Fuzzy coding in constrained ordinations

Canonical correspondence analysis and redundancy analysis are two methods of constrained ordination regularly used in the analysis of ecological data when several response variables (for example, species abundances) are related linearly to several explanatory variables (for example, environmental variables, spatial positions of samples). In this report I demonstrate the advantages of the fuzzy coding of explanatory variables: first, nonlinear relationships can be diagnosed; second, more variance in the responses can be explained; and third, in the presence of categorical explanatory variables (for example, years, regions) the interpretation of the resulting triplot ordination is unified because all explanatory variables are measured at a categorical level.

Biplots of fuzzy coded data

A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data.

Gene expression signatures delineate biological and prognostic subgroups in peripheral T-cell lymphoma

Peripheral T-cell lymphoma (PTCL) encompasses a heterogeneous group of neoplasms with generally poor clinical outcome. Currently 50% of PTCL cases are not classifiable: PTCL-not otherwise specified (NOS). Gene-expression profiles on 372 PTCL cases were analyzed and robust molecular classifiers and oncogenic pathways that reflect the pathobiology of tumor cells and their microenvironment were identified for major PTCL-entities, including 114 angioimmunoblastic T-cell lymphoma (AITL), 31 anaplastic lymphoma kinase (ALK)-positive and 48 ALK-negative anaplastic large cell lymphoma, 14 adult T-cell leukemia/lymphoma and 44 extranodal NK/T-cell lymphoma that were further separated into NK-cell and gdT-cell lymphomas. Thirty-seven percent of morphologically diagnosed PTCL-NOS cases were reclassified into other specific subtypes by molecular signatures. Reexamination, immunohistochemistry, and IDH2 mutation analysis in reclassified cases supported the validity of the reclassification. Two major molecular subgroups can be identified in the remaining PTCL-NOS cases characterized by high expression of either GATA3 (33%; 40/121) or TBX21 (49%; 59/121). The GATA3 subgroup was significantly associated with poor overall survival (P = .01). High expression of cytotoxic gene-signature within the TBX21 subgroup also showed poor clinical outcome (P = .05). In AITL, high expression of several signatures associated with the tumor microenvironment was significantly associated with outcome. A combined prognostic score was predictive of survival in an independent cohort (P = .004).

Application of fuzzy-rule-based postprocessing to correlation methods in pattern recognition

One of the most important problems in optical pattern recognition by correlation is the appearance of sidelobes in the correlation plane, which causes false alarms. We present a method that eliminate sidelobes of up to a given height if certain conditions are satisfied. The method can be applied to any generalized synthetic discriminant function filter and is capable of rejecting lateral peaks that are even higher than the central correlation. Satisfactory results were obtained in both computer simulations and optical implementation.

Fuzzy logic applied to the modeling of water dynamics in an Oxisol in northeastern Brazil

Modeling of water movement in non-saturated soil usually requires a large number of parameters and variables, such as initial soil water content, saturated water content and saturated hydraulic conductivity, which can be assessed relatively easily. Dimensional flow of water in the soil is usually modeled by a nonlinear partial differential equation, known as the Richards equation. Since this equation cannot be solved analytically in certain cases, one way to approach its solution is by numerical algorithms. The success of numerical models in describing the dynamics of water in the soil is closely related to the accuracy with which the water-physical parameters are determined. That has been a big challenge in the use of numerical models because these parameters are generally difficult to determine since they present great spatial variability in the soil. Therefore, it is necessary to develop and use methods that properly incorporate the uncertainties inherent to water displacement in soils. In this paper, a model based on fuzzy logic is used as an alternative to describe water flow in the vadose zone. This fuzzy model was developed to simulate the displacement of water in a non-vegetated crop soil during the period called the emergency phase. The principle of this model consists of a Mamdani fuzzy rule-based system in which the rules are based on the moisture content of adjacent soil layers. The performances of the results modeled by the fuzzy system were evaluated by the evolution of moisture profiles over time as compared to those obtained in the field. The results obtained through use of the fuzzy model provided satisfactory reproduction of soil moisture profiles.

Espectros Vis-NIR do Solo e Fuzzy K-Médias Aplicados na Delimitação de Unidades de Mapeamento de Solos em Topossequências

