Fuzzy clustering of fuzzy ecological data

Besides the problem of searching for effective methods for data analysis there are some additional problems with handling data of high uncertainty. Uncertainty problems often arise in an analysis of ecological data, e.g. in the cluster analysis of ecological data. Conventional clustering methods based on Boolean logic ignore the continuous nature of ecological variables and the uncertainty of ecological data. That can result in misclassification or misinterpretation of the data structure. Clusters with fuzzy boundaries reflect better the continuous character of ecological features. But the problem is, that the common clustering methods (like the fuzzy c-means method) are only designed for treating crisp data, that means they provide a fuzzy partition only for crisp data (e.g. exact measurement data). This paper presents the extension and implementation of the method of fuzzy clustering of fuzzy data proposed by Yang and Liu [Yang, M.-S. and Liu, H-H, 1999. Fuzzy clustering procedures for conical fuzzy vector data. Fuzzy Sets and Systems, 106, 189-200.]. The imprecise data can be defined as multidimensional fuzzy sets with not sharply formed boundaries (in the form of the so-called conical fuzzy vectors). They can then be used for the fuzzy clustering together with crisp data. That can be particularly useful when information is not available about the variances which describe the accuracy of the data and probabilistic approaches are impossible. The method proposed by Yang has been extended and implemented for the Fuzzy Clustering System EcoFucs developed at the University of Kiel. As an example, the paper presents the fuzzy cluster analysis of chemicals according to their ecotoxicological properties. The uncertainty and imprecision of ecotoxicological data are very high because of the use of various data sources, various investigation tests and the difficulty of comparing these data. The implemented method can be very helpful in searching for an adequate partition of ecological data into clusters with similar properties.     

Fuzzy methods for the detection of copy number variations in comparative genomic hybridization arrays

Genomic copy number variations (CNVs) are considered as a significant source of genetic diversity and widely involved in gene expression and regulatory mechanism, genetic disorders and disease risk, susceptibility to certain diseases and conditions, and resistance to medical drugs. Many studies have targeted the identification, profiling, analysis, and associations of genetic CNVs. We propose herein two new fuzzy methods, taht is, one based on the fuzzy inference from the pre-processed input, and another based on fuzzy C-means clustering. Our solutions present a higher true positive rate and a lower false negative with no false positive, efficient performance and consumption of least resources.     

Application of fuzzy VIKOR for evaluation of green supply chain management practices

Environmentally sustainable activities have received an increasing interest among the firms to improve their practices in the supply chain. Although environmental regulations force firms consider these issues, but, green issues are new, evolving every day, and requires a continuous study in the field to gain a complete understanding of the problems. In this study, we illustrate the case of a laptop manufacturer in Malaysia that pursues to evaluate green supply chain management (GSCM) indicators among its practitioners. This paper develops a quantitative evaluation model to measure the uncertainty of GSCM activities and applies an approach based on Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method which is an extension of intuitionistic fuzzy environment aiming to solve the green multi-criteria decision making (GMCDM) problem. The triangular fuzzy numbers (TFNs) were used to handle imprecise numerical quantities. Then, a hierarchical multiple criteria decision making (MCDM) model was proposed based on fuzzy sets theory and VIKOR method to deal with the problem. The results show the alternative ranks of the four evaluated companies which was based on their performance in GSCM initiatives. The results also indicated that the main criteria of the research ranked as follows respectively: eco-design, green production, green purchasing, green recycling, green transportation and green warehousing. Finally, a comparative analysis of results by fuzzy VIKOR is presented. Additionally the scope for future studies is provided at the end of the paper.     

Classification of antituberculosis herbs for remedial purposes by using fuzzy sets

Using fuzzy set theory, we created a system, that assesses a herb's usefulness for the treatment of tuberculosis, based on ethnobotanical data. We analysed two systems which contain different amount of inputs. The first system contains four inputs, the second one contains six inputs. We used the Takagi-Sugeno-Kanga model. Mamdani model is poor at representation as it needs more fuzzy rules than that of TSK to model a real world system where accuracy is demanded. It has been employed a fuzzy controller, and a fuzzy model, in successfully solving difficult control and modelling problems in practice. It is implemented in the Fuzzy Logic Toolbox in Matlab. The data for inputs are gathered in the database named SOPAT (selection of plants against tuberculosis), which is part of a project coordinated by the Oxford International Biomedical Centre. In this database there could be up to one million plant species. It would be cumbersome to select a remedy from one (or some) of these species looking at the data base one-by-one. By means of the fuzzy set theory this remedy can be chosen very quickly.     

