A quantum dynamic belief decision making model

The sure thing principle and the law of total probability are basic laws in classic probability theory. A disjunction fallacy leads to the violation of these two classical probability laws. In this paper, a new quantum dynamic belief decision making model based on quantum dynamic modelling and Dempster-Shafer (D-S) evidence theory is proposed to address this issue and model the real human decision-making process. Some mathematical techniques are borrowed from quantum mathematics. Generally, belief and action are two parts in a decision making process. The uncertainty in belief part is represented by a superposition of certain states. The uncertainty in actions is represented as an extra uncertainty state. The interference effect is produced due to the entanglement between beliefs and actions. Basic probability assignment (BPA) of decisions is generated by quantum dynamic modelling. Then BPA of the extra uncertain state and an entanglement degree defined by an entropy function named Deng entropy are used to measure the interference effect. Compared the existing model, the number of free parameters is less in our model. Finally, a classical categorization decision-making experiment is illustrated to show the effectiveness of our model.

[1]  Jennifer Trueblood,et al.  A Quantum Probability Account of Order Effects in Inference , 2011, Cogn. Sci..

[2]  Theresa E. DiDonato,et al.  Social Projection Can Solve Social Dilemmas , 2012 .

[3]  Xinyang Deng,et al.  On the axiomatic requirement of range to measure uncertainty , 2014 .

[4]  J. Busemeyer,et al.  Empirical Comparison of Markov and Quantum models of decision-making , 2009 .

[5]  Fang Yu,et al.  Enhancing user privacy in SARG04-based private database query protocols , 2015, Quantum Inf. Process..

[6]  Jian-Bo Yang,et al.  A group evidential reasoning approach based on expert reliability , 2015, Eur. J. Oper. Res..

[7]  Chao Fu,et al.  Determining attribute weights to improve solution reliability and its application to selecting leading industries , 2016, Ann. Oper. Res..

[8]  Ting-Ting Song,et al.  Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources , 2015, Scientific Reports.

[9]  Irina Basieva,et al.  Quantum-Like Representation Algorithm for Trichotomous Observables , 2011 .

[10]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[11]  Ariane Lambert-Mogiliansky,et al.  Bohr complementarity in memory retrieval , 2016 .

[12]  Sankaran Mahadevan,et al.  Combining dependent bodies of evidence , 2015, Applied Intelligence.

[13]  Harald Atmanspacher,et al.  The Potential of Using Quantum Theory to Build Models of Cognition , 2013, Top. Cogn. Sci..

[14]  James T. Townsend,et al.  Exploring the relations between categorization and decision making with regard to realistic face stimuli , 2000 .

[15]  Haozhen Situ.  Two-player conflicting interest Bayesian games and Bell nonlocality , 2016, Quantum Inf. Process..

[16]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[17]  J. Busemeyer,et al.  A quantum probability explanation for violations of ‘rational’ decision theory , 2009, Proceedings of the Royal Society B: Biological Sciences.

[18]  Didier Sornette,et al.  Decision theory with prospect interference and entanglement , 2011, ArXiv.

[19]  Emmanuel M. Pothos,et al.  Social Projection and a Quantum Approach for Behavior in Prisoner's Dilemma , 2012 .

[20]  Leong Chuan Kwek,et al.  Quantum prisoner dilemma under decoherence , 2003 .

[21]  A. Vourdas,et al.  Lower and upper probabilities in the distributive lattice of subsystems , 2014, 1410.2040.

[22]  Philippe Smets,et al.  The Transferable Belief Model , 1991, Artif. Intell..

[23]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[24]  Didier Sornette,et al.  Physics of risk and uncertainty in quantum decision making , 2008, ArXiv.

[25]  James T. Townsend,et al.  Quantum dynamics of human decision-making , 2006 .

[26]  Charles Lambdin,et al.  The disjunction effect reexamined: Relevant methodological issues and the fallacy of unspecified percentage comparisons , 2007 .

[27]  Diederik Aerts,et al.  Quantum Structure in Cognition , 2008, 0805.3850.

[28]  Yong Hu,et al.  New Failure Mode and Effects Analysis: An Evidential Downscaling Method , 2016, Qual. Reliab. Eng. Int..

[29]  Zheng Wang,et al.  Interference effects of categorization on decision making , 2016, Cognition.

[30]  Liguo Fei,et al.  Meausre divergence degree of basic probability assignment based on Deng relative entropy , 2015, 2016 Chinese Control and Decision Conference (CCDC).

[31]  Didier Sornette,et al.  Processing Information in Quantum Decision Theory , 2008, Entropy.

[32]  Diederik Aerts,et al.  Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought , 2012, Top. Cogn. Sci..

[33]  K. Vind.  A foundation for statistics , 2003 .

[34]  Emmanuel M. Pothos,et al.  A Quantum Probability Perspective on Borderline Vagueness , 2013, Top. Cogn. Sci..

[35]  Jing Zhao,et al.  Classification of power quality disturbances using quantum neural network and DS evidence fusion , 2012 .

[36]  Masanori Ohya,et al.  Quantum-Like Model for Decision Making Process in Two Players Game , 2011 .

[37]  Emmanuel M. Pothos,et al.  Structured representations in a quantum probability model of similarity , 2015 .

[38]  A. Vourdas,et al.  Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces , 2014, 1410.2044.

[39]  Richard M. Shiffrin,et al.  Context effects produced by question orders reveal quantum nature of human judgments , 2014, Proceedings of the National Academy of Sciences.

[40]  Andreas Wichert,et al.  Quantum-Like Bayesian Networks for Modeling Decision Making , 2016, Front. Psychol..

[41]  Laurianne Sitbon,et al.  A probabilistic framework for analysing the compositionality of conceptual combinations , 2013, ArXiv.

[42]  M. Singh,et al.  An Evidential Reasoning Approach for Multiple-Attribute Decision Making with Uncertainty , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[43]  Peter Nyman,et al.  On the Consistency of the Quantum-Like Representation Algorithm for Hyperbolic Interference , 2010, 1009.1744.

[44]  Zhiming Huang,et al.  Relativistic Quantum Bayesian Game Under Decoherence , 2016 .

[45]  G. Resconi,et al.  Tests and entity in evidence theory and quantum mechanics , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[46]  Didier Sornette,et al.  Quantum Decision Theory as Quantum Theory of Measurement , 2008, ArXiv.

[47]  Wen Jiang,et al.  An evidential sensor fusion method in fault diagnosis , 2016 .

[48]  Weiru Liu,et al.  An evidential fusion approach for gender profiling , 2016, Inf. Sci..

[49]  Jerome R. Busemeyer,et al.  A Quantum Question Order Model Supported by Empirical Tests of an A Priori and Precise Prediction , 2013, Top. Cogn. Sci..

[50]  A. Tversky,et al.  The Disjunction Effect in Choice under Uncertainty , 1992 .