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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.

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.

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.

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.

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.

This paper studies the stability problem of load frequency control (LFC) of a single area power system with communication delays both from remote measurements to the control centre and from control centre to generator units. The closed-loop LFC system with two transmission delays in communication networks can be expressed as the linear system with two additive time-varying delays. A stability criterion is derived via an affine second order Bessel-Legendre free-matrix-based inequality and Lyapunov stabiliity theory application. The stability criterion is in the form of linear matrix inequality (LMI), which can be easily solved via the MATLAB LMI-toolbox. Compared with some previously published results, the stability criterion in this paper is less conservative. Finally, an application of the LFC for a single area power system is presented to show the effectiveness of the proposed approach.

The modular microgrid based on distributed battery storages is a simple and reliable power supply way for the islands. Modules are interconnected to the transmission network through the three-port converter. The three-port converter supplies the local ac bus voltage within the module and realizes the power exchange between the module and the transmission network. Distributed battery power and SoC consensus tracking model considering communication time delay is established on the leader-following multi-agent consensus tracking theory. By using the delay decomposition method, where the delay interval is discretized into two segmentations with an equal width, a modified Lyapunov-Krasovskii functional is constructed. A delay-dependent sufficient condition for the absolute stability of the battery power and SoC consensus tracking is derived in terms of linear matrix inequalities (LMIs) by using the free-weighting matrix method. The maximum delay margin corresponding to different controller parameters is calculated with the LMI toolbox of MATLAB. The case study is carried out based on the DongAo Island microgrid demonstration project. Simulations of battery power and SoC consensus tracking with constant time or time-varying delays verifies the effectiveness of the maximum delay margin determined by the stability criteria. Experiments reveal that the three-port converter can meet the requirements of the modular microgrid networking and operation control. The distributed battery power and SoC consensus tracking of the modular microgrid can be achieved when the communication time delay is less than the maximum delay margin.

The outlier relies on its distinctive mechanism and valuable information to play an important role in expert and intelligent systems, and thus outlier detection has already been extensively applied in relevant fields including the fraud detection, medical diagnosis, public security, etc. The outlier detection methods of rough sets recently gain in-depth research, because they are data-driven and never require additional knowledge. However, classical rough set-based methods consider only categorical data; furthermore, neighborhood rough sets adhere to numeric and heterogeneous data, but their outlier detection is mainly restricted to numeric data now. According to the hybrid data-driving, this paper investigates outlier detection by the neighborhood information entropy and its developmental measures, and the applicable data sets widely concern categorical, numeric, and mixed data; as a result, the new method extends both the traditional distance-based and rough set-based methods to enrich outlier detection. Concretely, the neighborhood information system is first determined by the heterogeneous distance and self-adapting radius, the neighborhood information entropy is then defined to implement whole uncertainty measurement, three gradual information measures are further constructed to describe each single object, and finally the neighborhood entropy-based outlier factor (NEOF) is integratedly established to detect outliers; moreover, the NEOF-based outlier detection algorithm (called the NIEOD algorithm) is designed and applied. By virtue of UCI data experiments, the NIEOD algorithm is compared with six existing detection algorithms (including the NED, IE, SEQ, FindCBLOF, DIS, KNN algorithms), and the concrete results generally reflect the better effectiveness and adaptability of the new method.

Attribute reduction serves as a pivotal topic of rough set theory for data analysis. The ideas of tri-level thinking from three-way decision can shed new light on three-level attribute reduction. Existing classification-specific and class-specific attribute reducts consider only macro-top and meso-middle levels. This paper introduces a micro-bottom level of object-specific reducts. The existing two types of reducts apply to the global classification with all objects and a local class with partial objects, respectively. The new type applies to an individual object. These three types of reducts constitute tri-level attribute reducts. Their development and hierarchy are worthy of systematical explorations. Firstly, object-specific reducts are defined by object consistency from dependency, and they improve both classification-specific and class-specific reducts. Secondly, tri-level reducts are unified by tri-level consistency. Hierarchical relationships between object-specific reducts and class-specific, classification-specific reducts are analyzed, and relevant connections of three-way classifications of attributes are given. Finally, tri-level reducts are systematically analyzed, and two approaches, i.e., the direct calculation and hierarchical transition, are suggested for constructing a specific reduct. We build a framework of tri-level thinking and analysis of attribute reduction to enrich three-way granular computing. Tri-level reducts lead to the sequential development and hierarchical deepening of attribute reduction, and their results profit intelligence processing and system reasoning.