Ordination on the basis of fuzzy set theory

Fuzzy set theory is an extension of classical set theory where elements of a set have grades of membership ranging from zero for non-membership to one for full membership. Exactly as for classical sets, there exist operators, relations, and mappings appropriate for these fuzzy sets. This paper presents the concepts of fuzzy sets, operations, relations, and mappings in an ecological context. Fuzzy set theory is then established as a theoretical basis for ordination, and is employed in a sequence of examples in an analysis of forest vegetation of western Montana, U.S.A. The example ordinations show how site characteristics can be analyzed for their effect on vegetation composition, and how different site factors can be synthesized into complex environmental factors using the calculus of fuzzy set theory.In contrast to current ordination methods, ordinations based on fuzzy set theory require the investigator to hypothesize an ecological relationship between vegetation and environment, or between different vegatation compositions, before constructing the ordination. The plotted ordination is then viewed as evidence to corroborate or discredit the hypothesis.I am grateful to Dr R. D. Pfister (formerly USDA Forest Service) for kind permission to publish data from a Forest Service study.I would like to gratefully acknowledge the helpful comments and criticisms of Drs. G. Cottam, J. D. Aber, T. F. H. Allen, E. W. Beals, I. C. Prentice, C. G. Lorimer, and two anonymous reviewers.Taxonomic nomenclature follows Hitchcock & Cronquist (1973).I would like to thank the Dean of the College of Letters and Sciences, University of Wisconsin—Madison, for a fellowship which supported this research, and the Department of Botany for computer funds to perform the analyses.     

模糊ＩＳＯＤＡＴＡ在草地植物群落分类上的应用

 模糊集合理论在元素与集合的关系中引入了连续变化的隶属度,因而能适应植物群落作连续和明显间断分布同时存在的情况。本文运用以模糊集合理论为基础的ISODATA聚类分析方法对松嫩平原草地植物群落进行了数量分类,结果说明模糊ISODATA聚类比传统的分类方法有更为客观、灵活的特点,是一种较为理想的植被数量分类方法。     

Fuzzy methods for assessing criteria and indicators of sustainable forest management

This paper describes the general concepts, meaning, and definitions of sustainability and proposes the use of soft methodologies, particularly fuzzy set theory, for its assessment. Criteria and indicators (C&I) are described as instruments to assess forest sustainability. Basic elements and concepts of fuzzy sets are described, including membership functions and their interpretations in the context of sustainable forest management. Moreover, fuzzy operators that can combine the operational concepts of sustainability, namely criteria and indicators are described. A simple illustrative example is described to demonstrate the application of these methodologies.     

Using fuzzy numbers to propagate uncertainty in matrix-based LCI

Background, aim, and scope  Analysis of uncertainties plays a vital role in the interpretation of life cycle assessment findings. Some of these uncertainties arise from parametric data variability in life cycle inventory analysis. For instance, the efficiencies of manufacturing processes may vary among different industrial sites or geographic regions; or, in the case of new and unproven technologies, it is possible that prospective performance levels can only be estimated. Although such data variability is usually treated using a probabilistic framework, some recent work on the use of fuzzy sets or possibility theory has appeared in the literature. The latter school of thought is based on the notion that not all data variability can be properly described in terms of frequency of occurrence. In many cases, it is necessary to model the uncertainty associated with the subjective degree of plausibility of parameter values. Fuzzy set theory is appropriate for such uncertainties. However, the computations required for handling fuzzy quantities has not been fully integrated with the formal matrix-based life cycle inventory analysis (LCI) described by Heijungs and Suh (2002). Materials and methods  This paper integrates computations with fuzzy numbers into the matrix-based LCI computational model described in the literature. The approach uses fuzzy numbers to propagate the data variability in LCI calculations, and results in fuzzy distributions of the inventory results. The approach is developed based on similarities with the fuzzy economic input–output (EIO) model proposed by Buckley (Eur J Oper Res 39:54–60, 1989). Results  The matrix-based fuzzy LCI model is illustrated using three simple case studies. The first case shows how fuzzy inventory results arise in simple systems with variability in industrial efficiency and emissions data. The second case study illustrates how the model applies for life cycle systems with co-products, and thus requires the inclusion of displaced processes. The third case study demonstrates the use of the method in the context of comparing different carbon sequestration technologies. Discussion  These simple case studies illustrate the important features of the model, including possible computational issues that can arise with larger and more complex life cycle systems. Conclusions  A fuzzy matrix-based LCI model has been proposed. The model extends the conventional matrix-based LCI model to allow for computations with parametric data variability represented as fuzzy numbers. This approach is an alternative or complementary approach to interval analysis, probabilistic or Monte Carlo techniques. Recommendations and perspectives  Potential further work in this area includes extension of the fuzzy model to EIO-LCA models and to life cycle impact assessment (LCIA); development of hybrid fuzzy-probabilistic approaches; and integration with life cycle-based optimization or decision analysis. Additional theoretical work is needed for modeling correlations of the variability of parameters using interacting or correlated fuzzy numbers, which remains an unresolved computational issue. Furthermore, integration of the fuzzy model into LCA software can also be investigated.     

