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Higher Order Vagueness in Geographical Information: Empirical Geographical Population of Type n Fuzzy Sets

机译：地理信息中的高阶模糊性：n型模糊集的经验地理人口

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摘要

Fuzzy set theory has been suggested as a means for representing vague spatial phenomena, and is widely known for directly addressing some of the issues of vagueness such as the sorites paradox. Higher order vagueness is widely considered a necessary component of any theory of vagueness, but it is not so well known that it too is competently modelled by Type n Fuzzy sets. In this paper we explore the fuzzy representation of higher order vagueness with respect to spatial phenomena. Initially we relate the arguments on philosophical vagueness to Type n Fuzzy sets. As an example, we move on to an empirical generation of spatial Type 2 Fuzzy sets examining the spatial extent of mountain peaks in Scotland. We show that the Type 2 Fuzzy sets can be populated by using alternative parameterisations of a peak detection algorithm. Further ambiguities could also be explored using other parameters of this and other algorithms. We show some novel answers to interrogations of the mountain peaks of Scotland. The conclusion of this work is that higher order vagueness can be populated for Type 2 and higher fuzzy sets. It does not follow that it is always necessary to examine these higher order uncertainties, but a possible advantage in terms of the results of spatial inquiry is demonstrated.
机译：提出了模糊集理论作为表示模糊空间现象的一种手段，并且因直接解决模糊性问题（如sorites悖论）而广为人知。高阶模糊性被广泛认为是任何模糊性理论的必要组成部分，但众所周知它也不能通过n型模糊集来建模。在本文中，我们探索了关于空间现象的高阶模糊性的模糊表示。最初，我们将关于哲学模糊性的争论与n型模糊集联系起来。作为示例，我们继续进行空间类型2模糊集的经验生成，以检查苏格兰山峰的空间范围。我们显示可以通过使用峰值检测算法的替代参数来填充类型2模糊集。还可以使用此参数和其他算法的其他参数来探索更多的歧义。我们为审讯苏格兰山峰展示了一些新颖的答案。这项工作的结论是可以为类型2和更高的模糊集填充更高阶的模糊性。并不总是需要检查这些高阶不确定性，而是证明了在空间查询结果方面的可能优势。

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  • 来源
    《GeoInformatica》 |2007年第3期|311-330|共20页
  • 作者

    Peter Fisher; Tao Cheng; Jo Wood;

  • 作者单位

    Department of Information Science City University Northampton Square London EC1V 0HB UK;

    Department of Land Surveying and Geo-Informatics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong;

    Department of Information Science City University Northampton Square London EC1V 0HB UK;

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  • 原文格式 PDF
  • 正文语种 eng
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  • 关键词

    fuzzy sets; mountains; geomorphometry; type 2 fuzzy sets; vagueness; uncertainty;

    机译：模糊集;山脉;地貌;2型模糊集;模糊性;不确定性;

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