A representation of a class of quasi-arithmetic means using a unary modifier operator

Abstract

In this short communication, we will show that a quasi-arithmetic mean induced by an additive generator of a strict t-norm (strict t-conorm, respectively) can be represented by the composition of a unary operator (called the tau function) and the strict t-norm (strict t-conorm, respectively), both induced by the same generator function as the quasi arithmetic mean. Here, we will also state a connection between the idempotency of a transformed strict t-norm (strict t-conorm, respectively) and the tau function.