A quantum inspired MADM method and the application in E-commerce recommendation
Abstract
In this paper, a quantum inspired MADM method is proposed. Inspired by quantum theory, the decision process is considered as a quantum probability system. Before the decision is made, the preference state is considered as the superposition from the sub-states with respect to various attributes. Each sub-state is regarded as the entanglement from the alternatives. Once the final decision is made, the preference state collapses into a definite state corresponding to an alternative. Based on the proposed method, the decision steps are provided. Ultimately, the feasibility is illustrated through an application in E-commerce recommendation.
Keyword : quantum probability, preference state, superposition, MADM (Multi-attribute decision making), e-commerce recommendation
How to Cite
Liu, S. (2018). A quantum inspired MADM method and the application in E-commerce recommendation. Technological and Economic Development of Economy, 24(5), 1941-1954. https://doi.org/10.3846/20294913.2017.1318313
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Wang, W.; Liu, X. 2014. Some hesitant fuzzy geometric operators and their application to multiple attribute group decision making, Technological and Economic Development of Economy 20(3): 371–390. https://doi.org/10.3846/20294913.2013.877094
Xia, M.; Chen, J. 2015. Multi-criteria group decision making based on bilateral agreements, European Journal of Operational Research 240(3): 756–764. https://doi.org/10.1016/j.ejor.2014.07.035
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Yukalov, V. I.; Sornette, D. 2008. Quantum decision theory as quantum theory of measurement, Physics Letters A 372(46): 6867–6871. https://doi.org/10.1016/j.physleta.2008.09.053
Yukalov, V. I.; Sornette, D. 2010. Entanglement production in quantum decision making, Physics of Atomic Nuclei 73(3): 559–562. https://doi.org/10.1134/S106377881003021X
Asano, M.; Ohya, M.; Khrennikov, A. 2011. Quantum-like model for decision making process in two players game, Foundations of Physics 41(3): 538–548. https://doi.org/10.1007/s10701-010-9454-y
Ashtiani, M.; Azgomi, M. A. 2015. A survey of quantum-like approaches to decision making and cognition, Mathematical Social Sciences 75: 49–80. https://doi.org/10.1016/j.mathsocsci.2015.02.004
Busemeyer, J. R.; Bruza, P. D. 2012. Quantum models of cognition and decision. Cambridge University Press. https://doi.org/10.1017/CBO9780511997716
Busemeyer, J. R.; Wang, Z.; Lambert-Mogiliansky, A. 2009. Empirical comparison of Markov and quantum models of decision making, Journal of Mathematical Psychology 53(5): 423–433. https://doi.org/10.1016/j.jmp.2009.03.002
Hashemian, S. M.; Behzadian, M.; Samizadeh, R.; Ignatius, J. 2014. A fuzzy hybrid group decision support system approach for the supplier evaluation process, International Journal of Advanced Manufacturing Technology 73(5–8): 1105–1117. https://doi.org/10.1007/s00170-014-5843-2
Hillery, M.; Andersson, E.; Barnett, S. M.; Oi, D. K. L. 2010. Decision problems with quantum black boxes, Journal of Modern Optics 57(3): 244–252. https://doi.org/10.1080/09500340903203129
Jiang, Y.; Xu, Z.; Yu, X. 2015. Group decision making based on incomplete intuitionistic multiplicative preference relations, Information Sciences 295: 33–52. https://doi.org/10.1016/j.ins.2014.09.043
Kabak, M.; Dagdeviren, M. 2014. A hybrid MCDM approach to assess the sustainability of students’ preferences for university selection, Technological and Economic Development of Economy 20(3): 391–418. https://doi.org/10.3846/20294913.2014.883340
Khrennikov, A. 2009. Quantum-like model of cognitive decision making and information processing, Biosystems 95(3): 179–187. https://doi.org/10.1016/j.biosystems.2008.10.004
Khrennikov, A.; Basieva, I. 2015. Quantum(-like) decision making: on validity of the aumann theorem, in H. Atmanspacher, C. Bergomi, T. Filk, and K. Kitto (Eds.). Quantum Interaction 8951: 105–118.
