Abstract
The aim of this chapter is to revisit an experiment of Kahneman and Tversky to arrive at conclusions about Prospect theory and the ways of human thinking, but using a fuzzy approach, especially the compensatory one. New results shall be proved and others well-known shall be changed or confirmed. The study comprises the examination of logical predicates like those expressed by the following sentences: “if a scenario is probable then it is convenient”, “there exist probable and convenient scenarios” and “all the scenarios are probable and convenient”. According to the empirical results, the Reichenbach implication and the Geometric Mean are closest to the people’s way of thinking.
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Buchanan, B.G., Shortliffe, E.H.: Knowledge Engineering. Rule-Based Expert Systems –The MYCIN Experiments of the Stanford Heuristic Programming Project, pp. 147–158. Addison-Wesley, Massachusetts (1984)
Detyniecki, M.: Mathematical aggregation operators and their application to video querying. Paris, University of Paris VI. Ph.D. Thesis (2001)
Dubois, D., Prade, H.: Criteria Aggregation and Ranking of alternatives in the framework of Fuzzy Sets Theory. In: Zimmermann, H.J., Gaines, B.R., Zadeh, L.A. (eds.) Fuzzy Set and Decision Analysis, pp. 209–240. North Holland, Amsterdam (1984)
Dubois, D. et al.: Fuzzy-Set Based Logic- An History -Oriented Presentation of their Main Developments Handbook of the History of Logic. In: Gabbay, D.M., Woods, J. (eds.), pp. 325–449. North-Holland, Elsevier BV (2007)
Espin, R., et al.: Un sistema lógico para el razonamiento y la toma de decisiones: la Lógica Difusa Compensatoria Basada en la Media Geométrica (A logic system for reasoning and decision making: Compensatory Fuzzy Logic on Geometric Mean). Revista Investigación Operacional 32, 230–245 (2011) (in Spanish)
French, S.: Decision Theory: An Introduction to the Mathematics of Rationality. Halsted Press, New York (1986)
Jayaram, B.: On the Law of Importation in Fuzzy Logic. IEEE Transactions on Fuzzy Systems 16, 130–144 (2008)
Kahneman, D., Tversky, A.: Prospect Theory: An Analysis of Decision under Risk. Econometrica 47, 263–291 (1979)
Mitrinovic, D.S., et al.: Classical and New Inequalities in Analysis (1993)
Dordrecht/Boston/London. Kluwer Academic Publishers
Mizumoto, M.: Pictorial Representations of Fuzzy Connectives: Part II. Cases of Compensatory Operators and Self-Dual Operators. Fuzzy Sets and Systems 32, 45–79 (1989)
Trillas, E., et al.: When QM-operators are implication functions and conditional fuzzy relations. International Journal of Intelligent Systems 15, 647–655 (2000)
Turksen, I.B., et al.: A new class of Fuzzy Implications: Axioms of Fuzzy Implication revisited. Fuzzy Sets and Systems 100, 267–272 (1998)
Tversky, A., Kahneman, D.: Advances in Prospect Theory: Cumulative Representation of Uncertainty. Journal of Risk and Uncertainty 5, 297–323 (1992)
Zadeh, L.: Some reflections on soft computing, granular computing and their roles in the conception, design and utilization of information/intelligent systems. Soft Computing 2, 23–25 (1998)
Zadeh, L.: From computing with numbers to computing with words –from manipulation of measurements to manipulation of perceptions. International Journal of Applied Mathematics and Computational Sciences 3, 307–324 (2002)
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Andrade, R.A.E., González, E., Fernández, E., Gutiérrez, S.M. (2014). A Fuzzy Approach to Prospect Theory. In: Espin, R., Pérez, R., Cobo, A., Marx, J., Valdés, A. (eds) Soft Computing for Business Intelligence. Studies in Computational Intelligence, vol 537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53737-0_3
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