:10.1007/s10489-016-0777-z
Jiang W, Luo Y, Qin X, Zhan J (2015) An improved method to rank generalized fuzzy numbers with different left heights and right heights. J Int Fuzzy Syst 28(5):2343–2355
Tsai SB, Chien MF, Xue Y, Li L, Jiang X, Chen Q, Zhou J, Wang L (2015) Using the fuzzy dematel to determine environmental performance: A case of printed circuit board industry in taiwan. Plos One 10.
Wang J-Q, Wang D-D, Zhang H-Y, Chen X-H (2015) Multi-criteria group decision making method based on interval 2-tuple linguistic information and Choquet integral aggregation operators. Soft Comput 19(2):389–405
Nguyen H-T, Dawal SZM, Nukman Y, Aoyama H, Case K (2015) An integrated approach of fuzzy linguistic preference based AHP and fuzzy COPRAS for machine tool evaluation. PloS One 10(9):e0133599
Wang JQ, Wu JT, Wang J, Zhang HY, Chen XH (2014) Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Inf Sci 288(1):55– 72
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Fisher RA Iris data set, http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data
Mullins J, Ling Y, Mahadevan S, Sun L, Strachan A (2016) Separation of aleatory and epistemic uncertainty in probabilistic model validation. Reliab Eng Syst Saf 147:49– 59
Witten IH, Frank E (2005) Data mining: Practical machine learning tools and techniques. Morgan Kaufmann, San Francisco
De Maio C, Fenza G, Loia V, Senatore S (2012) Hierarchical web resources retrieval by exploiting fuzzy formal concept analysis. Inf Process Manag 48(3):399–418
De Maio C, Fenza G, Loia V, Senatore S (2009) Towards an automatic fuzzy ontology generation. In: IEEE International Conference on Fuzzy systems, 2009. IEEE, pp 1044–1049
Bobillo F, Straccia U (2016) Optimising fuzzy description logic reasoners with general concept inclusion absorption. Fuzzy Sets and Systems
Acknowledgments
The authors greatly appreciate the reviews’ suggestions and the editor’s encouragement. The work is partially supported by National Natural Science Foundation of China (Grant Nos. 61174022,61573290,61503237).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, J., Deng, Y. A method to determine basic probability assignment in the open world and its application in data fusion and classification. Appl Intell 46, 934–951 (2017). https://doi.org/10.1007/s10489-016-0877-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10489-016-0877-9