On Some Classes of Idempotent Operators

In this paper we deal with the idempotency equation H(x,x)=x for all x∈[0,1]. In particular we solve it for two special cases. First when H is a convex linear combination of a strict t-norm and its (1-j)-dual and second, when H is a convex linear combination of a special kind of aggregation functions F= and its N-dual, being these aggregation functions, called L-representable aggregation functions, a kind of functions verifying a similar representation theorem to the classical representation theorem for non strict Archimedean t-norms.