Uncertainty measures can effectively capture data features, and thus they serve as a fundamental tool to evaluate uncertainty in data analyses. In regard with the uncertainty measures, there are some studies in single grain interval-valued rough sets. As a novel uncertainty methodology, multigranulation interval-valued rough sets can deal with hierarchical issues in granulation processing, but they acquire less discussions on uncertainty measurement. Accordingly, this paper mainly constructs uncertainty measures regarding the multi-granulation interval-valued decision systems (MGIVDS). Firstly, MGIVDS are introduced. Secondly, some concepts of uncertainty measures are defined in multi-granulation interval-valued decision systems, including fusion θ-conditional entropy, fusion approximation roughness and fusion θ-decision entropy. Finally, properties of three types of information measures are obtained. Relevant researches offer novel insights into uncertainty measurement in multiple granulation and interval data.

The Dynamic Economic Emission Dispatch Problem (DEED) is a well-known problem in the study of thermal power generation. The goal of the DEED is to meet the demand change by arranging the capacities of power generators to reduce fuel cost and emission. In recent years, the high environmental awareness, the decreasing petrochemical energy, and the increasing energy demand such that the DEED is more important and popular than before. Most of algorithms for the DEED are either limited by less than ten power generators or without considering the power generation limit. The former is impractical due to that the number of power generators in current thermal power plants can be up to 14; the latter results in infeasible solutions. To overcome the above two obstacles, a new algorithm called the SSO-DE-SQP hybrid with the Simplified Swarm Optimization (SSO), Differential Evolution (DE), and Sequential Quadratic Programming (SQP) is developed to solve the larger-size DEED with the power generation limit. The performance of the SSO-DE-SQP is demonstrated by comparing with two existing well-known methods: DE-SQP and PSO-SQP with up to 15 generators for the DEED.

In terms of neighborhood rough sets, the tri-level granular structure of neighborhood system (carrying the neighborhood granule, swarm, and library) establishes a granular computing mechanism for knowledge-based learning. However, its hierarchical exploration is inadequate, while its measurement can be extended for robust applications. Regarding this tri-level granular structure, the double-quantification technology is novelly introduced to make a thorough investigation, especially on the double-quantitative distance measurement and classification learning. Firstly, the size valuation and logical operation are hierarchically supplemented at higher levels. Secondly, the relative and absolute distances of bottom neighborhood granules are linearly combined to a double-quantitative distance, and all the three types of distances are promoted to both the middle swarm level and the top library level. Finally, the double-quantitative distance powerfully characterizing the difference of neighborhood granules is utilized to generate a double-quantitative classifier KNGD, and relevant data experiments show that this new classifier outperforms or balances two existing classifiers, i.e., the relative classifier KNGR and absolute classifier KNGA. By theory, example, and experiment, this study hierarchically perfects the tri-level granular structure of neighborhood system, and the corresponding double-quantification integration and extension offer the robust knowledge measurement and effective classification learning.

IP-Accuracy is mined by systematic double-quantitative fusion of causality measures.IP-Accuracy GrC integration is constructed to gain benign granulation monotonicity.IP-Accuracy attribute reduction is studied to establish a hierarchical reduct system. Uncertainty measure mining and applications are fundamental, and it is possible for double-quantitative fusion to acquire benign measures via heterogeneity and complementarity. This paper investigates the double-quantitative fusion of relative accuracy and absolute importance to provide systematic measure mining, benign integration construction, and hierarchical attribute reduction. (1) First, three-way probabilities and measures are analyzed. Thus, the accuracy and importance are systematically extracted, and both are further fused into importance-accuracy (IP-Accuracy), a synthetic causality measure. (2) By sum integration, IP-Accuracy gains a bottom-top granulation construction and granular hierarchical structure. IP-Accuracy holds benign granulation monotonicity at both the knowledge concept and classification levels. (3) IP-Accuracy attribute reduction is explored based on decision tables. A hierarchical reduct system is thereby established, including qualitative/quantitative reducts, tolerant/approximate reducts, reduct hierarchies, and heuristic algorithms. Herein, the innovative tolerant and approximate reducts quantitatively approach/expand/weaken the ideal qualitative reduct. (4) Finally, a decision table example is provided for illustration. This paper performs double-quantitative fusion of causality measures to systematically mine IP-Accuracy, and this measure benignly constructs a granular computing platform and hierarchical reduct system. By resorting to a monotonous uncertainty measure, this study provides an integration-evolution strategy of granular construction for attribute reduction.

