Abstract
The fusion of highly conflicting evidence in the Dempster–Shafer evidence theory has been an important research topic. To solve this issue, many existing methods depicted the conflicts between evidence by various distance measures. Although the distances between evidence can reflect the conflicts of evidence to some extent, they only represent one aspect of the conflicts. In this study, we propose a new conflict measurement method based on both the distance and angle between evidence. To combine the evidence distance and evidence angle effectively, the angle–distance ordered weighted averaging (OWA) pair is constructed inspired by the induced ordered weighted averaging operator. In addition, the personalized quantifier is used to describe decision-makers’ individual attitudes and risk preferences. The original evidence is modified by using the ordered weight of each evidence to obtain the discount evidence. A numerical example and corresponding comparative analysis show the effectiveness of the proposed method in measuring the conflict between evidence.
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Zheng, X.Y., Easa, S.M., Ji, T., Jiang, Z.L.: Incorporating uncertainty into life-cycle sustainability assessment of pavement alternatives. J. Cleaner Prod. 264, 121466 (2020). https://doi.org/10.1016/j.jclepro.2020.121466
Deng, X., Jiang, W., Wang, Z.: Zero-sum poly-matrix games with link uncertainty: a Dempster-Shafer theory solution. Appl. Math. Comput. 340, 101–112 (2019)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341–356 (1982)
Zadeh, L.A.: A note on Z-numbers. Inf. Sci. 181(14), 2923–2932 (2011)
Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 382, 325–339 (1967)
Shafer, G.: A mathematical theory of evidence. Princeton University Press, London (1976)
Xu, H., Deng, Y.: Dependent evidence combination based on decision making trial and evaluation laboratory method. Int. J. Intell. Syst. 34(7), 1555–1571 (2019)
Seiti, H., Hafezalkotob, A., Herrera-Viedma, E.: A novel linguistic approach for multi-granular information fusion and decision-making using risk-based linguistic D numbers. Inf. Sci. 530, 43–65 (2020)
Koksalmis, E., Kabak, O.: Sensor fusion based on Dempster-Shafer theory of evidence using a large-scale group decision making approach. Int. J. Intell. Syst. 35(7), 1126–1162 (2020)
Xiao, F.Y.: A new divergence measure for belief functions in D-S evidence theory for multi-sensor data fusion. Inf. Sci. 514, 462–483 (2020)
Pan, Y., Zhang, L.M., Wu, X.G., Skibniewski, M.J.: Multi-classifier information fusion in risk analysis. Information Fusion 60, 121–136 (2020)
Tao, X.L., Kang, R.N., Liu, L.Y.: A parallel multi-classifier fusion approach based on selective ensemble. Comput. Eng. Sci. 40(5), 787–792 (2020)
Mokarram, M., Mokarram, M.J., Khosravi, M.R., Saber, A., Rahideh, A.: Determination of the optimal location for constructing solar photovoltaic farms based on multi-criteria decision system and Dempster-Shafer theory. Sci. Rep. 10(1), 8200 (2020). https://doi.org/10.1038/s41598-020-65165-z
Fei, L.G., Lu, J.D., Feng, Y.Q.: An extended best-worst multi-criteria decision-making method by belief functions and its applications in hospital service evaluation. Comput. Ind. Eng. 142, 106355 (2020). https://doi.org/10.1016/j.cie.2020.106355
Abellan, J., Bosse, E.: Critique of recent uncertainty measures developed under the evidence theory and belief intervals. IEEE Trans. Syst. Man Cybern. 50(3), 1186–1192 (2020)
Xiao, F.Y.: EFMCDM: evidential fuzzy multicriteria decision making based on belief entropy. IEEE Trans. Fuzzy Syst. 28(7), 1477–1491 (2020)
Haouas, F., Solaiman, B., Ben, D.Z., Hamouda, A., Bsaies, K.: Multi-temporal image change mining based on evidential conflict reasoning. ISPRS J. Photogr. Remote Sens. 151, 59–75 (2019)
Zadeh, L.A.: A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination. AI Magazine 7, 85–90 (1986)
