# Fuzzy approach to decision analysis with multiple criteria and uncertainty in health technology assessment

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## Abstract

Decision making in health technology assessment (HTA) involves multiple criteria (clinical outcomes vs. cost) and risk (criteria measured with estimation error). A survey conducted among Polish HTA experts shows that opinions how to trade off health against money should be treated as fuzzy. We propose an approach that allows to introduce fuzziness into decision making process in HTA. Specifically, in the paper we (i) define a fuzzy preference relation between health technologies using an axiomatic approach; (ii) link it to the fuzzy willingness-to-pay and willingness-to-accept notions and show the survey results in Poland eliciting these; (iii) incorportate uncertainty additionally to fuzziness and define two concepts to support decision making: *fuzzy expected net benefit* and *fuzzy expected acceptability* (the counterparts of expected net benefit and cost-effectiveness acceptability curves, CEACs, often used in HTA). Illustrative examples show that our fuzzy approach may remove some problems with other methods (CEACs possibly being non-monotonic) and better illustrate the amount of uncertainty present in the decision problem. Our framework can be used in other multiple criteria decision problems under risk where trade-off coefficients between criteria are subjectively chosen.

## Keywords

Multiple criteria decision making Fuzzy preferences Uncertainty Health technology assessment Willingness to pay Preference elicitation## Notes

### Acknowledgments

It would not have been possible to collect the survey results presented in the paper without the help from M. Niewada, who facilitated the contact with the respondents. We would like to acknowledge the help of HTA experts who participated in the survey: K. J. Filipiak, K. Jahnz-Różyk, and the others, who opted to remain anonymous. We also express our gratitude to D. Golicki, T. Macioch, W. Wrona, and again M. Niewada, who commented on the first version of the survey.

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