A new hybrid fuzzy-statistical membership function based on fuzzy estimators

Abstract

The ability of fuzzy logic systems to make use of human interpretable linguistic terms makes them very attractive for many applications. These systems make use of membership functions to represent the linguistic variables. The choice of type of the membership function to use and the associated parameters affect the performance of the system. The current types of membership functions like triangular, trapezoidal, Gaussian functions etc., make use of parameters that are possibilistic in nature thus requiring expert knowledge or other sophisticated methods in order to choose the parameters. In this paper, we propose a new type of membership function constructed based on fuzzy estimators. This membership function depends entirely on well-known statistical parameters like the mean, standard deviation and confidence intervals and thus the parameters are easier to choose. Another advantage of this membership function is that it is suitable for modeling systems that exhibit both randomness and fuzziness. Furthermore, in contrast to the parameters of other membership functions, in the case where the parameters are tuned and optimized for a particular application, the final parameters of the proposed membership function can have useful statistical interpretations and provide a better understanding of the system.