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Fuzzy rough set (FRS) theory is generally used to measure the uncertainty of data. However, this theory cannot work well when the class density of a data distribution differs greatly. In this work, a relative distance measure is first proposed to fit the mentioned data distribution. Based on the measure, a relative FRS model is introduced to remedy the mentioned imperfection of classical FRSs. Then, the positive region, negative region, and boundary region are defined to measure the uncertainty of data with the relative FRSs. Besides, a relative fuzzy dependency is defined to evaluate the importance of features to decision. With the proposed feature evaluation, we propose a feature selection algorithm and design a classifier based on the maximal positive region. The classification principle is that an unlabeled sample will be classified into the class corresponding to the maximal degree of the positive region. Experimental results show the relative fuzzy dependency is an effective and efficient measure for evaluating features, and the proposed feature selection algorithm presents better performance than some classical algorithms. Besides, it also shows the proposed classifier can achieve slightly better performance than the KNN classifier, which demonstrates that the maximal positive region-based classifier is effective and feasible.

Vibration measurement is a crucial task in industrial systems, where vibration characteristics reflect health conditions and indicate anomalies of the devices. Previous approaches either work in an intrusive manner or fail to capture the micrometer-level vibrations. In this work, we propose mmVib, a practical approach to measure micrometer-level vibrations with mmWave radar. First, we derive a metric called Vibration Signal-to-Noise Ratio (VSNR) that highlights the directions of reducing measurement errors of tiny vibrations. Then, we introduce the design of mmVib based on the concept of Multi-Signal Consolidation (MSC) for the error reduction and multi-object measurement. We implement a prototype of mmVib, and the experiments show that it achieves 3.946% relative amplitude error and 0.02487% relative frequency error in median. Typically, the average amplitude error is only 3.174um when measuring the 100um-amplitude vibration at around 5 meters. Compared to two existing mmWave-based approaches, mmVib reduces the 80th-percentile amplitude error by 69.21% and 97.99% respectively.

In 2002 Mauduit and Sarkozy started to study finite sequences of \begin{document}$ k $\end{document} symbols \begin{document}$ E_{N} = \left(e_{1},e_{2},\cdots,e_{N}\right)\in \mathcal{A}^{N}, $\end{document} where \begin{document}$ \mathcal{A} = \left\{a_{1},a_{2},\cdots,a_{k}\right\}(k\in \mathbb{N},k\geq 2) $\end{document} is a finite set of \begin{document}$ k $\end{document} symbols. Later many pseudorandom sequences of \begin{document}$ k $\end{document} symbols have been given and studied by using number theoretic methods. In this paper we study the pseudorandom properties of the \begin{document}$ k $\end{document} -ary Sidel'nikov sequences with length \begin{document}$ q-1 $\end{document} by using the estimates for certain character sums with exponential function, where \begin{document}$ q $\end{document} is a prime power. Our results show that Sidel'nikov sequences enjoy good well-distribution measure and correlation measure. Furthermore, we prove that the set of size \begin{document}$ \phi(q-1) $\end{document} of \begin{document}$ k $\end{document} -ary Sidel'nikov sequences is collision free and possesses the strict avalanche effect property provided that \begin{document}$ k = o(q^{\frac{1}{4}}) $\end{document} , where \begin{document}$ \phi $\end{document} denotes Euler's totient function.

The Picture Fuzzy Set (PFS) is a broadening of the fuzzy set and intuitionistic fuzzy set. Pattern recognition, picture segmentation, and decision-making are some of the applications of PFS. The dissimilarity measure technique is used to illustrate a decision-making issue on an image fuzzy set in this article. Decision-making is a technique that enables a computer to think like a person, and it is critical for machine learning and the application of artificial intelligence to machines. These aids robots in thinking like humans. Finally, the suggested approach is presented in this article using a case study based on a survey of 100 consumers performed at a two-wheeler showroom.

The various extensions of the fuzzy set are considerably applied in many complex problems of real world to describes the improper information. The PFS (pythagorean fuzzy set) which is the expanded form of IFS (intuitionistic fuzzy set) is more applicable and precise to measure the uncertainty. The research work presents the novel entropy measure defined on PFS which satisfied axioms of the entropy. The entropy measure is determined the uncertainty that defined the fuzziness degree on the fuzzy set. The applicability of the entropy is verified in selection of the advertising company and results compared to the existing entropies defined on PFS. The outcomes of the illustrative example show that the new entropy measure is more precise, simpler, and consistent as compare to existing entropies on PFS.