The purpose of this research is to perform an economic dispatch, formulate an optimisation model, and determine optimal operating strategies for stand-alone microgrid systems. The stand-alone microgrid is an off-grid system that is common in places where it is impossible to connect to the grid. Its economic dispatch, however, involves several constraints that impede the possibility of obtaining a feasible solution. To resolve this, the properties of the stand-alone modular microgrid mathematical model are developed to foreshorten the feasible regions of each variable. Furthermore, a new concept that involves the regeneration of a new feasible variable set is proposed. This new set replaces the infeasible variable set without the necessity of using the penalty function or regenerating entire solutions to reduce runtime. To integrate the two new foregoing concepts, which are anticipated to overcome the obstacle of infeasibility and exhibit better economic dispatch, an improved genetic algorithm is proposed. The performance of the proposed improved genetic algorithm is demonstrated through its comparison with simplified swarm optimisation, improved simplified swarm optimisation, and particle swarm optimisation on data obtained from the microgrid systems used in DongAo Island. The results show that the improved genetic algorithm, which integrates the two new proposed concepts, can handle problems with numerous constraints and is capable of obtaining a high-quality solution.

Due to the complex configuration and control framework, the conventional microgrid is not cost-effective for engineering applications with small or medium capacity. A stand-alone modular microgrid with separated AC bus and decentralized control strategy is proposed in this paper. Each module is a self-powered system, which consists of wind and solar power, a storage battery, load and three-port converter. The modules are interconnected by three-port converters to form the microgrid. Characteristics, operation principle, control of the modular microgrid and the three-port converter are analyzed in detail. Distributed storage batteries enable power exchanges among modules to enhance economic returns. Economic dispatch of the stand-alone modular microgrid is a mixed-integer programming problem. A day-ahead operation optimization model including fuel cost, battery operation cost, and power transmission cost is established. Because there are so many constraints, it is difficult to produce a feasible solution and even more difficult to have an improved solution. An improved simplified swarm optimization (iSSO) method is therefore proposed. The iSSO scheme designs the new update mechanism and survival of the fittest policy. The experimental results from the demonstration project on DongAo Island reflect the effectiveness of the stand-alone modular microgrid and the economic dispatch strategy based on the iSSO method.

Since Pawlak approximation accuracy does not reflect the influence of knowledge granularity on the approximation accuracy, scholars have put forward a series of improvements. These improvements, however, only consider the position correlation between the knowledge granularity and the approximation accuracy. They neglect the proportional relation of upper and lower approximation. Therefore, an new improved definition of approximation accuracy is proposed in this paper. The new definition not only reflects the influence of knowledge granularity on the approximation accuracy but also considers the proportional relation of upper and lower approximation. It keeps the consistency with the definition of classical approximation accuracy.

Quantitative attribute reduction exhibits applicability but complexity when compared to qualitative reduction. According to the two-category decision theoretic rough set model, this paper mainly investigates quantitative reducts and their hierarchies (with qualitative reducts) from a regional perspective. (1) An improved type of classification regions is proposed, and its preservation reduct (CRP-Reduct) is studied. (2) Reduction targets and preservation properties of set regions are analyzed, and the set-region preservation reduct (SRP-Reduct) is studied. (3) Separability of set regions and rule consistency is verified, and the quantitative and qualitative double-preservation reduct (DP-Reduct) is established. (4) Hierarchies of CRP-Reduct, SRP-Reduct, and DP-Reduct are explored with two qualitative reducts: the Pawlak-Reduct and knowledge-preservation reduct (KP-Reduct). (5) Finally, verification experiments are provided. CRP-Reduct, SRP-Reduct, and DP-Reduct expand layer by layer Pawlak-Reduct and exhibit quantitative applicability, and the experimental results indicate their effectiveness and hierarchies regarding Pawlak-Reduct and KP-Reduct.

Rough set theory is an important approach for data mining, and it refers to Shannon&rsquo, s information measures for uncertainty measurements. The existing local conditional-entropies have both the second-order feature and application limitation. By improvements of hierarchical granulation, this paper establishes double-granule conditional-entropies based on three-level granular structures (i.e., micro-bottom, meso-middle, macro-top ), and then investigates the relevant properties. In terms of the decision table and its decision classification, double-granule conditional-entropies are proposed at micro-bottom by the dual condition-granule system. By virtue of successive granular summation integrations, they hierarchically evolve to meso-middle and macro-top, to respectively have part and complete condition-granulations. Then, the new measures acquire their number distribution, calculation algorithm, three bounds, and granulation non-monotonicity at three corresponding levels. Finally, the hierarchical constructions and achieved properties are effectively verified by decision table examples and data set experiments. Double-granule conditional-entropies carry the second-order characteristic and hierarchical granulation to deepen both the classical entropy system and local conditional-entropies, and thus they become novel uncertainty measures for information processing and knowledge reasoning.

