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Bayesian model-based classifiers, both unsupervised and supervised, have been studied extensively and their value and versatility have been demonstrated on a wide spectrum of applications within science and engineering. A majority of the classifiers are built on the assumption of intrinsic discreteness of the considered data features or on the discretization of them prior to the modeling. On the other hand, Gaussian mixture classifiers have also been utilized to a large extent for continuous features in the Bayesian framework. Often the primary reason for discretization in the classification context is the simplification of the analytical and numerical properties of the models. However, the discretization can be problematic due to its \textit{ad hoc} nature and the decreased statistical power to detect the correct classes in the resulting procedure. We introduce an unsupervised classification approach for fuzzy feature vectors that utilizes a discrete model structure while preserving the continuous characteristics of data. This is achieved by replacing the ordinary likelihood by a binomial quasi-likelihood to yield an analytical expression for the posterior probability of a given clustering solution. The resulting model can be justified from an information-theoretic perspective. Our method is shown to yield highly accurate clusterings for challenging synthetic and empirical data sets.

To facilitate decision support in the ecosystem management, ecological expertise and site-specific data need to be integrated. Fuzzy logic can deal with highly variable, linguistic, vague and uncertain data or knowledge and, therefore, has the ability to allow for a logical, reliable and transparent information stream from data collection down to data usage in decision-making. Several environmental applications already implicate the use of fuzzy logic. Most of these applications have been set up by trial and error and are mainly limited to the domain of environmental assessment. In this article, applications of fuzzy logic for decision support in ecosystem management are reviewed and assessed, with an emphasis on rule-based models. In particular, the identification, optimisation, validation, the interpretability and uncertainty aspects of fuzzy rule-based models for decision support in ecosystem management are discussed.

In this paper, we propose a novel density-grid-based method for clustering k-dimensional data. KIDS, an acronym for K-dimensional Ink Drop Spread, detects densely-connected pieces of data in k-dimensional grids. It enables one to simultaneously exploit the advantages of fuzzy logic, as well as both density-based and grid-based clustering. In the proposed method, the k-dimensional data space is divided into different cells. Input data records are mapped to the cells. The data points are then spread in the k-dimensional cells, just like what happens to ink drops in water. So the cells adjacent to the data cells also represent the data. Eventually, the impacts of all data grid cells are condensed and compared with the threshold to compute the final clusters. The experimental results show that the method has superior quality and efficiency in both low and high dimensions. In addition, the method is not only robust to noise but it is also capable of finding clusters of arbitrary shapes. [ABSTRACT FROM AUTHOR]

Radar remote sensing has shown its potential for retrieving soil moisture from bare soil surfaces. Since the backscattering process is also influenced by soil roughness, the characterization of this roughness is crucial for an accurate soil moisture retrieval. However, several field experiments have shown a large variability of the roughness parameters. Describing these parameters by means of possibility distributions allows to account for their uncertainty. Verhoest et al. introduced a retrieval procedure which calculates from these uncertain roughness parameters the possibility distribution of retrieved soil moisture, from which a soil moisture value and uncertainty upon the retrieval are estimated. The main disadvantage of their technique is the high computational demand, which hampers an operational application. In this paper, a fuzzy modeling approach, which is based on fuzzy rules of the Takagi-Sugeno type, is introduced that accurately simulates the soil moisture and the uncertainty upon its retrieved value as obtained by the possibilistic procedure. Index Terms--Fuzzy model, possibility theory, SAR, soil moisture, soil roughness, uncertainty.

Probabilistic and fuzzy choice functions are used to describe decision situations in which some degree of uncertainty or imprecision is involved. We propose a way to equate these two formalisms by means of residual implication operations. Furthermore, a set of new rationality conditions for probabilistic choice functions is proposed and proved to be sufficient to ensure that the associated fuzzy choice function is rational. [ABSTRACT FROM AUTHOR]

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used. [ABSTRACT FROM PUBLISHER]

We present a fast bottom-up algorithm to compute all fixpoints of a fuzzy closure operator in a finite set over a finite chain of truth degrees, along with the partial order on the set of all fixpoints. Fuzzy closure operators appear in several areas of fuzzy logic and its applications, including formal concept analysis (FCA) that we use as a reference area of application in this paper. Several problems in FCA, such as computing all formal concepts from data with graded attributes or computing non-redundant bases of all attribute dependencies, can be reduced to the problem of computing fixpoints of particular fuzzy closure operators associated with the input data. The development of a general algorithm that is applicable, in particular, to these problems is the ultimate purpose of this paper. We present the algorithm, its theoretical foundations, and experimental evaluation. [ABSTRACT FROM AUTHOR]

