Fuzzy Bayesian Nets and Influence Diagrams with Cognitive Numerical Judgment of Imprecise Probabilities

The chapter will explain a connection between subjective uncertainty during the probability assessment and mental number representation of different probabilities expressed by approximate numbers. Subjective probabilities are represented as information granules described by linguistic terms and modeled as triangular fuzzy numbers. The proposed optimization functions proved to be efficient in determination of feasible probability bounds, yet corresponding to the human cognitive process. The usage of optimized fuzzy probabilities is illustrated on simple Influence diagram solving the e-commerce transaction. The quadratic programming model is proposed that can be easily solved, and simulation results are concurrent with the experimental findings of subjective probability assessment.

[1]  Ian Jenkinson,et al.  A Bayesian Network Approach for Offshore Risk Analysis through Linguistic Variables , 2007 .

[2]  Kurt Weichselberger,et al.  A Methodology for Uncertainty in Knowledge-Based Systems , 1990, Lecture Notes in Computer Science.

[3]  Robert S. Siegler,et al.  Fractions: the new frontier for theories of numerical development , 2013, Trends in Cognitive Sciences.

[4]  Lori N. K. Leonard,et al.  Trust in consumer-to-consumer electronic commerce , 2008, Inf. Manag..

[5]  H. Raghav Rao,et al.  A trust-based consumer decision-making model in electronic commerce: The role of trust, perceived risk, and their antecedents , 2008, Decis. Support Syst..

[6]  Yufei Yuan,et al.  Privacy protection in electronic commerce - a theoretical framework , 2001 .

[7]  Paul A. Pavlou,et al.  Consumer Acceptance of Electronic Commerce: Integrating Trust and Risk with the Technology Acceptance Model , 2003, Int. J. Electron. Commer..

[8]  Jeroen Keppens,et al.  Linguistic Bayesian Networks for reasoning with subjective probabilities in forensic statistics , 2003, ICAIL.

[9]  V. Kreinovich,et al.  Imprecise probabilities in engineering analyses , 2013 .

[10]  E. Ert,et al.  Trust and reputation in the sharing economy: The role of personal photos in Airbnb , 2015 .

[11]  Wei-Lun Chang,et al.  Estimating trust value: A social network perspective , 2014, Information Systems Frontiers.

[12]  Adam Lindgreen,et al.  Viral marketing: the use of surprise , 2005 .

[13]  Zheng Yan,et al.  Trust Modeling and Management: From Social Trust to Digital Trust , 2008 .

[14]  P. Keen,et al.  Electronic Commerce Relationships: Trust by Design , 1999 .

[15]  Stanislas Dehaene,et al.  The neural basis of the Weber–Fechner law: a logarithmic mental number line , 2003, Trends in Cognitive Sciences.

[16]  Jian-Bo Yang,et al.  Linguistic Assessment Approach for Hierarchical Safety Analysis and Synthesis , 2008 .

[17]  Amnon Rapoport,et al.  Measuring the Vague Meanings of Probability Terms , 1986 .

[18]  Ardion Beldad,et al.  How shall I trust the faceless and the intangible? A literature review on the antecedents of online trust , 2010, Comput. Hum. Behav..

[19]  Jason Bennett Thatcher,et al.  A Classification and Investigation of Trustees in B-to-C e-Commerce: General vs. Specific Trust , 2013, Commun. Assoc. Inf. Syst..

[20]  Qiang Shen,et al.  Towards a linguistic probability theory , 2002, 2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291).

[21]  J. Kyburg.  Higher order probability and intervals , 1988 .

[22]  Peijun Guo,et al.  Decision-making with interval probabilities , 2008, 2008 IEEE International Conference on Systems, Man and Cybernetics.

[23]  Stephen S. Yau.  Managing Trust in Distributed Agent Systems , 2006, ATC.

[24]  Mincong Tang,et al.  Building trust online: Interactions among trust building mechanisms , 2013, Inf. Manag..

[25]  ROBERT S. MOYER,et al.  Time required for Judgements of Numerical Inequality , 1967, Nature.

[26]  A. Sundararajan.  The Sharing Economy: The End of Employment and the Rise of Crowd-Based Capitalism , 2016 .

[27]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[28]  Ewald A. Kaluscha,et al.  Empirical research in on-line trust: a review and critical assessment , 2003, Int. J. Hum. Comput. Stud..