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Feature selection facilitates classification learning and can resort to uncertainty measurement of rough set theory. By fuzzy neighborhood rough sets, the fuzzy-neighborhood relative decision entropy (FNRDE) motivates a recent algorithm of feature selection, called AFNRDE. However, FNRDE has fusion defects for interaction priority and hierarchy deepening, and such fusion limitations can be resolved by operational commutativity; furthermore, subsequent AFNRDE has advancement space for effective recognition. For the measurement reinforcement, an improved measure (called IFNRDE) is proposed to pursue class-level priority fusion; for the algorithm promotion, the corresponding selection algorithm (called AIFNRDE) is designed to improve AFNRDE. Concretely, multiplication fusion of algebraic and informational measures is preferentially implemented at the class level, and the hierarchical summation generates classification-level IFNRDE. IFNRDE improves FNRDE, and its construction algorithm and granulation monotonicity are acquired. Then, IFNRDE motivates a heuristic algorithm of feature selection, i.e., AIFNRDE. Finally, relevant measures and algorithms are validated by table examples and data experiments, and new AIFNRDE outperforms current AFNRDE and relevant algorithms FSMRDE, FNRS, FNGRS for classification performances.

Attribute reduction based on rough sets is an effective approach of data learning in intelligent systems, and it has two basic types. Traditional classification-based attribute reducts mainly complete the classification task, while recent class-specific reducts directly realize the class-pattern recognition. Neighborhood rough sets have the covering-structure extension and data-diversity applicability, but their attribute reducts concern only the neighborhood classification-based reducts. This paper proposes class-specific attribute reducts based on neighborhood rough sets, so as to promote the optimal identification and robust processing of specific classes. At first, neighborhood class-specific reducts are defined, and their basic properties and heuristic algorithms are acquired by granulation monotonicity. Then, hierarchical relationships between the neighborhood classification-based and class-specific reducts are analyzed, and mutual derivation algorithms are designed. Finally, the theoretical constructions and mutual relationships are effectively verified by both decision table examples and data set experiments. The neighborhood class-specific reducts robustly extend the existing class-specific reducts, and they also provide a hierarchical mechanism for the neighborhood classification-based reducts, thus facilitating wide applications of class-pattern processing.

Outlier detection is widely used in many fields, such as intrusion detection, credit card fraud detection, medical diagnosis, and so on. Existing outlier detection algorithms are mostly designed for dealing with numeric or categorical attributes. However, data usually exist in the form of mixed attributes in real-world applications. In this article, we propose a novel mixed attribute outlier detection method based on multigranulation relative entropy by employing the neighborhood rough set. First, the neighborhood system is constructed by optimizing the mixed distance metric and the radius of the statistical value. Second, the neighborhood entropy is introduced as an uncertainty measure of data. Furthermore, the three kinds of multigranulation relative entropy-based matrices are defined by three kinds of attribute sequences, and the multigranulation relative entropy-based outlier factor is integrated to indicate the outlier degree of every object. Based on the proposed outlier detection model, the corresponding algorithm is designed. Finally, the proposed algorithm is compared with other nine algorithms through experiments on public data. The experimental results show that the proposed technique is adaptive and effective.

As an extension of traditional information systems, interval-set information systems have a strong expressive ability to describe uncertain information. Study of the rough set theory and the attribute reduction of interval-set information system are worth discussing. Here, the granularity structure of similar equivalence classes in an interval-set information system is mined, and an attribute reduction algorithm is constructed. The upper and lower approximation operators in the interval-set information system are defined. The accuracy and roughness are determined by these operators. At the same time, using rough sets, a concept of three branches of rough sets on the interval-set information system is constructed. The concepts of attribute dependency and attribute importance are induced by the positive number domain of the three branch domains, and they then lead to the attribute reduction algorithm. Experiments on the UCI datasets show that the uncertainty measure proposed in this paper is sensitive to the attributes and can effectively reduce redundant information of the interval-set information system.