In this article, a novel composite hierarchical antidisturbance control (CHADC) algorithm aided by the information-theoretic learning (ITL) technique is developed for non-Gaussian stochastic systems subject to dynamic disturbances. The whole control process consists of some time-domain intervals called batches. Within each batch, a CHADC scheme is applied to the system, where a disturbance observer (DO) is employed to estimate the dynamic disturbance and a composite control strategy integrating feedforward compensation and feedback control is adopted. The information-theoretic measure (entropy or information potential) is employed to quantify the randomness of the controlled system, based on which the gain matrices of DO and feedback controller are updated between two adjacent batches. In this way, the mean-square stability is guaranteed within each batch, and the system performance is improved along with the progress of batches. The proposed algorithm has enhanced disturbance rejection ability and good applicability to non-Gaussian noise environment, which contributes to extending CHADC theory to the general stochastic case. Finally, simulation examples are included to verify the effectiveness of theoretical results.

We introduce the problem of clustering the set of vertices in a given 3D mesh. The problem is motivated by the need for value engineering in architectural projects. We first derive a max-norm based metric to estimate the geometric disparity between a given pair of vertices, and characterize the problem in terms of this measure. We show that this distance can be computed by using Sequential Quadratic Programming (SQP). Next we introduce two different algorithms for clustering the set of vertices on a given mesh, respectively based on two disparity measurements: max-norm and L2-norm based metric. An equivalence is established between mesh vertices and physical joints in an architectural mesh. By replacing individual joints by their equivalent cluster representative, the number of unique joints in the facade mesh, and therefore the fabrication cost, is dramatically reduced. Finally, we present an algorithm for remeshing a given surface in order to further reduce the number of joint clusters. The framework is tested for a set of real-world architectural surfaces to illustrate the effectiveness and utility of our approach. Overall, this approach tackles the important problem reducing fabrication cost of joints without modifying the underlying connectivity that was specified by the architect.

There are several approaches for evaluating conflict within belief functions. In this paper, we develop one of them based on axioms and show its connections to the decomposition approach. We describe a class of conflict measures satisfying this system of axioms and show that measuring conflict can be realized through the clusterization of a body of evidence. We also show that well-known conflict measures like the auto-conflict measure and the measure of dissonance do not satisfy the proposed system of axioms. We also tackle the problem of simplifying a body of evidence based on clusterization and show the application of developed theoretical constructions for data processing.

The problem of having an identical speed when dealing with multiple motors always exists in the industry. There are several methods to address the problem, but all the methodologies have two common drawbacks. Firstly, the control design requires continuous information of the desired speed and the actual speed of motors; secondly, it is sometimes difficult to directly measure the speed variables. In the proposed study, both of these drawbacks are addressed by designing an observer-based event-triggered networked multi-agent system. The proposed method uses the leader following consensus approach with a centralized event triggering control design, so that whenever a follower's speed diverges from that of the leader, an event is triggered, which communicates and resets all the agents to the leader's speed. Moreover, an observer is designed such that the ith agent uses its jth neighbor agent and observer speed information to estimate the leader's speed. The stability of the proposed design is formulated by Lyapunov stability, while the simulation results endorse the design concepts and energy saving.

In communication networks, the existence of fractional factors can be characterized as the feasibility of data transmission. When some nonadjacent nodes with each other are damaged and a special channel is assigned, the possibility of data transmission in a communication network is equivalent to the existence of fractional ID-factor-critical covered graph. As a consequence, the existence of fractional ID- [ a , b ] -factor-critical covered graph plays a key role in studying data transmissions of communication networks. Neighborhood and minimum degree of a graph or a network are often used to measure the vulnerability and robustness of a graph or a network, which are two important parameters considered in network design. In this article, we mainly investigate the relationship between neighborhood of independent set, minimum degree and the fractional ID- [ a , b ] -factor-critical covered graph, and acquire a neighborhood of independent set and minimum degree condition for a graph being fractional ID- [ a , b ] -factor-critical covered, which is a generalization of the previous results.

