Linear and sigmoidal fuzzy cognitive maps: An analysis of fixed points
Linear and sigmoidal fuzzy cognitive maps: An analysis of fixed points
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DOI：
10.1016/j.asoc.2013.10.030
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发表时间：
2014-02-01
影响因子：
8.7
通讯作者：
Penn, Alexandra S.
中科院分区：
文献类型：
--
作者：
Knight, Christopher J. K.;Lloyd, David J. B.;Penn, Alexandra S.
模糊认知映射通常被用作参与性建模技术，利益相关者据此创建感兴趣的系统的半定量模型。这个模型通常被转化为一个迭代映射，它应该（理想情况下）有一个唯一的稳定不动点。在文献中已经使用了几种这样做的方法，但很少注意到这种不同方法产生的输出差异，或者是否确实存在唯一的稳定不动点。在本文中，我们试图强调和解决其中的一些问题。特别是，我们的状态下，在稳定的不动点的线性模糊认知地图（迭代）的变量的顺序是唯一的条件。此外，我们状态的条件（和一个参数的明确的界限）下，S形模糊认知地图是保证有一个唯一的不动点，这是稳定的。这些通用的结果表明，方法来完善模糊认知映射的方法。我们强调他们是如何被用于正在进行的案例研究转向生物为基础的经济在英国的亨伯地区。(C)2013爱思唯尔有限公司版权所有。
Fuzzy cognitive mapping is commonly used as a participatory modelling technique whereby stakeholders create a semi-quantitative model of a system of interest. This model is often turned into an iterative map, which should (ideally) have a unique stable fixed point. Several methods of doing this have been used in the literature but little attention has been paid to differences in output such different approaches produce, or whether there is indeed a unique stable fixed point. In this paper, we seek to highlight and address some of these issues. In particular we state conditions under which the ordering of the variables at stable fixed points of the linear fuzzy cognitive map (iterated to) is unique. Also, we state a condition (and an explicit bound on a parameter) under which a sigmoidal fuzzy cognitive map is guaranteed to have a unique fixed point, which is stable. These generic results suggest ways to refine the methodology of fuzzy cognitive mapping. We highlight how they were used in an ongoing case study of the shift towards a bio-based economy in the Humber region of the UK. (C) 2013 Elsevier B.V. All rights reserved.