Fuzzy systems vegetation theory

Fuzzy systems vegetation theory is a comprehensive framework for the expression of vegetation theory and conceptual models, as well as the development of vegetation analyses. It is applicable to vegetation/environment relations, vegetation dynamics, and the effects of environmental dynamics on vegetation composition. Fuzzy systems vegetation theory is a fuzzy set generalization of dynamical systems theory and incorporates a formal logic and mathematics. This paper presents the elements of fuzzy systems vegetation theory and discusses the relationship of the fuzzy systems theory to the geometric concepts generally employed in vegetation theory.     

模糊图论在山西植被区划中的应用

本文用模糊图论的最大树方法对山西植被区划进行了数量分类研究,将山西植被分为2个植被地带,6个植被地区,17个植被小区。与在植物群落学中应用的模糊聚类分析和其它方法相比,模糊图论的最大树方法直接依模糊相似系数矩阵得到树状图,从而避免了相似系数矩阵复杂的合成运算,而分类结果不仅更具直观性,而且也是令人满意的。我们认为模糊图论应用于植被区划是合适的。     

A fuzzy coding approach for the analysis of long-term ecological data

• 1 We present an unconventional procedure (fuzzy coding) to structure biological and environmental information, which uses positive scores to describe the affinity of a species for different modalities (i.e. categories) of a given variable. Fuzzy coding is essential for the synthesis of long-term ecological data because it enables analysis of diverse kinds of biological information derived from a variety of sources (e.g. samples, literature).
• 2 A fuzzy coded table can be processed by correspondence analysis. An example using aquatic beetles illustrates the properties of such a fuzzy correspondence analysis. Fuzzy coded tables were used in all articles of this issue to examine relationships between spatial-temporal habitat variability and species traits, which were obtained from a long-term study of the Upper Rhône River, France.
• 3 Fuzzy correspondence analysis can be programmed with the equations given in this paper or can be performed using ADE (Environmental Data Analysis) software that has been adapted to analyse such long-term ecological data. On Macintosh Apple^TM computers, ADE performs simple linear ordination, more recently developed methods (e.g. principal component analysis with respect to instrumental variables, canonical correspondence analysis, co-inertia analysis, local and spatial analyses), and provides a graphical display of results of these and other types of analysis (e.g. biplot, mapping, modelling curves).
• 4 ADE consists of a program library that exploits the potential of the HyperCard^TM interface. ADE in an open system, which offers the user a variety of facilities to create a specific sequence of programs. The mathematical background of ADE is supported by the algebraic model known as ‘duality diagram’.

     

直接模糊聚类的截取水平选择及其在植被数量分析中的应用

植被生态研究中常用的聚类法,是着眼于研究区域中植被和环境因子呈间断分布或变化梯度较大的一类情况,对原始数据中各个体按其属性进行归类。直接模糊聚类法则以各个体间的属性相近程度来定义一模糊关系矩阵,然后对矩阵取不同的水平截集,从而得出一等级分类。当模糊关系确定以后,截取水平的选择就成了聚类结果的决定性因素。至目前为止,直接模糊聚类中的截取水平通常由分析者主观给定,或者是以逐步试验,逐步修改的方法确定的。这样,聚类结果就不可避免地带有较大的主观和任意性。笔者认为截取水平应选在模糊关系变化较大之处,使聚类结果尽可能地反映原始数据的结构特征。这一原理已被实施于一通用软件中,实例分析表明,如此选择的截取水平确能比较客观地反映原始数据的特征,从而得出较为合理的聚类结果。     

Operator functional state estimation based on EEG-data-driven fuzzy model

This paper proposed a max–min-entropy-based fuzzy partition method for fuzzy model based estimation of human operator functional state (OFS). The optimal number of fuzzy partitions for each I/O variable of fuzzy model is determined by using the entropy criterion. The fuzzy models were constructed by using Wang–Mendel method. The OFS estimation results showed the practical usefulness of the proposed fuzzy modeling approach.     

