Abstract
Testing hypotheses could sometimes benefit from the fuzzy context of data or from the lack of precision in specifying the hypotheses. A fuzzy approach is therefore needed for reflecting the right decision regarding these hypotheses. Different methods of testing hypotheses in a fuzzy environment have already been presented. On the basis of the classical approach, we intend to show how to accomplish a fuzzy test. In particular, we consider that the fuzziness does not only come from data but from the hypotheses as well. We complete our review by explaining how to defuzzify the fuzzy test decision by the signed distance method in order to obtain a crisp decision. The detailed procedures are presented with numerical examples of real data. We thus present the pros and cons of both the fuzzy and classical approaches. We believe that both approaches can be used in specific conditions and contexts, and guidelines for their uses should be identified.
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Notes
- 1.
In several researches in fuzzy methods, the triangle shape has been chosen by default to model fuzzy numbers, principally because of the shape’s simplicity in terms of computations. For instance, Parchami et al. [7], and Filzmoser and Viertl [5] and others, used triangles in the context of fuzzy inference tests.
References
Berkachy, R., & Donzé, L. (2016). Individual and global assessments with signed distance defuzzification, and characteristics of the output distributions based on an empirical analysis. In Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 1: FCTA (pp. 75–82).
Berkachy, R., & Donzé, L. (2017). Testing fuzzy hypotheses with fuzzy data and defuzzification of the fuzzy p-value by the signed distance method. In Proceedings of the 9th International Joint Conference on Computational Intelligence (IJCCI 2017) (pp. 255–264).
Berkachy, R., & Donzé, L. (2017). Defuzzification of the fuzzy p-value by the signed distance: Application on real data. In Computational Intelligence. Studies in Computational Intelligence. Berlin: Springer.
Berkachy, R., & Donzé, L. (2018). A new approach of testing fuzzy hypotheses by confidence intervals and defuzzification of the fuzzy decision by the signed distance. In METRON. Berlin: Springer.
Filzmoser, P., & Viertl, R. (2004). Testing hypotheses with fuzzy data: The fuzzy p-value. In Metrika (Vol. 59, pp. 21–29). Berlin: Springer.
Grzegorzewski, P. (2000). Testing statistical hypotheses with vague data. Fuzzy Sets and Systems, 112(3), 501–510.
Parchami, A., Taheri, S. M., & Mashinchi, M. (2010). Fuzzy p-value in testing fuzzy hypotheses with crisp data. Statistical Papers, 51(1), 209–226.
Viertl, R. (2011). Statistical methods for fuzzy data. Hoboken: Wiley.
Yao, J., & Wu, K. (2000). Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and Systems, 116(2), 275–288.
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Berkachy, R., Donzé, L. (2019). Testing Hypotheses by Fuzzy Methods: A Comparison with the Classical Approach. In: Meier, A., Portmann, E., Terán, L. (eds) Applying Fuzzy Logic for the Digital Economy and Society. Fuzzy Management Methods. Springer, Cham. https://doi.org/10.1007/978-3-030-03368-2_1
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