Information measures in neighborhood decision systems underlie information processing and uncertainty measurement, especially regarding neighborhood rough sets. Their constructions on covering structuring and neighborhood counting can acquire theoretical extensions and practical compactness but become difficult and rare when comparing the sample counting approach and its defects. In terms of three-way information measures (i.e., information entropy, conditional entropy, and mutual information), classification-level and class-level complement information measures are established by extending equivalence decision systems to neighborhood decision systems; thus, the construction on nonrepetitive neighborhoods becomes ingenious, and the study of criss-cross structuring and granulation properties becomes valuable. At the classification level, neighborhood-complement information measures are proposed by imitation; they perfectly expand existing complement information measures, and thus, they offer an extended isomorphism regarding systematicity. At the class level, neighborhood-complement information measures are determined by decomposition to generate a hierarchical isomorphism, and they also induce equivalence-complement information measures to yield a degenerate isomorphism. Then, granulation nonmonotonicity and monotonicity of neighborhood-complement information measures are revealed at these two levels, and their uncertainty mechanisms are analyzed deeply by three-level granular structures. Finally, all complement measures are calculated programmatically, and their relationships and nonmonotonicity or monotonicity are effectively verified by virtue of table examples and data experiments. In summary, systematically, there are four criss-cross modes of three-way complement information measures based on two knowledge granulations and two decision levels; the variably extended and degenerated isomorphisms and hierarchically decomposed and integrated isomorphisms are thoroughly uncovered, the granulation nonmonotonicity and monotonicity are deeply mined, and all achievements are found to have good application prospects for feature reduction and rule induction in machine learning.

Feature selection facilitates intelligent information processing, and the unsupervised learning of feature selection has become important. In terms of unsupervised feature selection, the Laplacian score (LS) provides a powerful measurement and optimization method, and good performance has been achieved using the recent forward iterative Laplacian score (FILS) algorithm. However, there is still room for advancement. The aim of this paper is to improve the FILS algorithm, and thus, feature significance (SIG) is mainly introduced to develop a high-quality selection method, i.e., the incremental forward iterative Laplacian score (IFILS) algorithm. Based on the modified LS, the metric difference in the incremental feature process motivates SIG. Therefore, SIG offers a dynamic characterization by considering initial and terminal states, and it promotes the current FILS measurement on only the terminal state. Then, both the modified LS and integrated SIG acquire granulation nonmonotonicity and uncertainty, especially on incremental feature chains, and the corresponding verification is achieved by completing examples and experiments. Furthermore, a SIG-based incremental criterion of minimum selection is designed to choose optimization features, and thus, the IFILS algorithm is naturally formulated to implement unsupervised feature selection. Finally, an in-depth comparison of the IFILS algorithm with the FILS algorithm is achieved using data experiments on multiple datasets, including a nominal dataset of COVID-19 surveillance. As validated by the experimental results, the IFILS algorithm outperforms the FILS algorithm and achieves better classification performance.

A three-way approximation of a fuzzy set, as a generalization of the core and the support of the fuzzy set, provides a generalized qualitatively interpretation of a fuzzy set. An intuitionistic fuzzy set (IFS) generalizes a fuzzy set by using jointly a membership function and a nonmembership function. In this paper, we present a model for constructing a three-way approximation of an IFS according to the TAO (trisecting-acting-outcome) framework of three-way decision (3WD). Given an IFS, we use its membership and nonmembership functions as a pair of evaluations to trisect a universe of objects to produce a three-way approximation of the IFS. We present a general optimization model for determining the required parameters according to the principle of the minimum cost with respect to a distance function and costs of three actions. We use Manhattan distance to illustrate the basic ideas of the optimization model.

