Is mainstream LCA linear?
Is mainstream LCA linear?
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DOI：
10.1007/s11367-020-01810-z
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发表时间：
2020-08-21
影响因子：
4.8
通讯作者：
Heijungs, Reinout
中科院分区：
文献类型：
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作者：
Heijungs, Reinout
研究目的文献中经常提到生命周期评价是线性的，但没有证明，甚至没有明确定义线性的标准。在这里，我们研究术语线性的含义，以及与此相关的LCA是否确实是线性的问题。方法我们探讨了数学模型中线性一词的不同含义。这导致了线性函数、齐次函数、齐次线性函数、双线性函数和多线性函数之间的区别。每一个都是用容易理解的术语定义的，并举例说明。结果我们分析了传统的，基于矩阵的，LCA，并得出结论，LCA是不是线性的任何意义上定义。讨论和结论尽管研究问题的否定答案，有许多方面，LCA可以被视为，至少在某种程度上，线性。我们讨论几个这样的案例。我们还讨论了一些实际的影响，LCA的从业者和开发新的方法LCI和LCIA。
Purpose It is frequently mentioned in literature that LCA is linear, without a proof, or even without a clear definition of the criterion for linearity. Here we study the meaning of the term linear, and in relation to that, the question if LCA is indeed linear. Methods We explore the different meanings of the term linearity in the context of mathematical models. This leads to a distinction between linear functions, homogeneous functions, homogenous linear functions, bilinear functions, and multilinear functions. Each of them is defined in accessible terms and illustrated with examples. Results We analyze traditional, matrix-based, LCA, and conclude that LCA is not linear in any of the senses defined. Discussion and conclusions Despite the negative answer to the research question, there are many respects in which LCA can be regarded to be, at least to some extent, linear. We discuss a few of such cases. We also discuss a few practical implications for practitioners of LCA and for developers of new methods for LCI and LCIA.