{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:12:03Z","timestamp":1760242323889,"version":"build-2065373602"},"reference-count":79,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,4,21]],"date-time":"2017-04-21T00:00:00Z","timestamp":1492732800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61671384"],"award-info":[{"award-number":["61671384"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Basic Research Plan in Shaanxi Province of China","award":["2016JM6018"],"award-info":[{"award-number":["2016JM6018"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["3102017OQD020"],"award-info":[{"award-number":["3102017OQD020"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Aviation Science Foundation","award":["20165553036"],"award-info":[{"award-number":["20165553036"]}]},{"name":"Fund of SAST","award":["SAST2016083"],"award-info":[{"award-number":["SAST2016083"]}]},{"name":"Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University","award":["Z2016122"],"award-info":[{"award-number":["Z2016122"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The zero-sum matrix game is one of the most classic game models, and it is widely used in many scientific and engineering fields. In the real world, due to the complexity of the decision-making environment, sometimes the payoffs received by players may be inexact or uncertain, which requires that the model of matrix games has the ability to represent and deal with imprecise payoffs. To meet such a requirement, this paper develops a zero-sum matrix game model with Dempster\u2013Shafer belief structure payoffs, which effectively represents the ambiguity involved in payoffs of a game. Then, a decomposition method is proposed to calculate the value of such a game, which is also expressed with belief structures. Moreover, for the possible computation-intensive issue in the proposed decomposition method, as an alternative solution, a Monte Carlo simulation approach is presented, as well. Finally, the proposed zero-sum matrix games with payoffs of Dempster\u2013Shafer belief structures is illustratively applied to the sensor selection and intrusion detection of sensor networks, which shows its effectiveness and application process.<\/jats:p>","DOI":"10.3390\/s17040922","type":"journal-article","created":{"date-parts":[[2017,4,21]],"date-time":"2017-04-21T10:59:30Z","timestamp":1492772370000},"page":"922","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["Zero-Sum Matrix Game with Payoffs of Dempster-Shafer Belief Structures and Its Applications on Sensors"],"prefix":"10.3390","volume":"17","author":[{"given":"Xinyang","family":"Deng","sequence":"first","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5429-2748","authenticated-orcid":false,"given":"Wen","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiandong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,21]]},"reference":[{"key":"ref_1","unstructured":"Klir, G., and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1109\/TSMCA.2005.853483","article-title":"Measuring ambiguity in the evidence theory","volume":"36","author":"Jousselme","year":"2006","journal-title":"IEEE Trans. Syst. Man Cybern. Part A Syst. Hum."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","article-title":"Rough sets","volume":"11","author":"Pawlak","year":"1982","journal-title":"Int. J. Comput. Inf. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1214\/aoms\/1177698950","article-title":"Upper and lower probabilities induced by a multivalued mapping","volume":"38","author":"Dempster","year":"1967","journal-title":"Ann. Math. Stat."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Shafer, G. (1976). A Mathematical Theory of Evidence, Princeton University Press.","DOI":"10.1515\/9780691214696"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.inffus.2012.01.012","article-title":"Objective priors from maximum entropy in data classification","volume":"14","author":"Palmieri","year":"2013","journal-title":"Inf. Fusion"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3395","DOI":"10.1109\/JSTARS.2015.2483320","article-title":"Discriminative random fields based on maximum entropy principle for semisupervised SAR image change detection","volume":"9","author":"An","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1931","DOI":"10.3233\/JIFS-16139","article-title":"Ranking Z-numbers with an improved ranking method for generalized fuzzy numbers","volume":"32","author":"Jiang","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_10","unstructured":"Palmieri, F., and Ciuonzo, D. (2010, January 27\u201329). Data fusion with entropic priors. Procedings of the 20th Italian Workshop on Neural Networks, WIRN, Frontiers in Artificial Intelligence and Applications, Salerno, Italy."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/MIC.2005.123","article-title":"Dempster-Shafer theory for intrusion detection in ad hoc networks","volume":"9","author":"Chen","year":"2005","journal-title":"IEEE Internet Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1007\/s10489-016-0851-6","article-title":"A modified combination rule in generalized evidence theory","volume":"46","author":"Jiang","year":"2017","journal-title":"Appl. Intell."