Non-Rigid Structure-from-Motion (NRSfM) reconstructs a deformable 3D object from the correspondences established between monocular 2D images. Current NRSfM methods lack statistical robustness, which is the ability to cope with correspondence errors.This prevents one to use automatically established correspondences, which are prone to errors, thereby strongly limiting the scope of NRSfM. We propose a three-step automatic pipeline to solve NRSfM robustly by exploiting isometry. Step 1 computes the optical flow from correspondences, step 2 reconstructs each 3D point's normal vector using multiple reference images and integrates them to form surfaces with the best reference and step 3 rejects the 3D points that break isometry in their local neighborhood. Importantly, each step is designed to discard or flag erroneous correspondences. Our contributions include the robustification of optical flow by warp estimation, new fast analytic solutions to local normal reconstruction and their robustification, and a new scale-independent measure of 3D local isometric coherence. Experimental results show that our robust NRSfM method consistently outperforms existing methods on both synthetic and real datasets., Accepted in TPAMI 2021

Mature soybean phenotyping is an important process in soybean breeding; however, the manual process is time-consuming and labor-intensive. Therefore, a novel approach that is rapid, accurate and highly precise is required to obtain the phenotypic data of soybean stems, pods and seeds. In this research, we propose a mature soybean phenotype measurement algorithm called Soybean Phenotype Measure-instance Segmentation (SPM-IS). SPM-IS is based on a feature pyramid network, Principal Component Analysis (PCA) and instance segmentation. We also propose a new method that uses PCA to locate and measure the length and width of a target object via image instance segmentation. After 60,000 iterations, the maximum mean Average Precision (mAP) of the mask and box was able to reach 95.7%. The correlation coefficients R 2 of the manual measurement and SPM-IS measurement of the pod length, pod width, stem length, complete main stem length, seed length and seed width were 0.9755, 0.9872, 0.9692, 0.9803, 0.9656, and 0.9716, respectively. The correlation coefficients R 2 of the manual counting and SPM-IS counting of pods, stems and seeds were 0.9733, 0.9872, and 0.9851, respectively. The above results show that SPM-IS is a robust measurement and counting algorithm that can reduce labor intensity, improve efficiency and speed up the soybean breeding process.

This paper proposes a novel nonparametric method for estimating tail jump variation measures from short-dated options, which can achieve rate-efficiency and works in a general infinite jump activity setting, avoiding parametric or semiparametric assumptions for the jump measure. The method is based on expressing the measures of interest as integrals of the Laplace transforms of the jump compensator and developing methods for recovering nonparametrically the latter from the available option data. The separation of volatility from jumps is done in a novel way by making use of the second derivative of the Laplace transform of the returns, de-biased using either the value of the Laplace transform or of its second derivative evaluated at high frequencies. A Monte Carlo study shows the superiority of the newly-developed method over existing ones in empirically realistic settings. In an empirical application to S&P 500 index options, we find risk-neutral negative market tail jump variation that is on average smaller than previous estimates of it, is generated by smaller-sized jumps, and has less dependence on the level of diffusive volatility.

This article studies the localization and circumnavigation problem concerned with a cluster of nonholonomic vehicles independently of a uniform global coordinate. Particularly, the clustered vehicles collaboratively locate an unknown target and then circumnavigate it isometrically with desired distance and velocity. However, the vehicles have no access to any position information, including their own absolute positions and others’ relative positions. Instead, they are capable of measuring relative bearings only with respect to their neighbors within their local coordinates. Different local coordinates are not necessarily aligned. Moreover, only some of the vehicles can measure relative bearings with respect to the target. For the solution to the concerned localization and circumnavigation problem, a coordinate-free distributed algorithm composed by two parts is proposed. To be specific, the first distributed localization part guarantees that the vehicles accurately estimate the relative positions with respect to the target and neighbors given a persistently exciting condition. And the second distributed circumnavigation part further guarantees that the vehicles move around the target estimation isometrically with the desired distance and velocity. Also, the necessary persistently exciting condition is shown to be met. Finally, simulation and experiment are both given to confirm the effectiveness of the proposed distributed algorithm.