Yager, R.R.: On the Dempster-Shafer framework and new combination rules. Information Science 41(2), 93–137 (1987)
Smets, P.: The combination of evidence in the transferable belief model. IEEE Trans. Pattern Anal. Mach. Intell. 12(5), 447–458 (1990)
Dubois, D., Prade, H.: Representation and combination of uncertainty with belief functions and possibility measures. Computational Intelligence 4(3), 244–264 (1988)
J. Dezert, F. Smarandache, A new probabilistic transformation of belief mass assignment, International Conference on Information Fusion, Cologne, Germany, (2008) https://doi.org/10.1109/icif.2008.4632376
Jiang, W., Hu, W.W.: An improved soft likelihood function for Dempster-Shafer belief structures. Int. J. Intell. Syst. 33(6), 1264–1282 (2018)
Su, X.Y., Li, L.S., Qian, H., Mahadevan, S., Deng, Y.: A new rule to combine dependent bodies of evidence. Soft. Comput. 23(20), 9793–9799 (2019)
Murphy, C.K.: Combining belief functions when evidence conflicts. Decision Support System 29(1), 1–9 (2000)
Jousselme, A.L., Grenier, D., Bosse, É.: A new distance between two bodies of evidence. Information Fusion 2(2), 91–101 (2001)
Deng, Y., Shi, W., Zhu, Z., Liu, Q.: Combining belief functions based on distance of evidence. Dec. Supp. Syst. 38(3), 489–493 (2004)
A. Martin, A.L. Jousselme, C. Osswald, Conflict measure for the discounting operation on belief functions, In: International Conference on Information Fusion, Cologne, Germany, (2008) 1-8 https://doi.org/10.1109/icif.2008.4632320
Xiao, F.Y.: CED: A distance for complex mass functions. IEEE Trans. Neural Netw. Learn. Syst. (2020). https://doi.org/10.1109/tnnls.2020.2984918
Burger, T.: Geometric views on conflicting mass functions: from distance to angles. Int. J. Approx. Reason. 70, 36–50 (2016)
Deng, Z., Wang, J.Y.: A novel evidence conflict measurement for multi-sensor data fusion based on the evidence distance and evidence angle. Sensors 20(2), 381 (2020). https://doi.org/10.3390/s20020381
Yager, R.R.: On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)
Yager, R.R., Filev, D.P.: Induced ordered weighted averaging operators. IEEE Trans. Syst. Man Cybern. 29(2), 141–150 (1999)
Guo, K.H.: Quantifiers induced by subjective expected value of sample information. IEEE Trans. Syst. Man Cybern. 44(10), 2168–2267 (2014)
Luo, Z.Y., Deng, Y.: A vector and geometry interpretation of basic probability assignment in Dempster-Shafer theory. Int. J. Intell. Syst. 35(6), 944–962 (2020)
Smets, P.: Decision making in the TBM: the necessity of the pignistic transformation. Int. J. Approx. Reason. 38, 133–147 (2004)
Yager, R.R.: Quantifier guided aggregation using OWA operators. Int. J. Intell. Syst. 11(1), 49–73 (1996)
Zhou, L.G., Chen, H.Y.: Continuous generalized OWA operator and its application to decision making. Fuzzy Sets Syst. 168(1), 18–34 (2011)
Jin, L., Mesiar, R., Yager, R.R.: Ordered weighted averaging aggregation on convex poset. IEEE Trans. Fuzzy Syst. 27(3), 612–617 (2019)
Guo, K.H.: Quantifier induced by subjective expected value of sample information with bernstein polynomials. Eur. J. Oper. Res. 254, 226–235 (2016)
Guo, K.H., Xu, H.: Personalized quantifier by bernstein polynomials combined with interpolation spline. Int. J. Intell. Syst. 33, 1507–1533 (2018)
Tao, R., Xiao, F.Y.: Combine conflicting evidence based on the belief entropy and IOWA operator. IEEE Access 7, 120724–120733 (2019)
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The work was supported in part by the National Natural Science Foundation of China (Nos. 71971145, 71771156).
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Ren, Z., Liao, H. Combining Conflicting Evidence by Constructing Evidence’s Angle-Distance Ordered Weighted Averaging Pairs. Int. J. Fuzzy Syst. 23, 494–505 (2021). https://doi.org/10.1007/s40815-020-00964-0
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DOI: https://doi.org/10.1007/s40815-020-00964-0