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.eswa.2013.07.018","article-title":"Supplier selection using AHP methodology extended by D numbers","volume":"41","author":"Deng","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/j.eswa.2013.07.088","article-title":"Environmental impact assessment based on D numbers","volume":"41","author":"Deng","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sun, L., Liu, Y., Zhang, B., Shang, Y., Yuan, H., and Ma, Z. (2016). An integrated decision-making model for transformer condition assessment using game theory and modified evidence combination extended by D numbers. Energies, 9.","DOI":"10.3390\/en9090697"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.nucengdes.2016.12.001","article-title":"Dependence assessment in human reliability analysis based on D numbers and AHP","volume":"313","author":"Zhou","year":"2017","journal-title":"Nucl. Eng. Des."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4670","DOI":"10.1016\/j.eswa.2014.01.031","article-title":"Failure mode and effects analysis using D numbers and grey relational projection method","volume":"41","author":"Liu","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.ssci.2016.06.014","article-title":"D-DEMATEL: A new method to identify critical success factors in emergency management","volume":"91","author":"Zhou","year":"2017","journal-title":"Saf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2016.10.006","article-title":"Statistical physics of vaccination","volume":"664","author":"Wang","year":"2016","journal-title":"Phys. Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.plrev.2015.04.033","article-title":"Universal scaling for the dilemma strength in evolutionary games","volume":"14","author":"Wang","year":"2015","journal-title":"Phys. Life Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2070","DOI":"10.1109\/TCYB.2015.2462352","article-title":"Evidence combination from an evolutionary game theory perspective","volume":"46","author":"Deng","year":"2016","journal-title":"IEEE Trans. Cybern."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1109\/TEVC.2003.810069","article-title":"Chaotic sequences to improve the performance of evolutionary algorithms","volume":"7","author":"Caponetto","year":"2003","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lee, J., and Pak, D. (2016). A Game Theoretic Optimization Method for Energy Efficient Global Connectivity in Hybrid Wireless Sensor Networks. Sensors, 16.","DOI":"10.3390\/s16091380"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Abdalzaher, M.S., Seddik, K., Elsabrouty, M., Muta, O., Furukawa, H., and Abdel-Rahman, A. (2016). Game Theory Meets Wireless Sensor Networks Security Requirements and Threats Mitigation: A Survey. Sensors, 16.","DOI":"10.3390\/s16071003"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"e1601444","DOI":"10.1126\/sciadv.1601444","article-title":"Onymity promotes cooperation in social dilemma experiments","volume":"3","author":"Wang","year":"2017","journal-title":"Sci. Adv."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Chen, Y., Weng, S., Guo, W., and Xiong, N. (2016). A Game Theory Algorithm for Intra-Cluster Data Aggregation in a Vehicular Ad Hoc Network. Sensors, 16.","DOI":"10.3390\/s16020245"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Washburn, A. (2013). Two-Person Zero-Sum Games, Springer Science & Business Media.","DOI":"10.1007\/978-1-4614-9050-0"},{"key":"ref_28","unstructured":"von Neumann, J., and Morgenstern, O. (1944). Theory of Games and Economic Behavior, Princeton University Press."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Li, D.F. (2016). Linear Programming Models and Methods of Matrix Games With Payoffs of Triangular Fuzzy Numbers, Springer.","DOI":"10.1007\/978-3-662-48476-0"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10556781003796622","article-title":"Interval programming models for matrix games with interval payoffs","volume":"27","author":"Li","year":"2012","journal-title":"Optim. Methods Softw."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1016\/j.omega.2011.01.007","article-title":"Linear programming approach to solve interval-valued matrix games","volume":"39","author":"Li","year":"2011","journal-title":"Omega"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s00500-007-0207-6","article-title":"Studying interval valued matrix games with fuzzy logic","volume":"12","author":"Collins","year":"2008","journal-title":"Soft Comput."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Mitchell, C., Hu, C., Chen, B., Nooner, M., and Young, P. (2014, January 10\u201313). A computational study of interval-valued matrix games. Proceedings of the International Conference on Computational Science and Computational Intelligence (CSCI), Las Vegas, NV, USA.","DOI":"10.1109\/CSCI.2014.66"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1697","DOI":"10.1016\/j.cie.2008.06.002","article-title":"Matrix games with interval data","volume":"56","author":"Liu","year":"2009","journal-title":"Comput. Ind. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/TSMCB.2012.2212885","article-title":"An effective methodology for solving matrix games with fuzzy payoffs","volume":"43","author":"Li","year":"2013","journal-title":"IEEE Trans. Cybern."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/j.fiae.2014.12.003","article-title":"On Nash equilibrium strategy of two-person zero-sum games with trapezoidal fuzzy payoffs","volume":"6","author":"Dutta","year":"2014","journal-title":"Fuzzy Inf. