Further developments of a fuzzy set map comparison approach

Fuzzy set map comparison offers a novel approach to map comparison.The approach is specifically aimed at categorical raster maps and applies fuzzy set techniques, accounting for fuzziness of location and fuzziness of category, to create a similarity map as well as an overall similarity statistic: the Fuzzy Kappa. To date, the calculation of the Fuzzy Kappa (or K-fuzzy) has not been formally derived, and the documented procedure was only valid for cases without fuzziness of category. Furthermore, it required an infinitely large, edgeless map. This paper presents the full derivation of the Fuzzy Kappa; the method is now valid for comparisons considering fuzziness of both location and category and does not require further assumptions. This theoretical completion opens opportunities for use of the technique that surpass the original intentions. In particular, the categorical similarity matrix can be applied to highlight or disregard differences pertaining to selected categories or groups of categories and to distinguish between differences due to omission and commission.     

基于模糊集的土地利用变化自动发现方法探讨

传统的逐像素比较法忽略了地理对象的模糊性,缺乏区分噪声与真实变化信息的能力,难于处理空间数据的复杂性和不确定性。基于模糊集理论,根据邻域像元的空间位置关系确定变化的程度,并利用滑窗和景观指数表达比较不同时相遥感数据(TM、ETMI、KONOS)的分类专题图。试验结果表明,模糊集的描述更接近真实情况。     

Geocoding crime and a first estimate of a minimum acceptable hit rate

The Fuzzy Kappa statistic expresses the agreement between two categorical raster maps. The statistic goes beyond cell‐by‐cell comparison and gives partial credit to cells based on the categories found in the neighborhood. When matching categories are found at shorter distances the agreement is higher. Like the well‐established Kappa statistic the Fuzzy Kappa statistic expresses the mean agreement relative to the expected agreement. The model underlying the expected agreement assumes absence of spatial autocorrelation in both compared maps. In reality however, spatial autocorrelation does lower the expected agreement as matching categories become less likely to be found close‐by. Since most maps have some degree of spatial autocorrelation, the calculated expected agreement is generally higher than the true expected agreement. This leads to counterintuitive results when maps that appear to have considerable agreement obtain negative Fuzzy Kappa values. Furthermore, the Fuzzy Kappa may be biased, as it systematically attributes lower agreement to maps with stronger spatial autocorrelation. This paper proposes an improved Fuzzy Kappa statistic that is based on the same local agreement and has the same attractive properties as the original Fuzzy Kappa. The novelty is that the new statistic accounts for spatial autocorrelation, such that the expected Fuzzy Kappa for maps that are not cross‐correlated is equal to zero. The improved statistic is applied on two cases to demonstrate its properties.     

抗滑桩模糊优化设计

抗滑桩设计模型中含有大量的模糊参数。考虑抗滑桩设计中参数的模糊性，根据相关规范在抗滑桩普通优化模型基础上建立了抗滑桩实用模糊优化模型，给出了求解该模糊优化模型的计算方法，通过一个具体实例显示了该模型和方法的优化效果，并与普通优化模型优化结果做出了比较。结果显示，考虑参数模糊性后优化方案更为优秀、合理。     

基于GIS栅格数据的空间模糊综合评判方法与实践

针对模糊综合评判多集中于对区域整体的综合评判的局限,提出了基于GIS的空间模糊综合评判方法。介绍了该方法的关键内容——隶属层的形成过程以及基于栅格数据的综合运算方法,并将该方法应用于门头沟煤矿区生态环境综合评价。     

水资源承载能力评价的熵权模糊物元模型

以模糊物元分析理论为基础,结合熵值法和欧氏贴近度概念,构建用于评价水资源承载能力的熵权模糊物元分析模型。介绍了该模型的计算步骤,应用该模型对淮河流域各分区的水资源承载能力进行了综合评价,并与其他评价方法的评价结果进行了比较。结果表明,该文建立的模型合理且计算简单,可靠性、实用性强,适用于多种综合评价问题。     