Attribute reduction of rough set theory underlies knowledge acquisition and has two hierarchical types (classification-based and class-specific attribute reducts) and two perspectives from algebra and information theory; thus, there are four combined modes in total. Informational class-specific reducts are fundamental but lacking and are thus investigated by correspondingly constructing class-specific information measures. First, three types of information measures (i.e., information entropy, conditional entropy, and mutual information) are novelly established at the class level by hierarchical decomposition to acquire their hierarchical connection, systematical relationship, uncertainty semantics, and granulation monotonicity. Second, three types of informational class-specific reducts are correspondingly proposed to acquire their internal relationship, basic properties, and heuristic algorithm. Third, the informational class-specific reducts achieve their transverse connections, including the strength feature and consistency degeneration, with the algebraic class-specific reducts and their hierarchical connections, including the hierarchical strength and balance, with the informational classification-based reducts. Finally, relevant information measures and attribute reducts are effectively verified by decision tables and data experiments. Class-specific information measures deepen existing classification-based information measures by a hierarchical isomorphism, while the informational class-specific reducts systematically perfect attribute reduction by level and viewpoint isomorphisms; these results facilitate uncertainty measurement and information processing, especially at the class level.

Feature selection facilitates pattern recognition, and fuzzy neighborhood rough sets provide an effective tool. By fuzzy neighborhood rough sets, we propose a heuristic feature selection algorithm based on fuzzy-neighborhood relative decision entropy, called AFNRDE. At first, the fuzzy-neighborhood relative decision entropy is proposed by granulation extension and information fusion, and it acquires uncertainty measurement, integration computing, and granulation monotonicity; then, the corresponding feature selection and heuristic reduction algorithm are constructed; finally, the measure monotonicity and algorithm validity are verified by numerical example and data experiment. AFNRDE promotes initial algorithm FSMRDE based on relative decision entropy to numerical data processing, and it also outperforms two usual methods FNRS and FNGRS for classification performance.

Fuzzy rough sets are an effective tool for dealing with uncertainty information. The theory of three-way decisions provides a method of decision-making, when a two-way decision may be difficult to make. In this paper, we investigate the combination of fuzzy rough sets and three-way decisions, and construct robust fuzzy rough set models from a three-way decision perspective. In fuzzy rough sets, by introducing a pair of thresholds, we propose three-way approximations of the fuzzy similarity degree, and we construct three-way lower and upper approximations based on the idea of a three-way decision. Furthermore, we discuss the special cases of three-way approximations about of both the fuzzy similarity degree and dual approximations. Sixteen fuzzy rough set models are constructed for under different special cases. Among them, three improved models and the original model are selected to be compared as examples. Finally, for the four fuzzy rough set models, including one model based on three-way decisions, two models based on two-way decisions, and one original model, we design the experiments by introducing two types of data noise to test the robustness of the models. The results verify the better performance of the improved model based on three-way approximations in comparison with the two-way and original models.

This paper further studies the stability of the uncertain delayed neutral-type system by constructing a novel Lyapunov-Krasovskii functional (LKF) with some delay-dependent and N-dependent items. Some new delay-dependent robust stability criteria are proposed based on linear matrix inequality (LMI). The criteria proposed in this paper are less conservative than some recent previous ones. Some numerical examples, including a linear neutral-type system, the partial element equivalent circuit and a general linear system, are presented to show the effectiveness of the proposed approach.

Uncertainty measurements underlie the system interaction and data learning. Their relevant studies are extensive for the single-valued decision systems, but become relatively less for the interval-valued decision systems. Thus, three-level and three-way uncertainty measurements of the interval-valued decision systems are proposed, mainly by systematically constructing vertical-horizontal weighted entropies. Firstly, the interval-valued decision systems are endowed with three-level structures, including Micro-Bottom, Meso-Middle, and Macro-Top. Secondly, a three-level decomposition is hierarchically made for the existing conditional entropy. Thirdly, three-way weighted entropies are systematically and hierarchically constructed at the three levels, and they achieve their hierarchy, systematicness, algorithm, boundedness, and granulation monotonicity/non-monotonicity. The three-level and three-way weighted entropies deepen and extend the conditional entropy, and they realize the ingenious criss-cross informatization for the interval-valued decision systems. Their effectiveness of uncertainty measurements is ultimately verified by table examples and data experiments.

