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.     

Fuzzy set analysis of the Ethiopian rift valley vegetation in relation to anthropogenic influences

Vegetation data of the Rift Valley have been revisited using fuzzy set theory to give quantitative measures of the links between species and vegetation states. Vegetation is considered as a global indicator of both land use and natural conditions. Human activities in the area have influenced the physiognomy of vegetation so much that an apparently uniform state has developed over most of the Rift Valley floor. Fuzzy set theory has made it possible to interpret the pattern of variation in vegetation on the basis of some reference states corresponding to protected and cultivated sites. The concept of stratocoena is applied to analyse the anthropogenic influences on the tree-shrub and herb layers in order to investigate how they respond to human interference individually.     

Fuzzy species distribution models: a way to represent plant communities spatially

Fuzzy set theory has generally been applied to smooth classification cut‐offs, with an unavoidable loss of information. In this commentary, I rely on both advantages and disadvantages of the methods proposed in Duff et al., in this issue of the Journal of Vegetation Science, to map the variability over space of vegetation classes based on fuzzy sets and species distribution models.     

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 millon 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.     

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.     

Herbivore regulation and irreversible vegetation change in semi-arid grazing systems

Models made to explain sudden and irreversible vegetation shifts in semi-arid grasslands typically assume that herbivore density is independent of the state of the vegetation, e.g., under the control of humans. We relax this assumption and investigate the mathematical implications of vegetation-regulated herbivore population dynamics. We show that irreversible vegetation change may also occur in systems where herbivore population dynamics are affected by changes in plant standing crop. Our analysis furthermore shows that irreversible vegetation change may occur for a larger set of soil and climatic conditions when herbivore numbers are independent of the vegetation, as compared to systems where vegetation density determines herbivore population size. Hence, our analysis suggests that irreversible vegetation change is less likely to occur in systems with natural herbivore population dynamics than in systems where humans control herbivore density.     

The Fundamentals of Vegetation Change - Complexity Rules

Long-term vegetation dynamics based on paleo-pollen data display transient behaviour, often alternating in phase between predominant determinism and predominant 'turbulence', when viewed as a trajectory in a multivariate phase space. Given this, the metaphor of vegetation dynamics as a 'flowing stream', first introduced by Cooper in his classic 1926 paper entitled "The fundamentals of vegetation change", is re-examined and revealed to be not only useful, but strikingly realistic. Vegetation dynamic theory is reviewed and classic theories are found to reflect reality poorly. It is suggested that vegetation dynamics is a far from equilibrium system, and that the application of nonequilibrium thermodynamic theory is appropriate.     

A dynamical systems perspective on vegetation theory

A dynamical systems perspective is employed to develop a simple conceptual model of vegetation and environment as coupled dynamical systems. The conceptual model characterizes the influence of environment on vegetation, the effect of vegetation on the environment, and the subsequent response of vegetation to the modified environment. Vegetation and environmental dynamics are modeled as trajectories in complementary state spaces, with the trajectories jointly determined by the position of a given site in both spaces. The vegetation and environment state spaces are coupled by the physiological requirements of the component species and the modification of environment by vegetation. From a dynamical systems perspective, current vegetation theory and analyses overemphasize environmental determination of vegetation composition and neglect the effects of vegetation on environment. A dynamical systems perspective is capable of synthesizing previous concepts of vegetation; the continuum and community type concepts are possible consequences of site specific differences in vegetation metabolism and environmental plasticity.I would like to acknowledge the helpful comments and criticisms of Drs G. Cottam, J. D. Aber, T. F. H. Allen, R. P. McIntosh, C. G. Lorimer, and anonymous reviewers.I would like to thank the University of Wisconsin, Madison for a fellowship which supported this research. This paper is dedicated with great respect and gratitude to Professor G. Cottam on the occasion of his retirement from the University of Wisconsin.     

太白山针叶林的Fuzzy分类研究

应用模糊聚类分析法和模糊图论分析对太白山针叶林进行了数量分类比较研究。将２６个样地分为两大类共７个群落类型。研究结果表明,两种方法在植物群落分类研究中,不但是可行的,而且所分类的实际结果是等价的,与实际观测情况也是吻合的。其中的图论法直接依据模糊相似系数得到树状图,简便易行,显示出更大的适用性。     

A theoretical framework of ecological phase transitions for characterizing tree-grass dynamics

This paper describes a theoretical framework of ecological phase transitions for modeling tree-grass dynamics and analyzing the shifts or phase transitions from one vegetation structure to another in the southern Texas landscape. This framework implements the integration of percolation theory, fractal geometry and phase transition theory as a method for modeling the spatial patterns of tree-grass dynamics, and nonlinear Markov non-equilibrium thermodynamic stability theory as a method for characterizing temporal tree-grass dynamics and phase transition. An historical sequence of aerial photographs at a Prosopis - thornscrub savanna parkland site in southern Texas was used to determine the parameters of the models. The preliminary analytical result accords well with current understanding and field survey of vegetation dynamics in the southern Texas landscape. The potential of such approaches and other relevant theories such as self-organized criticality and synergetics to vegetation dynamics is also discussed.     

