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Problem‐based learning (PBL) is a learner‐centered educational method based on the principles of heuristics and collaboration. It has been considered an effective learning method in general and in professional education, especially in medical education. This article analyzes the thinking structure and philosophical background of PBL through the educational ideas of Socrates and the truth conception of Karl Popper. In the different phases of the PBL process, various truth conceptions will help to formulate the thinking framework of PBL—from Socrates' truth of openness toward the truth of scientific accuracy of our modern age. Meanwhile, Popper's scientific theory of falsifiability further leads us to discuss the relationship between PBL and critical thinking.

This paper applies fuzzy set theory to the Cox, Ross and Rubinstein (CRR) model to set up the fuzzy binomial option pricing model (OPM). The model can provide reasonable ranges of option prices, which many investors can use it for arbitrage or hedge. Because of the CRR model can provide only theoretical reference values for a generalized CRR model in this article we use fuzzy volatility and fuzzy riskless interest rate to replace the corresponding crisp values. In the fuzzy binomial OPM, investors can correct their portfolio strategy according to the right and left value of triangular fuzzy number and they can interpret the optimal difference, according to their individual risk preferences. Finally, in this study an empirical analysis of S&P 500 index options is used to find that the fuzzy binomial OPM is much closer to the reality than the generalized CRR model. Copyright Springer Science + Business Media, Inc. 2005fuzzy set theory, fuzzy binomial OPM, option pricing model (OPM), a generalized CRR model, triangular fuzzy number, portfolio strategy,