Fuzzy logistic regression with least absolute deviations estimators

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 $$(M_p)$$(Mp) and index of sensitivity $$(I_S)$$(IS). 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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