Abstract The paper deals with a problem of modeling of fuzzy systems in random environments. A model is proposed that is capable of handling two distinct forms of imprecision, viz. randomness and fuzziness. The model is required to cope with both of them while modeling a variety of problems in management, medical diagnosis, and unsupervised pattern recognition. The models proposed in the paper are constructed and evaluated in a formal framework established by fuzzy relation equations. Randomness is introduced as additional constraints imposed on the structure of the fuzzy relation equation (hence: structured fuzzy models). The forecasting (prediction) problem is studied in detail.
A rapid and accurate prediction of byproduct gas flow in steel industry can help not only to become aware of the operational situations of gas system, but it also provides the energy scheduling workers with sound decision-making mechanisms. In this study, a least square support vector machine (LS-SVM) model based on online hyperparameters optimization is proposed, where the variance of effective noise of the sample is estimated, while a conjugate gradient algorithm is developed to optimize the width of Gaussian kernels and the regularization factor. To assess the quality of the proposed method, we experiment with a test function affected by additive noise and an industrial gas flow data from Shanghai Baosteel Company Ltd. A series of comparative experiments are reported as well. The results demonstrate that the proposed method shows the shortest computing time while ensuring the prediction accuracy. These two features make the approach applicable to real-time prediction of gas flow in steel industry.
We discuss a problem of synthesis and analysis of granular rules emerging in data mining. Two descriptors of the rules (that is relevance and consistency) being viewed individually and en block are introduced. The relevance of the rules is quantified in terms of the data being covered by the antecedents and conclusions standing there. While this index describes each rule individually, the consistency of the rule deals with the quality of the rule viewed vis-a-vis other rules. It expresses how much the rule "interacts" with others in the sense that its conclusion is distorted by the conclusion parts coming from other rules. We show how the rules are formed by means of fuzzy clustering and their quality can be evaluated in terms of the above indexes. Global characteristics of a set of rules are also discussed and related to the number of information granules being constructed in the data space.
Accurate classification of biomedical data is often confounded by potentially imprecise class labels assigned by an external reference test. We present a gradation method using fuzzy set theory and a dispersion-adjusted similarity measure to assign, for each pattern in a design set, a degree of belongingness to each class. After training a classifier using this adjusted design set, its performance is measured using a validation set of patterns with their original class labels. We empirically demonstrate the effectiveness of this method using three publicly available biomedical datasets. Using the same classifier, we benchmark the results against the original datasets without gradation.
Along with the abundant appearance of interval-valued time series (ITS), the study on ITS clustering, especially on shape-based ITS clustering, is becoming increasingly important. As an effective approach to extracting trend information in time series, fuzzy trend-granulation addresses the needs of shape-based ITS clustering. However, when extracting trend information in ITS, unequal-size granules are inevitably produced, which makes ITS clustering difficult and challenging. Facing with this issue, this paper aims to generalize the widely used Fuzzy C-Means (FCM) algorithm to a fuzzy trend-granulation based FCM algorithm for ITS clustering. To this end, a suite of algorithms including ITS segmenting, segment merging and granule building algorithms are firstly developed for fuzzy trend-granulation of ITS, with which the given ITS are transformed into granular ITS which consist of double linear fuzzy information granules (DLFIGs) and may be of different lengths. With the defined distance between DLFIGs, the distance between granular ITS is further developed through the dynamic time warping (DTW) algorithm. In designing the fuzzy trend-granulation based FCM algorithm, the key step is to design the method for updating cluster prototypes to cope with the unequal lengths of granular ITS. Weighted DTW barycenter averaging (wDBA) method is a previously adopted prototype updating approach with the drawback of hardly changing the lengths of prototypes, which often makes prototypes less representative. Thus, a granule splitting and merging algorithm is designed to resolve this issue. Additionally, a prototype initialization method is also proposed to improve the clustering performance. The proposed fuzzy trend-granulation based FCM algorithm for clustering ITS, being a typical shape-based clustering algorithm, exhibits superior performance which is validated by the ablation experiments as well as the comparative experiments.
The notion of a rough set was originally proposed by Pawlak underwent a number of extensions and generalizations. Dubois and Prade (1990) introduced fuzzy rough sets which involve the use of rough sets and fuzzy sets within a single framework. Radzikowska and Kerre (2002) proposed a broad family of fuzzy rough sets, referred to as ( t)-fuzzy rough sets which are determined by some implication operator (implicator), and a certain t-norm. In order to describe the linguistically represented concepts coming from data available in some information system, the concept of fuzzy rough sets are redefined and further studied in the setting of the Axiomatic Fuzzy Set (AFS) theory. Compared with the ( t)-fuzzy rough sets, the advantages of AFS fuzzy rough sets are twofold. They can be directly applied to data analysis present in any information system without resorting to the details concerning the choice of the implication, t-norm and a similarity relation S. Furthermore such rough approximations of fuzzy concepts come with a well-defined semantics and therefore offer a sound interpretation. Some examples are included to illustrate the effectiveness of the proposed construct. It is shown that the AFS fuzzy rough sets provide a far higher flexibility and effectiveness in comparison with rough sets and some of their generalizations.