The multi-granulation rough sets serve as important hierarchical models for intelligent systems. However, their mainstream optimistic and pessimistic models are respectively too loose and strict, and this defect becomes especially serious in hierarchical processing on an attribute-expansion sequence. Aiming at the attribute-addition chain, compromised multi-granulation rough set models are proposed to systematically complement and balance the optimistic and pessimistic models. According to the knowledge refinement and measure order induced by the attribute-enlargement sequence, the basic measurement positioning and corresponding pointer labeling based on equilibrium statistics are used, and thus we construct four types of compromised models at three levels of knowledge, approximation, and accuracy. At the knowledge level, the median positioning of ordered granulations derives Compromised-Model 1; at the approximation level, the average positioning of approximation cardinalities is performed, and thus the separation and integration of dual approximations respectively generate Compromised-Models 2 and 3; at the accuracy level, the average positioning of applied accuracies yields Compromised-Model 4. Compromised-Models 1–4 adopt distinctive cognitive levels and statistical perspectives to improve and perfect the multi-granulation rough sets, and their properties and effectiveness are finally verified by information systems and data experiments.

The disposal effect of thermal desorption of oil-based cuttings is predicted by analyzing the material temperature rise, heat transfer, and liquid evaporation in the processing. Based on the characteristics of material conveying in the heating bed, this paper establishes the governing equations for the simulation calculation of thermal desorption processing and demonstrates the correlation model between the mass change of wet components and the heat required. Changes in the material temperature and mass content of wet components in the process are calculated using the finite-volume method. The minimum temperature of the material layer experienced three stages: slow rising stage, stagnation stage, and rapid rising stage. In the first two stages, material preheating and water evaporation are the dominant processes. The third stage is mainly the evaporation of the oil phase. The inflection point between the second and third stages in the temperature rise curve can be regarded as the end point of water evaporation. During conveying, residence time and material layer thickness significantly influence the liquid phases removal ratio. The material drying area gradually expands from the boundary to the center with the extension of residence time, and the average mass fraction of liquids decreases slowly. The evaluation results from the final temperature and residual oil content of solid slag after disposal are consistent with the tests and have better accuracy in predicting the disposal effect when the heating temperature is higher and the residence time is longer.

In terms of rough set theory, information-theoretical measures have been introduced to implement uncertainty measurements and system applications, and their robust construction and in-depth develop...

In order to explore a single-phase microinverter with boosting ability, simple structure, low-cost, and high power density, a new structure of a multilevel inverter (MLI) is proposed in this article. With this structure, two half-bridge modular switched-capacitor circuits are arranged on both left- and right-sides of a dc source. Circuit configuration of this MLI can be bilaterally symmetrical and this benefits to modular design and the voltage stress reduction of inverting bridges. Additionally, in order to reduce voltage ripple of capacitors and total harmonic distortion of output voltage simultaneously, a hybrid pulsewidth modulation strategy is developed to improve the performance of this MLI. As a result, capacitors of this MLI can be replenished repeatedly when they are taken as voltage sources to generate different voltage levels. Circuit configuration, operation principle, modulation, power loss, and voltage ripple are analyzed in detail. Both simulation and experimental results are provided to demonstrate the effectiveness of the proposed MLI and modulation strategy.

Attribute reduction of rough set theory is effective for intelligent information processing, and class-specific attribute reducts are beneficial for pattern recognition and rule reasoning. According to three-way decisions, class-specific reducts already have three-way types (namely, positive, negative, and positive-negative) of qualitative optimization, which adhere to classical rough sets. In terms of region preservations, there are no corresponding three-way types of quantitative optimization that match probabilistic rough sets. Thus, this paper constructs and investigates quantitative three-way class-specific attribute reducts based on region preservations. First, the uncertainty/nonmonotonicity of quantitative region change is revealed, and it naturally induces the reduction criteria of quantitative region preservations. Then, quantitative three-way class-specific reducts are constructed, and their basic properties regarding their necessary conditions, attribute cores, and reduct algorithms are achieved. Furthermore, their interrelation regarding equivalence and strengthening/balance are obtained for consistent and inconsistent decision classes, respectively, and their expansions for qualitative three-way class-specific reducts are proved. Finally, relevant concepts and obtained results are effectively verified by decision tables and data experiments. By virtue of sure region preservations, quantitative three-way class-specific attribute reducts robustly extend the existing qualitative three-way class-specific reducts and facilitate the optimal identification and quantitative reasoning of class-specific patterns.