Abstract: We introduce a new class of algebras called EQ-algebras. An EQ-algebra has three basic binary operations (meet, multiplication and a fuzzy equality) and a top element. These algebras are intended to become algebras of truth values for a higher-order fuzzy logic (a fuzzy type theory, FTT). The motivation stems from the fact that until now, the truth values in FTT were assumed to form either an IMTL-, BL-, or MV-algebra, all of them being special kinds of residuated lattices in which the basic operations are the monoidal operation (multiplication) and its residuum. The latter is a natural interpretation of implication in fuzzy logic; the equivalence is then interpreted by the biresiduum, a derived operation. The basic connective in FTT, however, is a fuzzy equality and, therefore, it is not natural to interpret it by a derived operation. This defect is expected to be removed by the class of EQ-algebras introduced and studied in this paper. From the algebraic point of view, the class of EQ-algebras generalizes, in a certain sense, the class of residuated lattices and so, they may become an interesting class of algebraic structures as such. [Copyright &y& Elsevier]

Most performance criteria which have been applied to train ecological models focus on the accuracy of the model predictions. However, these criteria depend on the prevalence of the training set and often do not take into account ecological issues such as the distinction between omission and commission errors. Moreover, a previous study indicated that model training based on different performance criteria results in different optimised models. Therefore, model developers should train models based on different performance criteria and select the most appropriate model depending on the modelling objective. This paper presents a new approach to train fuzzy models based on an adjustable performance criterion, called the adjusted average deviation (aAD). This criterion was applied to develop a species distribution model for spawning grayling in the Aare River near Thun, Switzerland. To analyse the strengths and weaknesses of this approach, it was compared to model training based on other performance criteria. The results suggest that model training based on accuracy-based performance criteria may produce unrealistic models at extreme prevalences of the training set, whereas the aAD allows for the identification of more accurate and more reliable models. Moreover, the adjustable parameter in this criterion enables modellers to situate the optimised models in the search space and thus provides an indication of the ecological model relevance. Consequently, it may support modellers and river managers in the decision making process by improving model reliability and insight into the modelling process. Due to the universality and the flexibility of the approach, it could be applied to any other ecosystem or species, and may therefore be valuable to ecological modelling and ecosystem management in general. [Copyright &y& Elsevier]

In this paper we characterize all idempotent uninorms defined on a finite ordinal scale. It is proved that any such discrete idempotent uninorm is uniquely determined by a decreasing function from the set of scale elements not greater than the neutral element to the set of scale elements not smaller than the neutral element, and vice versa. Based on this one-to-one correspondence, the total number of discrete idempotent uninorms on a finite ordinal scale of n + 1 elements is equal to 2n. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of obtaining the consensus evaluation of multiple objects based on the evaluations expressed by several experts. This problem is of relevance to several fields, in particular to the field of sensory evaluation, such as in food quality appraisal, and to the field of recommender systems, such as in movie recommendation and online dating systems. Unlike existing methods for obtaining a consensus evaluation, which strongly rely on a chosen distance function, we adhere to the natural property of monotonicity, resulting in an intuitively appealing consensus evaluation method in which the labels expressed for all objects are considered simultaneously. Three real-life and three synthetic examples illustrate the search for such consensus evaluation. [ABSTRACT FROM AUTHOR]

Abstract: Over the last decades, several data-driven techniques have been applied to model the rainfall–discharge dynamics of catchments. Among these techniques are fuzzy rule-based models, which attempt to describe the catchment response to rainfall input through fuzzy relationships. In this paper, we demonstrate three different methods for constructing fuzzy rule-based models of the Takagi–Sugeno type relating rainfall to catchment discharge. They correspond to the grid partitioning, subtractive clustering, and Gustafson–Kessel (GK) clustering identification methods. The data set used to parametrize and validate the models consists of hourly precipitation and discharge records. The models are parametrized using a 1-year identification data set and are then applied to a 4-year data set. Although the models show a similar performance, the best results are obtained for the GK method. A real-time flood forecasting algorithm is then developed, in which discharge measurements are assimilated into the model at either an hourly or a daily time step. The results suggest that the GK method can potentially be used as an operational flood forecasting tool with a low computational cost. [Copyright &y& Elsevier]