利用场模型拓扑表达GIS中的地理目标

该文阐述为了实现在GIS中描述自然界里带有模糊不确定性的地理目标 ,扩充GIS的模糊查询功能 ,首先基于集合论思想探讨了确定性地理目标的代数解析表达与其拓扑表达 ,指出了确定性点、线、面之间拓扑表达的构成机理 ;然后 ,基于场模型建立了模糊地理目标的空间表达 ,分析了模糊地理目标的位置不确定性 ,进而建立了模糊地理目标的拓扑表达模型 ,即点集拓扑内部、边界和外部。分析表明 ,公认的Egenhofer模型是该文模型在地理目标不带有误差或不确定性情况下的特例。最后 ,与Clementini(1996 )提出的模型做了比较分析 ,表明了该文模型的合理性。     

Same space – different perspectives: comparative analysis of geographic context through sketch maps and spatial video geonarratives

ABSTRACT

The importance of including a contextual underpinning to the spatial analysis of social data is gaining traction in the spatial science community. The challenge, though, is how to capture these data in a rigorous manner that is translational. One method that has shown promise in achieving this aim is the spatial video geonarrative (SVG), and in this paper we pose questions that advance the science of geonarratives through a case study of criminal ex-offenders. Eleven ex-offenders provided sketch maps and SVGs identifying high-crime areas of their community. Wordmapper software was used to map and classify the SVG content; its spatial filter extension was used for hot spot mapping with statistical significance tested using Monte Carlo simulations. Then, each subject’s sketch map and SVG were compared. Results reveal that SVGs consistently produce finer spatial-scale data and more locations of relevance than the sketch maps. SVGs also provide explanation of spatial-temporal processes and causal mechanisms linked to specific places, which are not evident in the sketch maps. SVG can be a rigorous translational method for collecting data on the geographic context of many phenomena. Therefore, this paper makes an important advance in understanding how environmentally immersive methods contribute to the understanding of geographic context.     

模糊坡位信息在精细土壤属性空间推测中的应用

坡位的空间渐变特征影响着小流域及坡面尺度上的土壤、水文、地貌等现象和过程,因此对精细尺度下的地理建模(如土壤空间信息推理)有重要作用。虽然目前已有多种模糊坡位信息定量提取方法,但所得到的模糊坡位信息还缺乏实际应用。本文以精细尺度下的土壤属性空间分布推测为例,对此展开探索。应用模型假设:(1)在小流域内,地形因素主导着土壤属性空间分布的变化;(2)典型坡位上对应分布着典型的土壤属性值,土壤属性与坡位之间存在协同变化关系。据此建立以模糊坡位信息对各类典型坡位上土壤样点属性值的加权平均模型,推测土壤属性的空间分布。模型应用于黑龙江省嫩江流域一个地形平缓的小区(面积约60 km²),通过一个以坡位典型位置作为原型的模糊坡位定量方法提取5类坡位(山脊、坡肩、背坡、坡脚、沟谷)的空间渐变信息,对土壤表层有机质含量的空间分布进行推测。推测结果通过研究区70个土壤采样点进行评价,以推测结果与评价样点集之间的相关系数、平均绝对误差、均方根误差作为定量评价指标,与使用常用地形属性的多元线性回归模型推测结果进行对比。评价结果表明,仅使用极少建模点的加权平均模型的推测结果优于多元线性回归模型的推测结果。     

空间数据挖掘的地理案例推理方法及试验

从空间数据挖掘的角度谈地理案例推理方法,认为地理案例推理是面向问题的一种空间数据挖掘方法。针对这一思想进行了基于地理案例的空间数据挖掘具体算法介绍。首先在明确地理案例具体定义的基础上,给出了面向问题的空间数据挖掘地理案例界定和组织方法;其次,鉴于地理空间的自然地带性和区域分异性规律的影响,深入探讨了地理案例自身或其间所可能存在的相互依赖和相互制约关系,并给出了采用粗糙集方法进行地理案例内蕴空间关系的定量挖掘方法;第三,针对地理案例表达时考虑的空间特征和空间关系的不同,给出了三种状况下的空间相似性计算模型;最后,以土地利用这一典型的地学现象为例,给出具体实例,一方面进行土地利用问题的定量分析与推测;另一方面,通过实例展示地理案例推理方法在地学问题求解以及空间数据定量分析上的特点和优势。     

