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Decision-making and Fuzzy Temporal Logic

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  • Jos'e Cl'audio do Nascimento

Abstract

This paper shows that the fuzzy temporal logic can model figures of thought to describe decision-making behaviors. In order to exemplify, some economic behaviors observed experimentally were modeled from problems of choice containing time, uncertainty and fuzziness. Related to time preference, it is noted that the subadditive discounting is mandatory in positive rewards situations and, consequently, results in the magnitude effect and time effect, where the last has a stronger discounting for earlier delay periods (as in, one hour, one day), but a weaker discounting for longer delay periods (for instance, six months, one year, ten years). In addition, it is possible to explain the preference reversal (change of preference when two rewards proposed on different dates are shifted in the time). Related to the Prospect Theory, it is shown that the risk seeking and the risk aversion are magnitude dependents, where the risk seeking may disappear when the values to be lost are very high.

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  • Jos'e Cl'audio do Nascimento, 2019. "Decision-making and Fuzzy Temporal Logic," Papers 1901.01970, arXiv.org, revised Feb 2019.
  • Handle: RePEc:arx:papers:1901.01970
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    References listed on IDEAS

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    1. Kirby, Kris N. & Marakovic, Nino N., 1995. "Modeling Myopic Decisions: Evidence for Hyperbolic Delay-Discounting within Subjects and Amounts," Organizational Behavior and Human Decision Processes, Elsevier, vol. 64(1), pages 22-30, October.
    2. Gretchen B. Chapman & Arthur S. Elstein, 1995. "Valuing the Future," Medical Decision Making, , vol. 15(4), pages 373-386, October.
    3. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    4. Daniel Bernoulli, 2011. "Exposition Of A New Theory On The Measurement Of Risk," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 2, pages 11-24, World Scientific Publishing Co. Pte. Ltd..
    5. James H. Holcomb & Paul S. Nelson, 1992. "Another Experimental Look at Individual Time Preference," Rationality and Society, , vol. 4(2), pages 199-220, April.
    6. Ole Peters & Murray Gell-Mann, 2014. "Evaluating gambles using dynamics," Papers 1405.0585, arXiv.org, revised Jun 2015.
    7. Sinha, Sitabhra, 2006. "Evidence for power-law tail of the wealth distribution in India," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 555-562.
    8. Pender, John L., 1996. "Discount rates and credit markets: Theory and evidence from rural india," Journal of Development Economics, Elsevier, vol. 50(2), pages 257-296, August.
    9. Drăgulescu, Adrian & Yakovenko, Victor M., 2001. "Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 213-221.
    10. Levy, Moshe & Solomon, Sorin, 1997. "New evidence for the power-law distribution of wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 90-94.
    11. Loewenstein, George, 1987. "Anticipation and the Valuation of Delayed Consumption," Economic Journal, Royal Economic Society, vol. 97(387), pages 666-684, September.
    12. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    13. Uri Benzion & Amnon Rapoport & Joseph Yagil, 1989. "Discount Rates Inferred from Decisions: An Experimental Study," Management Science, INFORMS, vol. 35(3), pages 270-284, March.
    14. Klass, Oren S. & Biham, Ofer & Levy, Moshe & Malcai, Ofer & Solomon, Sorin, 2006. "The Forbes 400 and the Pareto wealth distribution," Economics Letters, Elsevier, vol. 90(2), pages 290-295, February.
    15. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
    16. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    17. Sumitava Mukherjee & Arvind Sahay & V. S. Chandrasekhar Pammi & Narayanan Srinivasan, 2017. "Is loss-aversion magnitude-dependent? Measuring prospective affective judgments regarding gains and losses," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 12(1), pages 81-89, January.
    18. Takahashi, Taiki & Oono, Hidemi & Radford, Mark H.B., 2008. "Psychophysics of time perception and intertemporal choice models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2066-2074.
    19. Marjorie K. Shelley, 1993. "Outcome Signs, Question Frames and Discount Rates," Management Science, INFORMS, vol. 39(7), pages 806-815, July.
    20. Read, Daniel & Roelofsma, Peter H. M. P., 2003. "Subadditive versus hyperbolic discounting: A comparison of choice and matching," Organizational Behavior and Human Decision Processes, Elsevier, vol. 91(2), pages 140-153, July.
    21. Donald A. Redelmeier & Daniel N. Heller, 1993. "Time Preference in Medical Decision Making and Cost - Effectiveness Analysis," Medical Decision Making, , vol. 13(3), pages 212-217, August.
    22. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    23. Read, Daniel, 2001. "Is Time-Discounting Hyperbolic or Subadditive?," Journal of Risk and Uncertainty, Springer, vol. 23(1), pages 5-32, July.
    24. Loewenstein, George & Thaler, Richard H, 1989. "Intertemporal Choice," Journal of Economic Perspectives, American Economic Association, vol. 3(4), pages 181-193, Fall.
    25. Tversky, Amos & Kahneman, Daniel, 1986. "Rational Choice and the Framing of Decisions," The Journal of Business, University of Chicago Press, vol. 59(4), pages 251-278, October.
    26. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    27. Ole Peters, 2010. "The time resolution of the St. Petersburg paradox," Papers 1011.4404, arXiv.org, revised Mar 2011.
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    Cited by:

    1. Jos'e Cl'audio do Nascimento, 2019. "The Time Importance for Prospect Theory," Papers 1908.01709, arXiv.org, revised Aug 2021.

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