Weak pseudo-inverses and the associativity of two-place functions generated by left continuous monotone functions
| Autor: | Chen, Meng, Wang, Xue-ping |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | This article introduces a weak pseudo-inverse of a monotone function, which is applied to prove that the associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=t^{[-1]}(F(t(x),t(y)))$ where $F:[0,\infty]^2\rightarrow[0,\infty]$ is an associative function with neutral element in $[0,\infty]$, $t: [0,1]\rightarrow [0,\infty]$ is a left continuous monotone function and $t^{[-1]}:[0,\infty]\rightarrow[0,1]$ is the weak pseudo-inverse of $t$ depends only on properties of the range of $t$. Comment: 16. arXiv admin note: text overlap with arXiv:2409.02941 |
| Databáze: | arXiv |
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