On Some Classes of Idempotent Operators
- 1 August 1997
- journal article
- research article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
- Vol. 05 (04) , 401-410
- https://doi.org/10.1142/s0218488597000300
Abstract
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=<(f,N)> 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.Keywords
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