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The distributivity condition for uninorms and t-operators. (English) Zbl 1005.03047

Fuzzy Sets Syst. 128, No. 2, 209-225 (2002); corrigendum ibid. 153, No. 2, 297-299 (2005).
Summary: In this work we study the functional equation given by the distributivity condition: \[ F\bigl(x,G(y,z) \bigr)= G\bigl(F (x,y), F(x,z)\bigr) \text{ for all }x,y,z \in[0,1], \] where the unknown functions \(F,G\) are uninorms and/or t-operators. We characterize all the solutions in the four possible cases: (i) when \(F,G\) are t-operators, (ii) when \(F\) is a t-operator and \(G\) a uninorm, (iii) when \(F\) is a uninorm and \(G\) a t-operator and, finally, (iv) when \(F,G\) are uninorms.

MSC:

03E72 Theory of fuzzy sets, etc.

Citations:

Zbl 0996.03038
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Full Text: DOI

References:

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