RESUMO O conhecimento dos solos é cada vez mais importante para que o uso dele seja realizado corretamente na agropecuária, no crescimento urbano, na conservação dos recursos naturais, entre outros. Entretanto, verifica-se carência de profissionais qualificados para a caracterização e os mapeamentos pedológicos, particularmente em escalas de maior detalhamento. Essa carência, aliada aos avanços das ferramentas computacionais e do sensoriamento remoto, promoveu o surgimento do Mapeamento Digital de Solos (MDS), que busca auxiliar e agilizar as atividades de levantamento pedológico. Assim, este trabalho objetivou desenvolver uma metodologia de delimitaçao de unidades de solos em topossequências por meio do comportamento espectral dos solos no comprimento de onda do Visível-Infravermelho Próximo (Vis-NIR). A metodologia espectral consistiu na obtenção das curvas espectrais dos solos por meio do espectrorradiômetro FieldSpecPro e da redução do número de informações espectrais por meio da análise de Componentes Principais, seguida de agrupamento das amostras mediante método fuzzy k-médias. Foram selecionadas cinco topossequências com pontos equidistantes de 30 m para caracterizar as classes de solos e amostragens. Foram descritas oito classes de solos distintas, que tiveram caracterização detalhada e classificação em perfis pedológicos. No restante dos pontos, a caracterização das classes de solos foi feita com base na classificação dos solos realizada nos perfis pedológicos, com coleta de amostras por meio de tradagens nas profundidades de 0,00-0,20 e 0,80-1,00 m, perfazendo o total de 162 amostras ao longo das cinco topossequências. As amostras foram analisadas pelas metodologias convencional e espectral, para que os resultados pudessem ser comparados e avaliados. Dessa forma, foram realizadas análises morfológicas, físicas (textura) e químicas nas amostras de solo. Das cinco topossequências estudadas, os resultados foram satisfatoriamente semelhantes; alguns solos não foram perfeitamente individualizados pela metodologia espectral, em razão da grande semelhança em seus comportamentos espectrais, como demonstrado pelo Latossolo Vermelho Férrico e Nitossolo Vermelho Férrico. A metodologia espectral foi capaz de diferenciar solos com resposta espectral distinta e estabelecer limites nas topossequências, apresentando grande potencial para ser implementada em levantamentos pedológicos.

Identification of different heart tissues from MRI C-SENC images using an unsupervised multi-stage fuzzy clustering technique.

PURPOSE: To objectively characterize different heart tissues from functional and viability images provided by composite-strain-encoding (C-SENC) MRI. MATERIALS AND METHODS: C-SENC is a new MRI technique for simultaneously acquiring cardiac functional and viability images. In this work, an unsupervised multi-stage fuzzy clustering method is proposed to identify different heart tissues in the C-SENC images. The method is based on sequential application of the fuzzy c-means (FCM) and iterative self-organizing data (ISODATA) clustering algorithms. The proposed method is tested on simulated heart images and on images from nine patients with and without myocardial infarction (MI). The resulting clustered images are compared with MRI delayed-enhancement (DE) viability images for determining MI. Also, Bland-Altman analysis is conducted between the two methods. RESULTS: Normal myocardium, infarcted myocardium, and blood are correctly identified using the proposed method. The clustered images correctly identified 90 +/- 4% of the pixels defined as infarct in the DE images. In addition, 89 +/- 5% of the pixels defined as infarct in the clustered images were also defined as infarct in DE images. The Bland-Altman results show no bias between the two methods in identifying MI. CONCLUSION: The proposed technique allows for objectively identifying divergent heart tissues, which would be potentially important for clinical decision-making in patients with MI.

Effect of a lifestyle intervention on adiposity and fitness in socially disadvantaged subgroups of preschoolers: a cluster-randomized trial (Ballabeina).

OBJECTIVE: A multidimensional lifestyle intervention performed in 652 preschoolers (72% of migrant, 38% of low educational level (EL) parents) reduced body fat, but not BMI and improved fitness. The objective of this study is to examine whether the intervention was equally effective in children of migrant and/or low EL parents.¦METHODS: Cluster-randomized controlled single blinded trial, conducted in 2008/09 in 40 randomly selected preschools in Switzerland. The culturally tailored intervention consisted of a physical activity program and lessons on nutrition, media use and sleep. Primary outcomes included BMI and aerobic fitness. Secondary outcomes included %body fat, waist circumference and motor agility.¦RESULTS: Children of migrant parents benefitted similarly from the intervention compared to their counterparts (p for interaction≥ 0.09). However, children of low EL parents benefitted less, although these differences did not reach statistical significance (p for interaction≥ 0.06). Average intervention effect sizes for BMI were -0.10, -0.05, -0.11 and 0.04 kg/m(2) and for aerobic fitness were 0.55, 0.20, 0.37 and -0.05 stages for children of non-migrant, migrant, middle/high EL and low EL parents, respectively.¦CONCLUSIONS: This intervention was similarly effective among preschoolers of migrant parents compared to their counterparts, while children of low EL parents benefitted less.

A fuzzy-based decision model application on strategic management

In this article, the objective is to demonstrate the effects of different decision styles on strategic decisions and likewise, on an organization. The technique that was presented in the study is based on the transformation of linguistic variables to numerical value intervals. In this model, the study benefits from fuzzy logic methodology and fuzzy numbers. This fuzzy methodology approach allows us to examine the relations between decision making styles and strategic management processes when there is uncertainty. The purpose is to provide results to companies that may help them to exercise the most appropriate decision making style for its different strategic management processes. The study is leaving more research topics for further studies that may be applied to other decision making areas within the strategic management process.

Fuzzy logic algorithm to extract specific interaction forces from atomic force microscopy data

The atomic force microscope is not only a very convenient tool for studying the topography of different samples, but it can also be used to measure specific binding forces between molecules. For this purpose, one type of molecule is attached to the tip and the other one to the substrate. Approaching the tip to the substrate allows the molecules to bind together. Retracting the tip breaks the newly formed bond. The rupture of a specific bond appears in the force-distance curves as a spike from which the binding force can be deduced. In this article we present an algorithm to automatically process force-distance curves in order to obtain bond strength histograms. The algorithm is based on a fuzzy logic approach that permits an evaluation of "quality" for every event and makes the detection procedure much faster compared to a manual selection. In this article, the software has been applied to measure the binding strength between tubuline and microtubuline associated proteins.