Abstract
This study is an investigation of fuzzy logistic regression model for crisp input and fuzzy output data. The response variable is non-precise and is measured by linguistic terms. Especially this research develops least absolute deviations (LAD) method for modeling and compares the results with the least squares estimation (LSE) method. For these, two estimation methods, min–max method and fitting method, are provided in this research. This study presents new goodness-of-fit indices which are called measure of performance based on fuzzy distance \((M_p)\) and index of sensitivity \((I_S)\). The study gives two numerical examples in real clinical studies about systematic lupus erythematosus and the other one in the field of nutrition to explain the proposed methods. In addition, we investigate the sensitivity of two estimation methods in the case of outliers by a numerical example.
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Acknowledgments
The child’s appetite data which was used in the second numerical example of this paper was a part of a project which was funded by National Nutrition and Food Technology Research Institute of Shahid Beheshti University of Medical Sciences. The authors acknowledge their gratitude to Dr. M. Rezaei, Dr. N. Kalantari and Dr. N. Omidvar for that project. The authors acknowledge the anonymous reviewers for their valuable comments and suggestions to improve the article.
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Communicated by J.-W. Jung.
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Namdari, M., Yoon, J.H., Abadi, A. et al. Fuzzy logistic regression with least absolute deviations estimators. Soft Comput 19, 909–917 (2015). https://doi.org/10.1007/s00500-014-1418-2
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DOI: https://doi.org/10.1007/s00500-014-1418-2