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On locally internal monotonic operations

机译:关于本地内部单调操作

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This paper deals with monotonic binary operations F: [0,1]~2 → [0,1] with the property (called locally internal property) that the value at any point (x, y) is always one of its arguments x,y. After stating a theorem that characterizes this kind of operations, some special cases are studied in detail by considering additional properties of the operation: commutativity, existence of a neutral element and associativity. In case of locally internal, associative monotonic operations with neutral element, a characterization theorem gives an improvement of a well-known theorem of Czogala and Drewniak on idempotent, associative and increasing operations with neutral element, as well as an improvement of a characterization theorem for left (and right) continuous, idempotent uninorms.
机译:本文处理单调二进制运算F:[0,1]〜2→[0,1]具有以下属性(称为局部内部属性),即任意点(x,y)的值始终是其参数x之一, y。在陈述了表征这种运算的一个定理之后,通过考虑运算的其他属性来详细研究一些特殊情况:可交换性,中性元素的存在和关联性。对于带有中性元素的局部内部关联单调运算,特征定理对Czogala和Drewniak的公理定理进行了改进,其中带有中性元素的幂等,关联和增加运算,以及对左(和右)连续的幂等单位。

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