Publications

The relevance for fuzzy modelling of the concept of optimal I/O interfaces has been discussed, analyzed, and illustrated. A pair of directly connected numeric/linguistic and linguistic/numeric interfaces is said to be a pair of optimal interfaces if a zero conversion error is obtained. In this work, some optimal interfaces design options are outlined and discussed. These include the optimization of the numeric/linguistic interface, the optimization of the linguistic/numeric interface, and the simultaneous optimization of both interfaces. Simulation results are included.

The study is devoted to a granular analysis of data. We develop a new clustering algorithm that organizes findings about data in the form of a collection of information granules-hyperboxes. The clustering carried out here is an example of a granulation mechanism. We discuss a compatibility measure guiding a construction (growth) of the clusters and explain a rationale behind their development. The clustering promotes a data mining way of problem solving by emphasizing the transparency of the results (hyperboxes). We discuss a number of indexes describing hyperboxes and expressing relationships between such information granules. It is also shown how the resulting family of the information granules is a concise descriptor of the structure of the data-a granular signature of the data. We examine the properties of features (variables) occurring of the problem as they manifest in the setting of the information granules. Numerical experiments are carried out based on two-dimensional (2-D) synthetic data as well as multivariable Boston data available on the WWW.

In this paper, we consider a generic class of adaptive optimization problems under uncertainty, and develop a data-driven paradigm of adaptive probabilistic robust optimization (APRO) in a robust and computationally tractable manner. The paradigm comprises two phases: 1) bilayer information granulation (IG), which involves the data-mining techniques and nested decomposition of convex sets that establish and restructure the knowledge from data and 2) robustization and optimization over the restructured knowledge by the IG, which forms the APRO model. The tradeoff between the solution optimality and the robustness of the resulting data-driven APRO model can be achieved by adjusting the number of clusters and the number of nested decomposition units of the IG process. We draw the connections of the APRO model with the stochastic programming and the regular robust optimization models, respectively, and show that the APRO model can be regarded as a generalized version of both models. We show that the APRO model can be transformed into the second-order conic programming which is computationally tractable and can be solved efficiently by the off-the-shelf solvers. Furthermore, the model can be extended by robustizing the probability parameters. Finally, an application on two-stage facility location planning is presented, and the computational results demonstrate the performance and the insights of using the data-driven APRO models.

The absolute and relative quantifications between the equivalence class and the target concept are the two important research endeavours in rough set theory. Double‐quantitative decision‐theoretic rough set (Dq‐DTRS) models utilise both absolute quantification and relative quantification in their upper and lower approximations to reflect the distinctive degrees of quantitative information. Herein, the authors apply the information theory to Dq‐DTRS model to characterise and measure these two types of quantitative information. The expressions of the information entropy with regard to the two quantifications and their corresponding information co‐entropy are presented in DqI‐DTRS model and DqII‐DTRSmodel, respectively. This work makes a further study of Dq‐DTRS models by discussing the information measures with respect to absolute and relative quantification.

Determining the optimal number of clusters in cluster analysis without prior knowledge remains a critical and challenging task. Existing methods often depend on calculating clustering validity indices (CVIs), which increases complexity and may reduce efficiency. Furthermore, different CVIs frequently suggest varying optimal cluster numbers, complicating the selection process. To address these challenges, we propose a novel clustering algorithm, self-regulating possibilistic C-means (PCM) with high-density points (SR-PCM-HDP), which simplifies cluster number determination while improving clustering efficiency. First, the density-based knowledge extraction (DBKE) method is introduced to estimate an appropriate initial cluster number and identify high-density points. DBKE enhances the density peak clustering (DPC) algorithm by removing the need for a predefined density radius. Second, SR-PCM-HDP refines the clustering process by incorporating a parameter to balance the interactions between high-density points and cluster centers, reducing sensitivity to initial configurations and accelerating convergence. Third, the parameter adjustment mechanism in classical PCM is redefined to enable adaptive updates during SR-PCM-HDP iterations. This mechanism facilitates the gradual elimination of obsolete clusters and iterative cluster formation. The theoretical foundations of the SR-PCM-HDP cluster elimination mechanism are rigorously established. Experimental results validate the accuracy and effectiveness of SR-PCM-HDP in determining cluster numbers and ensuring clustering validity, particularly for datasets with overlapping or imbalanced distributions. Comparisons are conducted against 13 state-of-the-art algorithms, including fuzzy clustering, possibilistic clustering, and CVI-based cluster determination methods.

Meteorological volumetric radar data are used to detect thunderstorms, storm events responsible for nearly all severe summer weather. Discriminating between different types of thunderstorms is challenge due to the high dimensionality of the data, the paucity of labeled data, and the imprecision of the labels. Several classification strategies and preprocessing techniques are tested to facilitate the discrimination between four types of storm events: wind, heavy rain, tornado and hail.