Abstract
Membership function estimation is one of the less explored, albeit important, areas in fuzzy sets. This paper aims to define a new family of fuzzy sets called general continuous linguistic variables (GCLV), which represents a linguistic variable rather than a set of linguistic values. We refer to it as the principle of representation of linguistic variables. They are based on the well-known sigmoidal functions and contain at least three different classes of membership functions, namely, an increasing sigmoidal function, a decreasing sigmoidal function, and a convex one. These diverse features are essential to represent linguistic values exhibiting different semantics. We explore the properties of GCLV, including those ones over that allow us to approximate every continuous membership function. Finally, we illustrate the applicability of GCLV as a fuzzy tool. This leads to the development of the foundations of a new vehicle in fuzzy sets useful in data mining and time series prediction.