Dynamic Quality Index for agricultural soils based on fuzzy logic

The increasing number of successful applications of fuzzy logic and fuzzy sets theory to dealing with the uncertainty, imprecision and subjectivity inherent to environmental quality assessments, and the recent development of new procedures based on fuzzy logic for the design of environmental quality indexes open new ways to carry out more rigorous and realistic estimations of soil quality. With these considerations in mind, the aim of this work is to design an index based on fuzzy logic, which is especially addressed to assess the dynamic quality of agricultural soils – Soil Dynamic Quality Index (S-DQI). This index is described by a group of three indexes (S-DQI_PHYS, S-DQI_CHEM, S-DQI_BIOL), each one designed to evaluate the dynamic quality of agricultural soils with regard to their physical, chemical and biological characteristics, respectively. Each index is determined from the joint opinion of a panel of experts, which decides: (i) the attributes or properties of soil which determine its dynamic quality for farming; (ii) the most suitable indicator for quantifying each of them; (iii) the influence of the values taken by these indicators on the quality of agricultural soils, which is expressed by means of membership functions, and (iv) the relative importance of the attributes in the respective index, which is expressed by means of normalized priority vectors. The value of each of these indexes is finally obtained as a result of a fuzzy inference procedure, which is a crisp value ranging from 0 to 1. This procedure allows us to express the values taken by the indicators in a particular agroecosystem by means of both crisp values and fuzzy numbers, the latter being frequently a more rigorous and realistic way of representing the estimations of the soil properties in any emplacement. Verification tests show the satisfactory response capability of the index to changes in the soil properties. The use of the designed S-DQI for routine monitoring of the quality of farming soil allows the estimation of the changes induced in the soil due to use, which is helpful to assess systematically the sustainability of the agricultural practices.     

A combination of fuzzy set ordination with detrended correspondence analysis: One way to combine multi-environmental variables with vegetation data

This paper examines one possible way of Fuzzy Set Ordination by using multi-environmental variables. FSO's function is improved through combination with Detrended Correspondence Analysis which is used to summarize environmental information. It can be used to analyse the relationships between vegetation and environment no matter how many environmental variables are involved. An example with vegetation and environmental data collected from upland grasslands in Northern Snowdonia, Wales, is presented. Its results are consistent with that of CCA and DCCA.Abbreviations FSO Fuzzy set ordination - DCA Detrended correspondence analysis - CCA Canonical correspondence analysis - DCCA Detrended canonical correspondence analysis     

On the Application of Fuzzy Decision Theory in Chemotherapy

1IntreductionTheliteratUreonmulti-Criteriondecisionmaking(MCDM)problemshas~tremendouslyintherecentpast.TwomajorareashaveevolvedwhiChbothconcentrateondecisionmakingwithseveralcriteria:multiobjectivedecisionmaking(MODM)andmulti-attributedecisionmaking(MADM).TheformerconcentratesoncontinuousdecisionspaceandthelatterfocusesonproblemswithdiscreteSPace.FuzzysettheoryhascontributedtoMODMproblemsaswellastheMADMProblems.ThegeneralMODMproblemcanbedeft.edLllasfollows:Twostagescangenerallybe…     

粗糙集模糊聚类分析法在昆虫分类研究中的应用

本文根据昆虫图像,对半翅目、鳞翅目、鞘翅目的28种昆虫提取的形状参数、叶状性、球状性等7项数学形态特征进行了粗糙集模糊聚类分析。在粗糙集处理的基础上,分别进行7指标和3指标（相对约简）两种不同的模糊聚类分析法相比较。结果显示,在作为目级阶元分类指标时,各项特征的重要性依次为：(似圆度、偏心率)＞（亮斑数、球状性、圆形性）＞（叶状性、形状参数）;粗糙集分类正确率优于模糊聚类分析法;粗糙集处理后的3指标分类正确率优于未处理的7指标分类正确率。结论认为,粗糙集理论在昆虫依据数学形态特征进行分类方面与统计分析方法相比更有优势,粗糙集滤过指标后再进行模糊聚类法分析在昆虫分类研究上具有重要意义。     

小麦品种对麦长管蚜抗性的模糊综合决策

应用50个小麦品种对麦长管蚜抗性鉴定指标值进行模糊统计回归分析,提出了品种自然感蚜量、蚜虫在品种上的累积存活率、平均发育历期、产仔率、内禀增长率(r_m)及品种耐害性等抗性指标的模糊隶属函数,建立了品种抗性的模糊综合决策模型。对10个品种的抗蚜性综合决策结果表明,陕167的综合抗蚜性最强,83(37)65、(87)113、82246次之,小偃6号最差。同时,综合型决策模型的决策结果最优,精度高,保留较多信息。     

主要土壤肥力因素指标的筛选模型

根据主成分分析模型中的相关结构分析理论及模糊聚类分析的方法,构造了一个对主要土壤肥力因素指标进行筛选的数学模型,运用该模型可对土壤的主要盈力因素指标进行筛选,并对筛选结果的可靠性进行检验,文章的最后给出了模型的应用实例。     

9种啮齿动物骨骼形态的模糊聚类分析

本文上关系数对９种啮齿动物的骨骼形态进行模糊聚类分析，所用公式，结果表明：聚类分析是一种适合于啮齿动物骨骼形态的数量分类方法。可用于探讨属，种间的亲缘系。