As a combination of fuzzy sets and covering rough sets, fuzzy β covering has attracted much attention in recent years. The fuzzy β neighborhood serves as the basic granulation unit of fuzzy β covering. In this article, a new discernibility measure with respect to the fuzzy β neighborhood is proposed to characterize the distinguishing ability of a fuzzy covering family. To this end, the parameterized fuzzy β neighborhood is introduced to describe the similarity between samples, where the distinguishing ability of a given fuzzy covering family can be evaluated. Some variants of the discernibility measure, such as the joint discernibility measure, conditional discernibility measure, and mutual discernibility measure, are then presented to reflect the change of distinguishing ability caused by different fuzzy covering families. These measures have similar properties as the Shannon entropy. Finally, to deal with knowledge reduction with fuzzy β covering, we formalize a new type of decision table, that is, fuzzy β covering decision tables. The data reduction of fuzzy covering decision tables is addressed from the viewpoint of maintaining the distinguishing ability of a fuzzy covering family, and a forward attribute reduction algorithm is designed to reduce redundant fuzzy coverings. Extensive experiments show that the proposed method can effectively evaluate the uncertainty of different types of datasets and exhibit better performance in attribute reduction compared with some existing algorithms.

We study the distribution of successor states in Boolean networks (BNs). The state vector y is called a successor of x if y = F(x) holds, where x,y ∊ {0,1}n are state vectors and F is an ordered set of Boolean functions describing the state transitions. This problem is motivated by analyzing how information propagates via hidden layers in Boolean threshold networks (discrete model of neural networks) and is kept or lost during time evolution in BNs. In this article, we measure the distribution via entropy and study how entropy changes via the transition from x to y, assuming that x is given uniformly at random. We focus on BNs consisting of exclusive OR (XOR) functions, canalyzing functions, and threshold functions. As a main result, we show that there exists a BN consisting of d-ary XOR functions, which preserves the entropy if d is odd and n > d, whereas there does not exist such a BN if d is even. We also show that there exists a specific BN consisting of d-ary threshold functions, which preserves the entropy if n mod d = 0. Furthermore, we theoretically analyze the upper and lower bounds of the entropy for BNs consisting of canalyzing functions and perform computational experiments using BN models of real biological networks.

Infrared (IR) small target detection is one of the key technologies of infrared search and track (IRST) systems. Existing methods have some limitations in detection performance, especially when the target size is irregular or the background is complex. In this paper, we propose a pixel-level local contrast measure (PLLCM), which can subdivide small targets and backgrounds at pixel level simultaneously. With pixel-level segmentation, the difference between the target and the background becomes more obvious, which helps to improve the detection performance. First, we design a multiscale sliding window to quickly extract candidate target pixels. Then, a local window based on random walker (RW) is designed for pixel-level target segmentation. After that, PLLCM incorporating probability weights and scale constraints is proposed to accurately measure local contrast and suppress various types of background interference. Finally, an adaptive threshold operation is applied to separate the target from the PLLCM enhanced map. Experimental results show that the proposed method has a higher detection rate and a lower false alarm rate than the baseline algorithms, while achieving a high speed.

This article studies the state estimation for probabilistic Boolean networks via observing output sequences. Detectability describes the ability of an observer to uniquely estimate system states. By defining the probability of an observed output sequence, a new concept called detectability measure is proposed. The detectability measure is defined as the limit of the sum of probabilities of all detectable output sequences when the length of output sequences goes to infinity, and it can be regarded as a quantitative assessment of state estimation. A stochastic state estimator is designed by defining a corresponding nondeterministic stochastic finite automaton, which combines the information of state estimation and probability of output sequences. The proposed concept of detectability measure further performs the quantitative analysis on detectability. Furthermore, by defining a Markov chain, the calculation of detectability measure is converted to the calculation of the sum of probabilities of certain specific states in Markov chain. Finally, numerical examples are given to illustrate the obtained theoretical results.

Besides mimicking bio-chemical and multi-scale communication mechanisms, molecular communication forms a theoretical framework for virus infection processes. Towards this goal, aerosol and droplet transmission has recently been modeled as a multiuser scenario. In this letter, the "infection performance" is evaluated by means of a mutual information analysis, and by an even simpler probabilistic performance measure which is closely related to absorbed viruses. The so-called infection rate depends on the distribution of the channel input events as well as on the transition probabilities between channel input and output events. The infection rate is investigated analytically for five basic discrete memoryless channel models. Numerical results for the transition probabilities are obtained by Monte Carlo simulations for pathogen-laden particle transmission in four typical indoor environments: two-person office, corridor, classroom, and bus. Particle transfer contributed significantly to infectious diseases like SARS-CoV-2 and influenza., Comment: 4 pages, 3 figures, submitted to IEEE Transactions on Molecular, Biological, and Multi-Scale Communications Letters

