Fuzzy systems are a kind of knowledge based system where information and knowledge are represented in the form of fuzzy statements. Modeling the negation of these statements plays an important role in fuzzy inference. As any other knowledge based system, fuzzy systems may be affected by a lack of information. In particular, in the case of type-2 fuzzy systems, the fuzzy set 1 (1(x) = 1 for all x ∈ [0, 1]) represents a lack of information. Consequently, it is interesting to consider how this set (representing lack of information) is transformed through a negation.

The analysis in this paper takes place in the framework defined by M, the set of all functions from [0, 1] to [0, 1]. These functions constitute the membership functions characterizing type-2 fuzzy sets. In particular we will concentrate on L, the set of normal and convex functions in M. In a first step, we will explore strong negations in L to obtain any possible image of the function 1 through them. The particular case of strong negations mapping 1 to 1 has been previously studied. In this work we will generalize the previous results by considering the main properties of those strong negations in L where the image of the function 1 is not this same function.