A new belief entropy and its application in software risk analysis
DOI:
https://doi.org/10.15837/ijccc.2023.2.5299Keywords:
Dempster-Shafer evidence theory, Deng entropy, Uncertainty measure, Software risk analysis, Belief entropyAbstract
The measurement of uncertainty has been an important topic of research. In Dempster’s framework, Deng entropy serves as a reliable tool for such measurements. However, it fails to consider more comprehensive information, resulting in the loss of critical data. An improved belief entropy is proposed in this paper, which preserves all the merits of Deng entropy. When there is only a single element, it can be degraded to Shannon entropy. When dealing with multiple elements, the partitioning method employed for mass functions makes it more responsive and efficient than alternative measures of uncertainty. Some numerical examples are given to further illustrate the effectiveness and applicability of the proposed entropy measure. Additionally, a case study is conducted on software risk analysis, demonstrating the practical value and relevance of the proposed method in real-world scenarios.References
Boehm, B.W., 1991. Software risk management: principles and practices. IEEE software 8, 32-41.
https://doi.org/10.1109/52.62930
Chen, L., Deng, Y., Cheong, K.H., 2021. Probability transformation of mass function: A weighted network method based on the ordered visibility graph. Engineering Applications of Artificial Intelligence 105, 104438.
https://doi.org/10.1016/j.engappai.2021.104438
Chen, X., Deng, Y., 2022. An evidential software risk evaluation model. Mathematics 10, 2325.
https://doi.org/10.3390/math10132325
Cui, H., Liu, Q., Zhang, J., Kang, B., 2019. An improved deng entropy and its application in pattern recognition. IEEE Access 7, 18284-18292.
https://doi.org/10.1109/ACCESS.2019.2896286
Dempster, A.P., 2008. Upper and lower probabilities induced by a multivalued mapping, in: Classic works of the Dempster-Shafer theory of belief functions. Springer, pp. 57-72.
https://doi.org/10.1007/978-3-540-44792-4_3
Deng, J., Deng, Y., 2021. Information volume of fuzzy membership function. International Journal of Computers Communications & Control 16, 4106.
https://doi.org/10.15837/ijccc.2021.1.4106
Deng, X., Jiang, W., 2020. On the negation of a dempster-shafer belief structure based on maximum uncertainty allocation. Information Sciences 516, 346-352.
https://doi.org/10.1016/j.ins.2019.12.080
Deng, Y., 2016. Deng entropy. Chaos, Solitons & Fractals 91, 549-553.
https://doi.org/10.1016/j.chaos.2016.07.014
Deng, Y., 2020a. Information volume of mass function. International Journal of Computers Communications & Control 15, 3983.
https://doi.org/10.15837/ijccc.2020.6.3983
Deng, Y., 2020b. Uncertainty measure in evidence theory. SCIENCE CHINA Information Sciences 63, 210201.
https://doi.org/10.1007/s11432-020-3006-9
Dubois, D., 2006. Possibility theory and statistical reasoning. Computational statistics & data analysis 51, 47-69.
https://doi.org/10.1016/j.csda.2006.04.015
Dubois, D., Prade, H., 1985. A note on measures of specificity for fuzzy sets. International Journal of General System 10, 279-283.
https://doi.org/10.1080/03081078508934893
Gao, X., Deng, Y., 2019. The generalization negation of probability distribution and its application in target recognition based on sensor fusion. International Journal of Distributed Sensor Networks 15, 1550147719849381.
https://doi.org/10.1177/1550147719849381
George, T., Pal, N.R., 1996. Quantification of conflict in dempster-shafer framework: a new approach. International Journal Of General System 24, 407-423.
https://doi.org/10.1080/03081079608945130
Hohle, U., 1982. Entropy with respect to plausibility measures, in: Proc. of 12th IEEE Int. Symp. on Multiple Valued Logic, Paris, 1982.
Jishuang, Q., Chao, W., Zhengzhi, W., 2003. Structure-context based fuzzy neural network approach for automatic target detection, in: IGARSS 2003. 2003 IEEE International Geoscience and Remote Sensing Symposium. Proceedings (IEEE Cat. No. 03CH37477), Ieee. pp. 767-769.