This article describes a novel approach to achieve motion coordination in a multirobot system based on the concept of deformation. Our main novel contribution is to link these two elements (namely, coordination and deformation). In particular, the core idea of our approach is that the robots’ motions minimize a global measure of the deformation of their positions relative to a prescribed shape. Based on this idea, we propose a linear shape controller that also incorporates a term modeling an affine deformation. We show that the affine term is particularly useful when the deformation to be controlled is large. We also propose controls for the other variables (centroid, rotation, and size) that define the geometric configuration of the team. Importantly, these additional controls are completely decoupled from the shape control. The overall approach is simple and robust, and it creates closely coordinated robot motions. Being based on deformation, it is useful in several scenarios involving manipulation tasks, e.g., handling of a highly deformable object, control of an object’s shape, or regulation of the shape formed by the fingertips of a robotic hand. We present simulation and experimental results to validate the proposed approach.

Much work has already been studied on the interrelation between the epidemic spreading and awareness spreading to prevent infections in a social network. By selecting seed users to spread awareness, we can control epidemic spreading. However, selecting seed users with the maximum influential users may not be the best solution in location-based social networks. Therefore, it is challenging to determine users to spread the information (the awareness of prevention) in these networks. The minimized epidemic infection (MEI) problem aims to find a seed set with k seed users such that the infection users can be minimized. In this article, we propose a piecewise function to measure the probability of each user being infected, which considers the distance and time. Then, we propose an algorithm called location-infected-greedy (LIG) to solve the MEI problem by finding the seed nodes that consider the probability of infection, time of check-in, location information, and influence of users. In the meantime, LIG can obtain an upper bound of the data-dependent approximate ratio, and it runs in O(kn²), where n is the total number of nodes and k is the number of seed nodes. Finally, extensive contrast experiments on real-world location-based social networks show that our algorithm is efficient and effective.

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.

The issue of mining influential nodes in complex networks is a topic of immense interest. Recently, many methods have been proposed, but they suffer from certain limitations. In this paper, a novel centrality measure based on Local Fuzzy Information Centrality (LFIC) is proposed. LFIC puts forward the concept that the inner structure of a node's box contains information about the node's importance. LFIC uses the amount of information contained in the node's box as a measure of its importance. In LFIC, the uncertainty of information contained in nodes' boxes is measured by the improved Shannon entropy. Most importantly, fuzzy logic is applied to deal with the uncertainty of neighbor nodes' contributions to the center node's importance, which is neglected by most existing methods. To verify the effectiveness of our proposed method, six existing methods are used for comparison and five experiments are conducted using six real-world complex networks. The experimental results indicate that the influential nodes identified by LFIC can cause a wider scope of infection in networks and have a larger effect on the network connectivity, thereby proving the effectiveness and accuracy of LFIC. The correlation between nodes' LFIC values and their real infection ability is highly positive according to Kendall's tau coefficient, proving LFIC's credibility and superiority. The extension of LFIC, namely the Bi-directional Local Fuzzy Information Centrality (Bd-LFIC), is also proposed to explore its feasibility in weighted directed complex networks.

Evidential reasoning (ER) rule has been widely used in dealing with uncertainty. As an important parameter to measure the inherent property of evidence, the evidence reliability makes the ER rule constitute a generalized reasoning framework. In current research of the ER rule, the evidence reliability tends to be expressed in the form of quantitative value by certain methods or expert knowledge. The single quantitative value lacks the ability to describe the statistical property of reliability, which leads to unreasonable results. In this article, a new ER rule with continuous probability distribution of reliability denoted by ERr-CR is proposed. The combination of two pieces of evidence is discussed in detail, where the reliability is profiled as random variables with specific probability distribution. To characterize the output of ERr-CR, a novel concept of expectation of the expected utility is proposed. In addition, the ERr-CR is expanded to multiple pieces of evidence to show its universality. Further, the basic performances of the ERr-CR are explored to illustrate the rationality. Moreover, a case study of safety assessment of natural gas storage tanks (NGSTs) is conducted to show the potential applications of ERr-CR, which makes the proposed method more practical.

