Hesitant fuzzy agglomerative hierarchical clustering algorithms

Recently, hesitant fuzzy sets (HFSs) have been studied by many researchers as a powerful tool to describe and deal with uncertain data, but relatively, very few studies focus on the clustering analysis of HFSs. In this paper, we propose a novel hesitant fuzzy agglomerative hierarchical clustering algorithm for HFSs. The algorithm considers each of the given HFSs as a unique cluster in the first stage, and then compares each pair of the HFSs by utilising the weighted Hamming distance or the weighted Euclidean distance. The two clusters with smaller distance are jointed. The procedure is then repeated time and again until the desirable number of clusters is achieved. Moreover, we extend the algorithm to cluster the interval-valued hesitant fuzzy sets, and finally illustrate the effectiveness of our clustering algorithms by experimental results.     

A clustering technique for the identification of piecewise affine systems

We propose a new technique for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional domain. In order to achieve our goal, we provide an algorithm that exploits the combined use of clustering, linear identification, and pattern recognition techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures. Moreover, the clustering step (used for classifying the datapoints) is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure.     

Generalized Yule-walker and two-stage identification algorithms for dual-rate systems

1 Introduction Presenting new identification methods and performance analysis of identification algorithms under weak conditions are everlasting themes and melodies of identification studies and are also my everlasting pursuits in life [1～4]. Multirate systems with different input and output sampling periods are very active in process industries [5～7], e.g. fermenta- tion processes [8], and petroleum production [9]. The stud- ies of multirate systems involve various areas of control, in- clu…     

The least-squares identification of FIR systems subject to worst-case noise

The least-squares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudo-random binary sequence. A lower bound on the worst-case transfer function error shows that the least-square estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding trade-off in the random error case: with a worst-case formulation, the model complexity should not increase indefinitely as the size of the data set increases.     

Applying hierarchical grey relation clustering analysis to geographical information systems - A case study of the hospitals in Taipei City

Deng proposed grey clustering analysis (GCA) in 1987. Later, Jin presented a new method in 1993, called grey relational clustering (GRC) method that combined grey relational analysis with clustering. However, the GRC method cannot use a tree diagram to make appropriate classification decisions without re-computation. This study thus attempts to combine GRC and hierarchical clustering analysis. Given the existence of an excess of medical resources in the Taipei area, this study attempts to understand the degree of concentration of medical resources in this area. Specifically, this study applies a geographical information system (GIS) to present the geographical distribution of hospitals in Taipei. Additionally, a new-type of cluster analysis, known as hierarchical grey relation clustering analysis, is used to analyze the distribution of hospitals and understand how they compete with one another. The analytical results demonstrate that hierarchical grey relation clustering analysis is a suitable method of analyzing geographical position. Tree diagrams can help policymakers make appropriate classification decisions without re-computation. The study results can inform hospitals of their competitors and help them to develop appropriate responses. Additionally, the analytical results can also provide a reference to government or hospital policymakers to help them position hospitals in areas, thus achieving a better distribution of medical resources in Taipei.     

Range identification for nonlinear parameterizable paracatadioptric systems

In this paper, a new range identification technique for a calibrated paracatadioptric system mounted on a moving platform is developed to recover the range information and the three-dimensional (3D) Euclidean coordinates of a static object feature. The position of the moving platform is assumed to be measurable. To identify the unknown range, first, a function of the projected pixel coordinates is related to the unknown 3D Euclidean coordinates of an object feature. This function is nonlinearly parameterized (i.e., the unknown parameters appear nonlinearly in the parameterized model). An adaptive estimator based on a min-max algorithm is then designed to estimate the unknown 3D Euclidean coordinates of an object feature relative to a fixed reference frame which facilitates the identification of range. A Lyapunov-type stability analysis is used to show that the developed estimator provides an estimation of the unknown parameters within a desired precision. Numerical simulation results are presented to illustrate the effectiveness of the proposed range estimation technique.     

A novel approach to fault diagnosis for time-delay systems

In this paper, a novel fault detection and identification (FDI) scheme for time-delay systems is presented. Different from the existing FDI design methods, the proposed approach utilizes fault tracking approximator (FTA) and iterative learning algorithm to obtain estimates of the fault functions. Performance of the FTA is rigorously analyzed by investigating its stability and fault tracking sensitivity properties in the presence of slowly developing or abrupt faults for state delayed dynamic systems. A novel feature of the FTA is that it can simultaneously detect and identify the shape and magnitude of the faults. Additionally, an extension to a class of nonlinear time-delay systems is made by using nonlinear control theories. Finally, the applicability and effectiveness of the proposed FDI scheme is illustrated by a practical industrial process.     

An addendum and correction to: ‘On identification and adaptive estimation for systems with interrupted observations’

An error in the proof of the Theorem 1 of a previous paper of the author's is corrected. It is also pointed out that an important class of system/signal models, called composite sources, can be cast into the framework of the model considered in the referenced paper. Thus, the parameter estimation/system identification results of the paper are applicable to the composite source system model.