Kocaslan, G. 2014. Quantum interpretation to decision making under risk: the observer effect in Allais
Paradox, Neuroquantology 12(3): 412–418. https://doi.org/10.14704/nq.2014.12.3.776
Kou, G.; Peng, Y.; Lu, C. 2014. MCDM approach to evaluating bank loan default models, Technological and Economic Development of Economy 20(2): 292–311. https://doi.org/10.3846/20294913.2014.913275
Liu, S. L.; Liu, X. W. 2016. A sample survey based linguistic MADM method with Prospect Theory for online shopping problems, Group Decision and Negotiation 25(4): 749–774. https://doi.org/10.1007/s10726-015-9459-1
Palopoli, L.; Rosaci, D.; Sarné, G. M. L. 2016. A distributed and multi-tiered software architecture for assessing e-Commerce recommendations, Concurrency and Computation: Practice and Experience 28(18): 4507–453. https://doi.org/10.1002/cpe.3798
Palopoli, L.; Rosaci, D.; Sarné, G. M. L. 2013. Introducing specialization in e-commerce recommender systems, Concurrent Engineering-Research and Applications 21(3): 187–196. https://doi.org/10.1177/1063293X13493915
Pereira, J. G.; Jr., Ekel, P. Y.; Palhares, R. M.; Parreiras, R. O. 2015. On multicriteria decision making under conditions of uncertainty, Information Sciences 324: 44–59. https://doi.org/10.1016/j.ins.2015.06.013
Pothos, E. M.; Busemeyer, J. R. 2009. A quantum probability explanation for violations of ‘rational’ decision theory, in Proceedings of the Royal Society B-Biological Sciences 276(1665): 2171–2178. https://doi.org/10.1098/rspb.2009.0121
Ran, L.-G.; Wei, G.-W. 2015. Uncertain prioritized operators and their application to multiple attribute group decision making, Technological and Economic Development of Economy 21(1): 118–139. https://doi.org/10.3846/20294913.2014.979454
Rosaci, D. 2007. CILIOS: connectionist inductive learning and inter-ontology similarities for recommending information agents, Information Systems 32(6): 793–825. https://doi.org/10.1016/j.is.2006.06.003
Shankar, K. H. 2014. Quantum random walks and decision making, Topics in Cognitive Science 6(1): 108–113. https://doi.org/10.1111/tops.12070
Silva, V. B. S.; Morais, D. C. 2014. A group decision-making approach using a method for constructing a linguistic scale, Information Sciences 288: 423–436. https://doi.org/10.1016/j.ins.2014.08.012
Sun, B.; Ma, W. 2015. An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application, Omega-International Journal of Management Science 51: 83–92. https://doi.org/10.1016/j.omega.2014.09.006
Taobao.com. n.d. Chinese E-commerce shopping website [online]. Available from Internet: www.taobao.com
Wang, J.-q.; Peng, J.-j.; Zhang, H.-y.; Liu, T.; Chen, X.-h. 2015. An uncertain linguistic multi-criteria group decision-making method based on a Cloud Model, Group Decision and Negotiation 24(1): 171–192. https://doi.org/10.1007/s10726-014-9385-7
Wang, W.; Liu, X. 2014. Some hesitant fuzzy geometric operators and their application to multiple attribute group decision making, Technological and Economic Development of Economy 20(3): 371–390. https://doi.org/10.3846/20294913.2013.877094
Xia, M.; Chen, J. 2015. Multi-criteria group decision making based on bilateral agreements, European Journal of Operational Research 240(3): 756–764. https://doi.org/10.1016/j.ejor.2014.07.035
Yue, Z. 2014. TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting, Information Sciences 277: 141–153. https://doi.org/10.1016/j.ins.2014.02.013
Yukalov, V. I.; Sornette, D. 2008. Quantum decision theory as quantum theory of measurement, Physics Letters A 372(46): 6867–6871. https://doi.org/10.1016/j.physleta.2008.09.053
Yukalov, V. I.; Sornette, D. 2010. Entanglement production in quantum decision making, Physics of Atomic Nuclei 73(3): 559–562. https://doi.org/10.1134/S106377881003021X