Kanal, L.N., Lemmer, J.F., 2014. Uncertainty in artificial intelligence. Elsevier.
Kazemi, M.R., Tahmasebi, S., Buono, F., Longobardi, M., 2021. Fractional deng entropy and extropy and some applications. Entropy 23, 623.
https://doi.org/10.3390/e23050623
Klir, G., Wierman, M., 1999. Uncertainty-based information: elements of generalized information theory. volume 15. Springer Science & Business Media.
https://doi.org/10.1007/978-3-7908-1869-7
Klir, G.J., Parviz, B., 1992. A note on the measure of discord, in: Uncertainty in Artificial Intelligence, Elsevier. pp. 138-141.
https://doi.org/10.1016/B978-1-4832-8287-9.50023-2
Klir, G.J., Ramer, A., 1990. Uncertainty in the dempster-shafer theory: a critical re-examination. International Journal of General System 18, 155-166.
https://doi.org/10.1080/03081079008935135
Levkina, R., Kravchuk, I., Sakhno, I., Kramarenko, K., Shevchenko, A., et al., 2019. The economic-mathematical model of risk analysis in agriculture in conditions of uncertainty. Financial and credit activity problems of theory and practice 3, 248-255.
https://doi.org/10.18371/fcaptp.v3i30.179560
Li, D., Du, Y., 2017. Artificial intelligence with uncertainty. CRC press.
https://doi.org/10.1201/9781315366951
Liang, H., Cai, R., 2021. A new correlation coefficient of bpa based on generalized information quality. International Journal of Intelligent Systems .
https://doi.org/10.1002/int.22490
Liao, H., Ren, Z., Fang, R., 2020. A deng-entropy-based evidential reasoning approach for multi-expert multi-criterion decision-making with uncertainty. International Journal of Computational Intelligence Systems 13, 1281-1294.
https://doi.org/10.2991/ijcis.d.200814.001
Mambe, M.D., Tchimou N'Takp'e, T., Nogbou, G.A., Oumtanaga, S., et al., 2018. A new uncertainty measure in belief entropy framework. International Journal of Advanced Computer Science and Applications 9.
https://doi.org/10.14569/IJACSA.2018.091184
Olshausen, B.A., 2004. Bayesian probability theory. The Redwood Center for Theoretical Neuroscience, Helen Wills Neuroscience Institute at the University of California at Berkeley, Berkeley, CA .
Pan, L., Deng, Y., 2018. A new belief entropy to measure uncertainty of basic probability assignments based on belief function and plausibility function. Entropy 20, 842.
https://doi.org/10.3390/e20110842
Pan, Y., Zhang, L., Li, Z., Ding, L., 2019. Improved fuzzy bayesian network-based risk analysis with interval-valued fuzzy sets and d-s evidence theory. IEEE Transactions on Fuzzy Systems 28, 2063-2077.
https://doi.org/10.1109/TFUZZ.2019.2929024
Pawlak, Z., 1982. Rough sets. International journal of computer & information sciences 11, 341-356.
https://doi.org/10.1007/BF01001956
Raimondo, S., De Domenico, M., 2021. Measuring topological descriptors of complex networks under uncertainty. Physical Review E 103, 022311.
https://doi.org/10.1103/PhysRevE.103.022311
Sangaiah, A.K., Samuel, O.W., Li, X., Abdel-Basset, M., Wang, H., 2018. Towards an efficient risk assessment in software projects-fuzzy reinforcement paradigm. Computers & Electrical Engineering 71, 833-846.
https://doi.org/10.1016/j.compeleceng.2017.07.022
Shafer, G., 1976. A mathematical theory of evidence. Princeton university press.
https://doi.org/10.1515/9780691214696
Shannon, C.E., 1948. A mathematical theory of communication. The Bell system technical journal 27, 379-423.
https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
Song, H., Wu, D., Li, M., Cai, C., Li, J., 2010. An entropy based approach for software risk assessment: A perspective of trustworthiness enhancement, in: The 2nd International Conference on Software Engineering and Data Mining, IEEE. pp. 575-578.