Integration of multi-source remote sensing data for land cover change detection

The objective of this study is to develop a methodology to integrate multi-source remote sensing data into a homogeneous time series of land cover maps in order to carry out change detection. We developed a method to increase the comparability between land cover maps coming from panchromatic aerial photographs and SPOT XS (multi-spectral) data by equalizing their levels of thematic content and spatial details. The methodology was based on the hypotheses that: (1) map generalization can improve the integration of data for change detection purpose, and (2) the spatial structure of a land cover map, as measured by a set of landscape metrics, is an indicator of the level of generalization of that map. Firstly, the methodology for data integration was developed by using land cover maps generated from near-synchronous data. Results revealed that, by controlling successively the parameters that influence the level of map generalization, the percentage of agreement between the near-synchronous land cover maps can be increased from 42% to 93%. The computation of five landscape metrics for a set of generalized land cover maps and for the target map allowed us to optimize the level of generalization by measuring the similarity in landscape pattern of the maps. The optimum level of generalization of the land cover map obtained from the aerial photographs for comparison with a land cover map derived from SPOT XS data was found at a resolution of 41m for two generalization levels of the thematic content. The spatial structure of a land cover map, as measured by a set of landscape metrics, is thus a good indicator of the level of generalization of this map. Secondly, the method was applied by integrating a land cover map obtained from aerial photographs of 1954 with a land cover map obtained from a SPOT XS image of 1992.     

Fuzziness in Geographical Information Systems: contributions from the analytic hierarchy process†

Abstract

Recent developments in geographical information systems have drawn upon concepts of fuzzy set theory and multi-criteria methodology. In this paper we argue that there is a method, Saaty’s Analytic Hierarchy Process (AHP), that is compatible with both these research directions. The contributions of the AHP are highlighted in the light of recent developments in GIS, with particular attention to the concept of fuzzy set theory. An example of a GIS application is provided to show how the AHP can deal operationally with fuzziness, factor diversity and complexity in problems of land evaluation involving the location of a public facility.     

西方区域多中心测度与效应研究进展

通过系统梳理西方多中心概念、测度与效应等方面的相关文献,发现多中心效应的不确定性与其定义的模糊性以及测度方法和指标的选择有关;某一尺度的多中心政策在其他尺度上会产生不同影响;历史特殊性和地方情景是影响多中心政策实施的关键因素。认为并不存在可适用于所有区域的空间组织模式和政策措施,今后的研究应仔细区分形态多中心与功能多中心,正确选择测度方法与指标。     

认知地图的空间句法研究

将意识层面的空间意象外化为可被度量及分析的对象,一直是行为学、地理学、旅游学等学科关注的重要课题。本文主要从构建空间意象的结构而非意义入手,对该领域研究中的两种重要方法,即认知地图法和空间句法进行了比较,意图找到两种方法在空间结构性认知方面的相关性。基于句法空间结构的表达模型,分别就长沙太平街历史街区集成度及其认知地图的调研结果进行了比对,通过真实地图句法集成度与579 份认知地图意象要素出现频率等指标的比较,发现集成度指标与意象出现频率等指标存在较好的相关性。在对认知地图样本进行轴线化转换并比照真实地图的轴线索引后,对真实地图句法集成度与579 份认知地图平均句法集成度进行比较,发现认知地图与真实地图的句法分析在结果上仍有较好的相关性,且节点、标志物两要素的出现频次等指标也与所在街道的集成度存在较为明显的对应性。结论说明空间构形对人们结构性意象的形成有着重要的影响力,认知地图的句法分析对揭示人们空间知识的形成机制具有一定的参考价值,两种方法有相互补充的可能性。     

Spatial and Longitudinal Patterns in County Age-Specific Net Migration in the United States 1950–2010