The successful applications of deep transfer learning to intelligent fault diagnosis testify to a positive correlation between transferable feature similarity and knowledge transferability across diagnostic tasks. This correlation makes feature similarity possible to assess diagnostic knowledge transferability. Therefore, researchers have attempted various measures for feature similarity, and distance metrics have been adopted as an objective measure for feature distribution discrepancy. However, the commonly used distance metrics cannot address the joint distribution discrepancy (JDD) due to the difficulty in fitting conditional distributions of target-domain samples. To overcome the problem, we resort to explore cluster-conditional distributions instead and propose an optimal transport-embedded joint distribution similarity measure (OT-JDSM) that is implemented in two steps. First, a cluster-true label propagation spreads labels from a small number of labelled target domain samples to the whole. Second, the JDD of transferable features is produced via an efficient solution of optimal transport. OT-JDSM is demonstrated on synthetic examples and 144 transfer diagnosis tasks that are created by public and private bearing datasets. The results show that OT-JDSM of transferable features has a stronger correlation with diagnostic knowledge transferability than other distance metrics. Moreover, the OT-JDSM gain can quantify the transfer performance of diagnostic models on tasks.

In this article, we refocus on the distributed observer construction of a continuous-time linear time-invariant (LTI) system, which is called the target system, by using a network of observers to measure the output of the target system. Each observer can access only a part of the component information of the output of the target system, but the consensus-based communication among them can make it possible for each observer to estimate the full state vector of the target system asymptotically. The main objective of this article is to simplify the distributed reduced-order observer design for the LTI system on the basis of the consensus communication pattern. For observers interacting on a directed graph, we first address the problem of the distributed reduced-order observer design for the detectable target system and provide sufficient conditions involving the topology information to guarantee the existence of the distributed reduced-order observer. Then, the dependence on the topology information in the sufficient conditions will be eliminated by using the adaptive strategy and so that a completely distributed reduced-order observer can be designed for the target system. Finally, some numerical simulations are proposed to verify the theoretical results.

In this paper, the problem of online distributed optimization with a set constraint is solved by employing a network of agents. Each agent only has access to a local objective function and set constraint, and can only communicate with its neighbours via a digraph which is not necessarily balanced. Moreover, agents do not have prior knowledge of their future objective functions. Different from existing works on online distributed optimization, we consider the scenario where objective functions at each time step are nonconvex. To handle this challenge, we propose an online distributed algorithm based on the consensus algorithm and the mirror descent algorithm. Of particular interest is that regrets involving first-order optimality condition are used to measure the performance of the proposed algorithm. Under mild assumptions on the communication graph and objective functions, we prove that regrets grow sublinearly. Finally, a simulation example is worked out to demonstrate the effectiveness of our theoretical results.

The goal of the present research work is to develop a new family of aggregation operators (AOs) under the fractional orthotriple fuzzy (FOF) information and apply them to MCDM problems. At the start, the Archimedean coupla and co-coupla are extended to handle FOF information, and some operational law for fractional orthotriple fuzzy numbers (FOFNs) based on extended Archimedean copula (EAC) and extended Archimedean co-copula (EACC) is presented. The fractional orthotriple fuzzy Banzhaf Choquet-Copula aggregation operator and fractional orthotriple fuzzy Banzhaf Choquet-Copula geometric operators are defined based on the proposed operational laws of FOFNs. In addition, the modified maximum deviation approach and the Banzhaf function model are created to objectively determine the fuzzy measure (FM) of criteria sets. Finally, based on the defined AOs, the appropriate decision-making procedures are developed. The proposed approaches can effectively overcome the FMs of criteria sets that are subjectively assigned by decision makers, as well as some decision-making problems in which the weights of the criteria are incomplete (completely) unknown, and there is a correlation between all criteria set.

We consider a general electric vehicle (EV) charging system with stochastic demand, demand request locations, and predetermined charging facilities (including charging station locations and charger capacities). The objective is to design a good routing strategy that accommodates well demand-request dynamics so as to satisfy the charging system’s stability constraints and also minimize the EV’s mean response time. We introduce a class of flexible and measurement-based routing policies called “partition-based random routing” (PBRR) and show that the performance measure of interest can be formulated as a constrained optimization problem with a convex objective function when the system is heavily loaded. This formulation enables us to establish strong theoretical results that are in aid of finding the optimal routing solution; however, in practice, finding this solution requires rather involved numerical calculations. To that end, we propose a surrogate, easy to design and implement, optimization algorithm for finding the desired optimal routing solution. Numerical work based on synthetic data shows that the performance of the developed routing strategy and its fast implementation is highly satisfactory for a number of system settings.

