Generating Z-number by Logistic Regression

L. Zadeh came up with the idea of Z-number to reflect human decision-making ability in environments where information is uncertain. According to his idea, a Z-number consists of a classical fuzzy part and its reliability. Although there are linguistic based studies exist in the literature, designing the reliability part is still an open issue. In this paper, Logistic Regression is used to determine reliability part. Since the reliability part contains probability information and fuzzy granular information, both statistical and probability based methods must be proposed. The features such as giving probabilistic output, being optimization based via a cost function makes the Logistic Regression one of the best methods for generating Z-number. According to the proposed method, Z-numbers and Z-number based fuzzy if-then rules are written. We tried the Z-number based classifier on Fisher Iris Dataset. The results showed us the more reliable fuzzy membership functions give the more accurate outputs as expected. Another important issue is the reliability of input information, i.e. sensor data, was not known, so the reliability based calculations could not be performed. The reliability of input data can be calculated via proposed method.