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1650047","DOI":"10.1142\/S0217595916500470","article-title":"A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers","volume":"33","author":"Kumar","year":"2016","journal-title":"Asia Pac. J. Oper. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1016\/j.ejor.2015.05.011","article-title":"On solving matrix games with pay-offs of triangular fuzzy numbers: Certain observations and generalizations","volume":"246","author":"Chandra","year":"2015","journal-title":"Eur. J. Oper. Res."},{"key":"ref_39","first-page":"117","article-title":"Solving matrix game with rough payoffs using genetic algorithm","volume":"16","author":"Roy","year":"2016","journal-title":"Oper. Res."},{"key":"ref_40","first-page":"280","article-title":"A lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers","volume":"3","author":"Nan","year":"2010","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1142\/S0218488509006157","article-title":"A nonlinear programming approach to matrix games with payoffs of Atanassov\u2019s intuitionistic fuzzy sets","volume":"17","author":"Li","year":"2009","journal-title":"Int. J. Uncertain. Fuzziness Knowl. Based Syst."},{"key":"ref_42","first-page":"159","article-title":"Matrix games with intuitionistic fuzzy pay-offs","volume":"36","author":"Seikh","year":"2015","journal-title":"J. Inf. Optim. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.1109\/TFUZZ.2010.2065812","article-title":"Mathematical-programming approach to matrix games with payoffs represented by Atanassov\u2019s interval-valued intuitionistic fuzzy sets","volume":"18","author":"Li","year":"2010","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Xu, L., Zhao, R., and Ning, Y. (2006, January 16\u201319). Two-person zero-sum matrix game with fuzzy random payoffs. Proceedings of the International Conference on Intelligent Computing, Kunming, China.","DOI":"10.1007\/11816171_101"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.knosys.2011.08.019","article-title":"Lattice-valued matrix game with mixed strategies for intelligent decision support","volume":"32","author":"Xu","year":"2012","journal-title":"Knowl. Based Syst."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.knosys.2014.06.019","article-title":"Ambiguous games played by players with ambiguity aversion and minimax regret","volume":"70","author":"Xiong","year":"2014","journal-title":"Knowl. Based Syst."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"531987","DOI":"10.1155\/2014\/531987","article-title":"Games under ambiguous payoffs and optimistic attitudes","volume":"2014","author":"Xiong","year":"2014","journal-title":"J. Appl. Math."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1016\/j.amc.2014.07.065","article-title":"An evidential game theory framework in multi-criteria decision making process","volume":"244","author":"Deng","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1109\/TCYB.2015.2417121","article-title":"Evaluating Belief Structure Satisfaction to Uncertain Target Values","volume":"46","author":"Yager","year":"2016","journal-title":"IEEE Trans. Cybern."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.knosys.2016.11.001","article-title":"Data classification using evidence reasoning rule","volume":"116","author":"Xu","year":"2017","journal-title":"Knowl. Based Syst."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/j.chaos.2016.07.014","article-title":"Deng entropy","volume":"91","author":"Deng","year":"2016","journal-title":"Chaos Solitons Fractals"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Jiang, W., Xie, C., Zhuang, M., and Tang, Y. (2017). Failure mode and effects analysis based on a novel fuzzy evidential method. Appl. Soft Comput.","DOI":"10.1016\/j.asoc.2017.04.008"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1998","DOI":"10.1109\/TIA.2016.2518995","article-title":"Probabilistic Wind Generation Forecast Based on Sparse Bayesian Classification and Dempster-Shafer Theory","volume":"52","author":"Yang","year":"2016","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Deng, X., Xiao, F., and Deng, Y. (2017). An improved distance-based total uncertainty measure in belief function theory. Appl. Intell.","DOI":"10.1007\/s10489-016-0870-3"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1109\/TSMC.2015.2421883","article-title":"Evaluation of probability transformations of belief functions for decision making","volume":"46","author":"Han","year":"2016","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.patrec.2015.11.027","article-title":"An angle-based neighborhood graph classifier with evidential reasoning","volume":"71","author":"Yang","year":"2016","journal-title":"Pattern Recogn. Lett."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.cie.2016.09.009","article-title":"A visibility graph power averaging aggregation operator: A methodology based on network analysis","volume":"101","author":"Jiang","year":"2016","journal-title":"Comput. Ind. Eng."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"023117","DOI":"10.1063\/1.4977186","article-title":"Ordered visibility graph average aggregation operator: An application in produced water management","volume":"27","author":"Jiang","year":"2017","journal-title":"Chaos"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1142\/S0218488516500379","article-title":"A new aggregating operator in linguistic decision making based on D numbers","volume":"24","author":"Mo","year":"2016","journal-title":"Int. J. Uncertain. Fuzziness Knowl. Based Syst."