Choosing membership functions of linguistic terms
Choosing membership functions of linguistic terms
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选择语言术语的隶属函数
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
R. John
中科院分区：
文献类型：
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作者：
J. Garibaldi;R. John
模糊系统中使用的术语的形状采用了几种“惯例”。术语几乎总是归一化的（具有最大隶属度值为 1）、凸形（具有单个最大值或平台最大值）和独特的（在重叠程度方面受到限制：通常表示为概念的某种变体，即讨论域中任何点的所有隶属度值总和为整个域中的 I）。这些项的形状是由某些公认的隶属函数生成的：分段线性函数（有限制）、高斯函数或 S 型函数几乎全部被使用。因此，这些仅构成术语可能形状的总集合的一小部分。这些约定很大程度上是经验性的，或者是通过基于可笼统地称为“模糊控制原理”的论证来证明其合理性的。本文重点介绍了模糊控制范式之外的模糊系统开发人员可以考虑作为替代方案的许多隶属函数。特别是，我们强调了包含的模糊集，讨论了非凸模糊集的优点，并提出了使用次正规模糊集的医学应用。这些想法通过例子得到了强化。
The shapes of terms used in fuzzy systems have adopted several 'conventions'. Terms are almost invariably normalised (having a maximum membership value of 1), convex (having a single maximum or plateau maxima) and distinct (being restricted in their degree of overlap: often expressed as some variation on the concept that all membership values at any point in the universe of discourse sum to I across that universe). The shape of these terms are generated by certain accepted membership functions: piecewise linear functions (with restrictions), Gaussians or Sigmoids are almost exclusively used. As such these constitute only a small subset of the total set of possible shapes of terms. These conventions are largely empirical or are justified by arguments based on what might loosely be called 'fuzzy control principles'. The paper highlights a number of membership functions that developers of fuzzy systems outside the paradigm of fuzzy control may consider as alternatives. In particular, we highlight subsumed fuzzy sets, discuss the merits of non-convex fuzzy sets and present a medical application where sub-normal fuzzy sets have been used. These ideas are reinforced by examples.