The mutual recognition of community opinion in multiple attribute group decision making (MAGDM) is an efficient way to solve complex system, which has widely application in practice. In this paper, the MAGDM under uncertain linguistic variables is studied. In order to achieve a desirable consensus in group decision making, a new algorithm is proposed to develop a satisfactory consensus reaching process, where the main point is to shrink the range of opinion values among decision makers. The whole MAGDM is automated by this model of consensus support system. The proposed algorithm and method have fundamental significance for recognition of community opinion in MAGDM, especially under uncertain linguistic variables. Finally, one example is represented to verify the method in practical problems.

Wireless (smart) sensor networks (WSNs), networks made up of embedded wireless smart sensors, are an important paradigm with a wide range of applications, including the internet of things (IoT), smart grids, smart production systems, smart buildings and many others. WSNs achieve better execution efficiency if their energy consumption can be better controlled, because their component sensors are either difficult or impossible to recharge, and have a finite battery life. In addition, transmission cost must be minimized, and signal transmission quantity must be maximized to improve WSN performance. Thus, a multi-objective involving energy consumption, cost and signal transmission quantity in WSNs needs to be studied. Energy consumption, cost and signal transmission quantity usually have uncertain characteristics, and can often be represented by fuzzy numbers. Therefore, this work suggests a fuzzy simplified swarm optimization algorithm (fSSO) to resolve the multi-objective optimization problem consisting of energy consumption, cost and signal transmission quantity of the transmission process in WSNs under uncertainty. Finally, an experiment of ten benchmarks from smaller to larger scale WSNs is conducted to demonstrate the effectiveness and efficiency of the proposed fSSO algorithm.

Conventional microgrids have a specific system configuration and a complex hierarchical control structure, which has resulted in difficulties in their economic development. A modular microgrid based on distributed battery storage has been proposed to realize the rapid economic development of small-to-medium microgrids. Control of modular microgrids is simplified to voltage control within modules and exchange power control among modules. Battery power has great influence on battery performance. Space-time complementary power characteristics among modules help to alleviate power fluctuations, prolong the service life and realize the unified maintenance of distributed batteries. Leader-following consensus theory of multi-agent systems is adopted to realize the power and capacity consensus tracking of distributed battery storage in a modular microgrid. Sufficient and necessary conditions for continuous-time and sampled-data bounded power and capacity consensus tracking of distributed battery storages are deduced by a matrix analytical method. Steady regions of sampling period and sampling delay for sampled-data bounded power and capacity consensus tracking are determined by analytical or numerical solutions. Simulations and experiments on a modular microgrid demonstration project located on DongAo Island (China) show the effectiveness and robustness of the proposed power and capacity consensus tracking strategy for distributed storage systems. The power and capacity consensus tracking strategy determines the exchange power among modules and improves the control technology of modular microgrids.

Rough set theory (RS-Theory) is a fundamental model of granular computing (GrC) for uncertainty information processing, and information entropy theory provides an effective approach for its uncertainty representation and attribute reduction. Thus, this paper hierarchically constructs three-way weighted entropies (i.e., the likelihood, prior, and posterior weighted entropies) by adopting a GrC strategy from the concept level to classification level, and it further explores three-way attribute reduction (i.e., the likelihood, prior, and posterior attribute reduction) by resorting to a novel approach of Bayesian inference. From two new perspectives of GrC and Bayesian inference, this study provides some new insights into the uncertainty measurement and attribute reduction of information theory-based RS-Theory.

Based on BP neural network, the paper set up an island microgrid system to forecast electricity load. In order to improve forecast accuracy and convergence speed, author updates BP neural network in two ways. on one hand, putting forward several limitations of the basic algorithm for BP, the paper firstly gives several commonly used improved BP algorithm to be compared and then select the LM algorithm as the subject of load forecasting network algorithm. On the other hand, the orthogonal least squares method is applied to select the variables on the accuracy impact for input, thereby seasonal classification is made on this historical data. A new method of data normalization and further data processing is proposed, it could therefore improve the design of neural network input layer. Compared to existed common network, the improved BP neural network could be able to serve better on fitting the original data, and owns a more substantial increase on the island load forecasting accuracy and convergence speed.

The paper is to combine precision and grade, and explore new extended rough set model. Based on logical AND requirement of precision and grade, this paper proposes logical AND model of variable precision upper approximation operator and grade lower approximation operator. In the new model, basic structure and properties are obtained, and furthermore regular algorithm and structural algorithm are proposed. The new model has extended classical rough set model partially, and a medical example is given to illustrate it.

Grade is an important quantitative index, and graded rough set model is an important improved rough set model. This paper is to explore new improved rough set model. Based on logical AND operation of grade approximation operators, this paper proposes logical AND model of grade approximation operators. In the new model, basic structure and properties are obtained, and macroscopic algorithm and structural algorithm are proposed. Finally logical AND model of grade approximation operators is explained by a medical example.