Song, Y., Wang, X., Zhu, J., Lei, L., 2018. Sensor dynamic reliability evaluation based on evidence theory and intuitionistic fuzzy sets. Applied Intelligence 48, 3950-3962.
https://doi.org/10.1007/s10489-018-1188-0
Suresh, K., Dillibabu, R., 2020. A novel fuzzy mechanism for risk assessment in software projects. Soft Computing 24, 1683-1705.
https://doi.org/10.1007/s00500-019-03997-2
Vashishtha, G., Kumar, R., 2022. Pelton wheel bucket fault diagnosis using improved shannon entropy and expectation maximization principal component analysis. Journal of Vibration Engineering & Technologies 10, 335-349.
https://doi.org/10.1007/s42417-021-00379-7
Wang, L., Bao, Y., 2021. An improved method for multisensor high conflict data fusion. Journal of Sensors 2021.
https://doi.org/10.1155/2021/9335300
Wang, T., Liu, W., Zhao, J., Guo, X., Terzija, V., 2020. A rough set-based bio-inspired fault diagnosis method for electrical substations. International Journal of Electrical Power & Energy Systems 119, 105961.
https://doi.org/10.1016/j.ijepes.2020.105961
Wu, S., Fu, Y., Shen, H., Liu, F., 2018. Using ranked weights and shannon entropy to modify regional sustainable society index. Sustainable cities and society 41, 443-448.
https://doi.org/10.1016/j.scs.2018.05.052
Wu, X., Liao, H., 2021. An adaptive evidence combination method for decision analysis under uncertainty. Journal of the Operational Research Society , 1-15.
Xiao, F., 2020. Generalization of dempster-shafer theory: A complex mass function. Applied Intelligence 50, 3266-3275.
https://doi.org/10.1007/s10489-019-01617-y
Xiao, F., 2021. Ceqd: A complex mass function to predict interference effects. IEEE Transactions on Cybernetics .
https://doi.org/10.1109/TCYB.2020.3040770
Xiong, L., Su, X., Qian, H., 2021. Conflicting evidence combination from the perspective of networks. Information Sciences 580, 408-418.
https://doi.org/10.1016/j.ins.2021.08.088
Yager, R.R., 2008. Entropy and specificity in a mathematical theory of evidence, in: Classic works of the Dempster-Shafer theory of belief functions. Springer, pp. 291-310.
https://doi.org/10.1007/978-3-540-44792-4_11
Yan, Z., Zhao, H., Mei, X., 2021. An improved conflicting-evidence combination method based on the redistribution of the basic probability assignment. Applied Intelligence , 1-27.
https://doi.org/10.1007/s10489-021-02404-4
Yang, W., Xu, K., Lian, J., Ma, C., Bin, L., 2018. Integrated flood vulnerability assessment approach based on topsis and shannon entropy methods. Ecological Indicators 89, 269-280.
https://doi.org/10.1016/j.ecolind.2018.02.015
Zadeh, L.A., 1979. On the validity of Dempster's rule of combination of evidence. Infinite Study.
Zadeh, L.A., 1996. Fuzzy sets, in: Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by Lotfi A Zadeh. World Scientific, pp. 394-432.
https://doi.org/10.1142/9789814261302_0021
Zhang, S., Xiao, F., 2023. A tfn-based uncertainty modeling method in complex evidence theory for decision making. Information Sciences 619, 193-207.
https://doi.org/10.1016/j.ins.2022.11.014
Zhao, K., Li, L., Chen, Z., Sun, R., Yuan, G., Li, J., 2022. A survey: Optimization and applications of evidence fusion algorithm based on dempster-shafer theory. Applied Soft Computing , 109075.
https://doi.org/10.1016/j.asoc.2022.109075
Zhou, D., Tang, Y., Jiang, W., 2017. An improved belief entropy and its application in decisionmaking. Complexity 2017, 1-15.
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