The present paper extends some previous works studying automorphisms in type-2 fuzzy sets. The framework for the analysis is the set of convex and normal functions from $[0,1]$ to $[0,1]$ (fuzzy truth values). The paper concentrates on those automorphisms that, in this framework, leave the constant function 1 fixed. This function is quite important since it defines the boundary between the functions that represent “TRUE” (increasing functions) and those that represent “FALSE” (decreasing functions), being at the same time the only normal function that is simultaneously increasing and decreasing. While C.L. Walker, E.A. Walker and J. Harding introduced in 2008 a family of functions leaving the constant function 1 fixed, the main goal of this paper is to prove that the functions of that family are in fact automorphisms, and moreover, that they are the only automorphisms (in the mentioned set of convex and normal functions from $[0,1]$ to $[0,1]$) that preserve the function 1.

本文扩展了先前研究2型模糊集中自同构的一些著作。分析的框架是从$[0，\mathrm{1个}]$ 至 $[0，\mathrm{1个}]$（模糊的真值）。本文着重于那些在该框架中使常数函数1固定不变的自同构。该函数非常重要，因为它定义了代表“ TRUE”（递增函数）的函数与代表“ FALSE”（递减函数）的函数之间的边界，同时它们是唯一同时递增和递减的常规函数​​。尽管CL Walker，EA Walker和J. Harding在2008年推出了一个函数家族，使常数1固定不变，但本文的主要目标是证明该族的功能实际上是自同构的，而且它们是自同构的。唯一的自同构（在上述凸函数和法线函数集中$[0，\mathrm{1个}]$ 至 $[0，\mathrm{1个}]$）保留功能1。