Estimating the Membership Function of the Fuzzy Willingness-to-Pay/Accept for Health via Bayesian Modelling

  • Michał JakubczykEmail author
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 361)


Determining how to trade off individual criteria is often not obvious, especially when attributes of very different nature are juxtaposed, e.g. health and money. The difficulty stems both from the lack of adequate market experience and strong ethical component when valuing some goods, resulting in inherently imprecise preferences. Fuzzy sets can be used to model willingness-to-pay/accept (WTP/WTA), so as to quantify this imprecision and support the decision making process. The preferences need then to be estimated based on available data. In the paper, I show how to estimate the membership function of fuzzy WTP/WTA, when decision makers’ preferences are collected via survey with Likert-based questions. I apply the proposed methodology to a data set on WTP/WTA for health. The mathematical model contains two elements: the parametric representation of the membership function and the mathematical model how it is translated into Likert options. The model parameters are estimated in a Bayesian approach using Markov-chain Monte Carlo. The results suggest a slight WTP-WTA disparity and WTA being more fuzzy as WTP. The model is fragile to single respondents with lexicographic preferences, i.e. not willing to accept any trade-offs between health and money.


Membership Function Lexicographic Preferences Likert Answer JAGS Code 5-level Likert 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The research was done during my stay at The Tippie College of Business, The University of Iowa, USA, thanks to the Fulbright Senior Award. This opportunity is greatly appreciated.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Decision Analysis and Support UnitSGH Warsaw School of EconomicsWarsawPoland

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