油松毛虫幼虫,蛹种群聚集动态的分析

本文用灰色聚类分析、模糊聚类分析方法研究油松毛虫(Dendrolimustabulaeformis)幼虫、蛹种群的聚集动态。两种聚类分析方法综合分析结果表明:油松毛虫从越冬幼虫至蛹的种群聚集动态过程可分为:高度聚集,中等聚集程度和低聚集度三个阶段,它们各自相应的生物学阶段是:“刚刚上树期”,“上树后重新分布,扩散期(死亡率较高期)”,“取食盛期”以及蛹期,其中前二个阶段为“高聚集度”阶段。     

基于区间值模糊集理论的顺势疗法药物选择(英文)

利用区间值模糊集理论,将Sanchez的医疗诊断方法应用到了顺势疗法的药物选择中.文章中讨论了两类区间值模糊关系和选择指数,并给出了一种新的利用软情报学的方法.     

FUZZY SET THEORY APPLIED TO PRODUCT CLASSIFICATION BY A SENSORY PANEL1

It is frequently impossible to meet the assumptions underlying the statistical approach to classification of food products by a sensory panel. To find an alternative, we have investigated the applicability of the fuzzy set theory. Within a fuzzy set framework it is acceptable that a product belongs to several classes simultaneously and no assumptions regarding the distribution of sensory properties for a product class are made. Fuzzy classification models can be constructed from a set of training objects by linking the soft class labels to the sensory attributes applying an inference procedure based on fuzzy logic. A number of fuzzy inference procedures has been evaluated using a number of attribute sets. A satisfactory classification has been found using a very simple implication rule and a set of three attributes.     

Ecological Monitoring and Health Research in Luambe National Park,Zambia: Generation of Baseline Data Layers

Classifying, describing and understanding the natural environment is an important element of studies of human, animal and ecosystem health, and baseline ecological data are commonly lacking in remote environments of the world. Human African trypanosomiasis is an important constraint on human well-being in sub-Saharan Africa, and spillover transmission occurs from the reservoir community of wild mammals. Here we use robust and repeatable methodology to generate baseline datasets on vegetation and mammal density to investigate the ecology of warthogs (Phacochoerus africanus) in the remote Luambe National Park in Zambia, in order to further our understanding of their interactions with tsetse (Glossina spp.) vectors of trypanosomiasis. Fuzzy set theory is used to produce an accurate landcover classification, and distance sampling techniques are applied to obtain species and habitat level density estimates for the most abundant wild mammals. The density of warthog burrows is also estimated and their spatial distribution mapped. The datasets generated provide an accurate baseline to further ecological and epidemiological understanding of disease systems such as trypanosomiasis. This study provides a reliable framework for ecological monitoring of wild mammal densities and vegetation composition in remote, relatively inaccessible environments.     

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.     

Analysis of vegetation structural diversity by Burnaby's similarity index

The application of Burnaby's similarity index is discussed by using structural data from mediterranean vegetation. The index, suggested to compare objects described by characters measured on different scales (mixed data), was applied in a fuzzy theory context. Ordinations of vegetation relevés and structural characters by joint plots have been obtained. These are very useful to map vegetation structural diversity in multidimensional spaces and to test the efficiency of an intuitive classification based on qualitative assessment.     

Improving the interpretation of fuzzy partitions in vegetation science with constrained ordinations

Classification and ordination techniques based in fuzzy set theory are now being commonly used in vegetation studies. However, several problems have been detected in spite of the significant theoretical advantages of the theory. In this paper we have improved the interpretability of fuzzy partitions by combining fuzzy partitions with correspondence analysis (CA) and detrended canonical correspondence analysis (DCCA) in an analysis of the beech forests of Basque Country, northern Spain. Our results seem to overcome difficulties in the interpretation of multi-group partitions.     

峡谷暖区柑桔气候生态的定量研究

作为山地气候[7,8] 类型之一的峡谷地形气候 ,在农业上的应用研究已引起广泛的关注。研究其农业地形气候[10 ] ,特别是对作物气候生态进行定量研究 ,有助于峡谷区域农业气候资源的合理开发与利用。本文所述及的峡谷主要是指鄂西南的长江三峡、清江河谷及香溪河谷。因峡谷地形特别 ,气候的突出特征是峡谷暖区 (因海拔 80 0ｍ附近的冬季气温接近于同纬度的江汉平原而可定为暖区的上限 )的形成 ,其表现为隆冬少有低温冻害 ;难有积雪、雨凇和雾凇 ;风力弱、无偏北大风 ;有效辐射小、净辐射量大。其成因为 :冷空气难进易出 ;西南暖槽的保护作用[2…     

Mapping historical forest types in Baraga County Michigan,USA as fuzzy sets

Data on tree location and species in a portion of Northern Michigan were gathered from General Land Office (GLO) survey notes (ca. 1850), digitized, and generalized to represent forest types. Fuzzy membership values describing the degree of membership of each species in each forest type were derived from (a) semantic information in the forestry literature and (b) a fuzzy clustering routine applied to data from randomly placed circular plots. The fuzzy membership values assigned to each tree point for each forest type were interpolated to form continuous surfaces using kriging and co-kriging. Advantages of this method over traditional discrete mapping methods include: (a) multiple options are available for the display and analysis; (b) classification uncertainty and the continuity of natural vegetation can be represented; and (c) the classification scheme is applied systematically across the entire map area and can be altered to produce alternative maps. The subset of available display and analytical products presented include: discrete forest type maps; a surface representing the confusion between forest types; fuzzy logical overlays of forest types; and discrete class maps with color value altered within each class to indicate degree of confusion at each location.