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1002\/int.21861","article-title":"A new interval numbers power average operator in multiple attribute decision making","volume":"32","author":"Song","year":"2017","journal-title":"Int. J. Intell. Syst."},{"key":"ref_61","first-page":"2976","article-title":"Channel-aware decision fusion in distributed MIMO wireless sensor networks: Decode-and-fuse vs. decode-then-fuse","volume":"11","author":"Ciuonzo","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Wang, H., Yao, K., Pottie, G., and Estrin, D. (2004, January 26\u201327). Entropy-based sensor selection heuristic for target localization. Proceedings of the 3rd International Symposium on Information Processing in Sensor Networks, Berkeley, CA, USA.","DOI":"10.1145\/984622.984628"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/TSP.2012.2223694","article-title":"Optimality of received energy in decision fusion over Rayleigh fading diversity MAC with non-identical sensors","volume":"61","author":"Ciuonzo","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"7771","DOI":"10.3390\/s91007771","article-title":"Advances in multi-sensor data fusion: Algorithms and applications","volume":"9","author":"Dong","year":"2009","journal-title":"Sensors"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"28772","DOI":"10.3390\/s151128772","article-title":"Multi-sensor data fusion identification for shearer cutting conditions based on parallel quasi-newton neural networks and the Dempster-Shafer theory","volume":"15","author":"Si","year":"2015","journal-title":"Sensors"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.engappai.2015.04.012","article-title":"Evidential framework for data fusion in a multi-sensor surveillance system","volume":"43","author":"Reynaud","year":"2015","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Jiang, W., Zhuang, M., Xie, C., and Wu, J. (2017). Sensing attribute weights: A novel basic belief assignment method. Sensors, 17.","DOI":"10.3390\/s17040721"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.inffus.2011.08.001","article-title":"Multisensor data fusion: A review of the state-of-the-art","volume":"14","author":"Khaleghi","year":"2013","journal-title":"Inf. Fusion"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0031-3203(99)00210-1","article-title":"Fusion of correlated decisions for writer verification","volume":"34","author":"Zois","year":"2001","journal-title":"Pattern Recogn."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Tselios, K., Zois, E.N., Nassiopoulos, A., and Economou, G. (2011, January 11\u201313). Fusion of directional transitional features for off-line signature verification. Proceedings of the International Joint Conference on Biometrics (IJCB), Washington, DC, USA.","DOI":"10.1109\/IJCB.2011.6117515"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"2080","DOI":"10.1109\/TSMCB.2004.833772","article-title":"Cumulative distribution functions from Dempster-Shafer belief structures","volume":"34","author":"Yager","year":"2004","journal-title":"IEEE Trans. Syst. Man Cybern. Part B Cybern."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s10700-013-9163-z","article-title":"Joint cumulative distribution functions for Dempster-Shafer belief structures using copulas","volume":"12","author":"Yager","year":"2013","journal-title":"Fuzzy Optim. Decis. Mak."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.ijar.2005.04.001","article-title":"Belief functions on real numbers","volume":"40","author":"Smets","year":"2005","journal-title":"Int. J. Approx. Reason."},{"key":"ref_74","first-page":"239","article-title":"Comparison of three methods for selecting values of input variables in the analysis of output from a computer code","volume":"21","author":"McKay","year":"1979","journal-title":"Technometrics"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0951-8320(03)00058-9","article-title":"Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems","volume":"81","author":"Helton","year":"2003","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.ress.2015.12.002","article-title":"The generalization of Latin hypercube sampling","volume":"148","author":"Shields","year":"2016","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"2027","DOI":"10.1016\/j.cor.2004.01.005","article-title":"A preference aggregation method through the estimation of utility intervals","volume":"32","author":"Wang","year":"2005","journal-title":"Comput. Oper. Res."},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Ammari, H.M. (2014). The Art of Wireless Sensor Networks, Springer.","DOI":"10.1007\/978-3-642-40009-4"},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Liu, Y., Man, H., and Comaniciu, C. (2006, January 11\u201315). A game theoretic approach to efficient mixed strategies for intrusion detection. Proceedings of the IEEE International Conference on Communications, Istanbul, Turkey.","DOI":"10.1109\/ICC.2006.255097"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/4\/922\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:33:10Z","timestamp":1760207590000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/4\/922"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,21]]},"references-count":79,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,4]]}},"alternative-id":["s17040922"],"URL":"https:\/\/doi.org\/10.3390\/s17040922","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,4,21]]}}}