Many migration studies describe various counties by adopting a priori county typologies, such as the U.S. Department of Agriculture Economic Research Service county typology, which might not be suitable for identifying different age migration patterns of the U.S. counties. This study employs a spatial clustering method that exhaustively compares all U.S. counties on their age migration similarity and spatial proximity to investigate signature age-specific net migration profiles across six decades of U.S. county age-specific net migration data from 1950 to 2010. All of the six-decade data are integrated into a common spatial county boundary on which counties below a population threshold are merged with the nearest county to mitigate the small population problem in net migration rates. As counties are merged by increasing large population thresholds, the Getis-Ord Gi* spatial autocorrelation statistic is applied to examine how the spatial migration patterns are affected. It is found that U.S. county age-specific net migration profiles exhibit four signature patterns. Although these patterns are persistent across the past six decades, their spatial distributions have experienced dramatic variation. The small population problem in net migration rates affects the extent and location of the significant spatial migration patterns.     

基于GIS建模的海水环境质量可变模糊识别评价

基于对立统一与质量互变定理的可变模糊评价方法引入海水水质综合评价,构建基于对立统一与质量互变定理的海洋环境质量可变模糊评价模型,首先分析可变模糊评价方法的原理和方法,然后结合GIS栅格数据在表达空间信息方面具有的独特优势,以栅格数据为基础,利用地理信息系统空间叠置分析、地理信息系统空间建模等计算,建立基于多源栅格数据的海水环境可变模糊综合评价模型,得到莱州湾2004~2010年海水环境空间分布图。实践证明,该模型应用于海水水质综合评价是完全可行的,为海洋环境领域的多目标综合评价与决策提供了新的思路与方法。     

基于临近相似性考虑的犯罪热点密度图预测准确性比较——以DP半岛街头抢劫犯罪为例

在无时空考虑的密度估计算法基础上,分别加入了案件点之间的时间临近相似性、空间临近相似性和时空临近相似性的考虑,利用DP半岛2006~2007年的街头抢劫犯罪数据为基础计算无时空临近相似性、时间临近相似性、空间临近相似性和时空临近相似性4种不同算法所得到的犯罪热点图,并以之预测2008年的街头抢劫。通过Natural breaks（Jenks）分级方法和等比例面积选取两种方式来划定热点区域进行预测并进行PAI指数得分比较,结果表明时空临近相似性的密度估计算方法在犯罪预测的优势比较显著。     

A spatial fuzzy influence diagram for modelling spatial objects’ dependencies: a case study on tree-related electric outages

Spatial objects can be interconnected and mutually dependent in complex ways. In Geographical Information Science, spatial objects’ topological relationships are not discussed together with their attributes’ dependencies, and the vagueness of spatial objects is often ignored during the spatial modelling process. To address this, a spatial fuzzy influence diagram (SFID) is introduced. Compared to the traditional statistical or fuzzy modelling approach, the influence diagram brings advantages in helping decision-makers structure complex interdependency problems. A questionnaire was developed to evaluate the applicability of using an influence diagram in modelling spatial objects’ dependencies. As a case study, an SFID is applied to tree-related electric outages. The result of the case study is represented as a vulnerability map of electrical networks. The map shows areas at risk due to tree-related electric outages. The results were first validated by using a visual comparison of the vulnerability map and electricity fault data. In the second validation step, the percentage of fault data, which has received values in different vulnerability categories, was calculated. The results of the case study can be used to support the decision-making process of electrical network maintenance and planning.     

Computing the fuzzy topological relations of spatial objects based on induced fuzzy topology

For modeling the topological relations between spatial objects, the concepts of a bound on the intersection of the boundary and interior, and the boundary and exterior are defined in this paper based on the newly developed computational fuzzy topology. Furthermore, the qualitative measures for the intersections are specified based on the α‐cut induced fuzzy topology, which are (A_α∧?A)(x)<1?α and ((A^c)_α∧?A)(x)<1?α. In other words, the intersection of the interior and boundary or boundary and exterior are always bounded by 1?α, where α is a value of a level cutting. Specifically, the following areas are covered: (a) the homeomorphic invariants of the fuzzy topology; (b) a definition of the connectivity of the newly developed fuzzy topology; (c) a model of the fuzzy topological relations between simple fuzzy regions in GIS; and (d) the quantitative values of topological relations can be calculated.