Summary
The main goal of this paper is to solve the idempotency equationF(x, x) = x, x ∈ [0, 1] for a class of functions of the type “convex linear combination of at-norm and at-conorm”. In the non-strict Archimedean case and for eachk ∈ (0, 1), we obtain a unique solutionF k for this equation. While these functionsF k are not associative, we also prove that they satisfy the bisymmetry condition.
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Mayor, G. On a family of quasi-arithmetic means. Aeq. Math. 48, 137–142 (1994). https://doi.org/10.1007/BF01832981
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DOI: https://doi.org/10.1007/BF01832981