Fuzzy rationality in the elicitation of subjective quantiles

The paper presents the application of a modification of the bisection method - the triple bisection - for assessment of quantiles of subjective distributions of continuous random variables. The techniques for assessment of distributions of discrete and continuous random variables are discussed. An algorithm for practical assessment of quantiles of subjective probability distributions of continuous random variables is proposed, using the triple bisection. The possible results of a real observer (with infinite discriminating abilities) and of an ideal observer (without such abilities) are analyzed from the point of view of fuzzy logic. The latter is used to describe the residual rationality of real observers. This provides results that reflect the opinion of the observer in the best possible way, which also obtain the highest possible precision.