Situation awareness (SA) has received much attention in recent years because of its importance for operators of dynamic systems. Electroencephalography (EEG) can be used to measure mental states of operators related to SA. However, cross-subject EEG-based SA recognition is a critical challenge, as data distributions of different subjects vary significantly. Subject variability is considered as a domain shift problem. Several attempts have been made to find domain-invariant features among subjects, where subject-specific information is neglected. In this work, we propose a simple but efficient subject matching framework by finding a connection between a target (test) subject and source (training) subjects. Specifically, the framework includes two stages: (1) we train the model with multi-source domain alignment layers to collect source domain statistics. (2) During testing, a distance is computed to perform subject matching in the latent representation space. We use a reciprocal exponential function as a similarity measure to dynamically select similar source subjects. Experiment results show that our framework achieves a state-of-the-art accuracy 74.32% for the Taiwan driving dataset. National Research Foundation (NRF) This research is supported by the National Research Foundation, Singapore under its International Research Centres in Singapore Funding Initiative.

Saturation flow is a fundamental performance measure parameter used for the design of intersections. However, in mixed traffic conditions, the evaluation of saturation flow is more sensitive due to heterogeneous traffic where vehicles are travelling in the same right of way without any lane separation. In such cases, the passenger car unit (PCU) plays a major role in analysing heterogeneity using an equivalent value for each vehicle. This paper presents a novel approach using the optimisation technique to determine PCU values and saturation flow for mixed traffic streams. Field data were collected at six signalised intersections in three Indian cities. The optimisation technique produced reasonable PCU values and an accurate estimation of saturation flow of 1906 PCUs/h. The saturation flow prediction model was developed using the multi-linear regression technique as per Pearson's correlation between saturation flow and vehicle compositional share. The developed saturation flow model was validated using field data from another site and the predicted value was in good agreement with the observed value. Finally, the predictive model was used to analyse the impact of traffic composition on saturation flow in mixed traffic streams.

In this paper, we consider the dynamical modeling of a class of quantum network systems consisting of qubits. Qubit probes are employed to measure a set of selected nodes of the quantum network systems. For a variety of applications, a state space model is a useful way to model the system dynamics. To construct a state space model for a quantum network system, the major task is to find an accessible set containing all of the operators coupled to the measurement operators. This paper focuses on the generation of a proper accessible set for a given system and measurement scheme. We provide analytic results on simplifying the process of generating accessible sets for systems with a time-independent Hamiltonian. Since the order of elements in the accessible set determines the form of state space matrices, guidance is provided to effectively arrange the ordering of elements in the state vector. Defining a system state according to the accessible set, one can develop a state space model with a special pattern inherited from the system structure. As a demonstration, we specifically consider a typical 1D-chain system with several common measurements, and employ the propo

Starting from the notion of a multidistance, we formalize, through a suitable system of axioms, the concept of an inequality measure defined on a nonempty set with no additional structure implemented a priori. Among inequality measures, apart from multidistances we pay special attention to dispersions, and study their main features. Classical concepts will be generalized to this abstract setting. Multidistances are then revisited, and some new methods to generate them are implemented. A wide spectrum of interdisciplinary applications is outlined in the final section. This work is partially supported by the research projects ECO2015-65031-R , MTM2015-63608-P , TIN2016-77356-P , TIN2017-87600-P (MINECO/AEI-FEDER, UE) and PID2019-108392GB-I00 (AEI/10.13039/501100011033)

Attribute reduction is one of the most important preprocessing steps in machine learning and data mining. As a key step of attribute reduction, attribute evaluation directly affects classification performance, search time, and stopping criterion. The existing evaluation functions are greatly dependent on the relationship between objects, which makes its computational time and space more costly. To solve this problem, we propose a novel separability-based evaluation function and reduction method by using the relationship between objects and decision categories directly. The degree of aggregation (DA) of intraclass objects and the degree of dispersion (DD) of between-class objects are first defined to measure the significance of an attribute subset. Then, the separability of attribute subsets is defined by DA and DD in fuzzy decision systems, and we design a sequentially forward selection based on the separability (SFSS) algorithm to select attributes. Furthermore, a postpruning strategy is introduced to prevent overfitting and determine a termination parameter. Finally, the SFSS algorithm is compared with some typical reduction algorithms using some public datasets from UCI and ELVIRA Biomedical repositories. The interpretability of SFSS is directly presented by the performance on MNIST handwritten digits. The experimental comparisons show that SFSS is fast and robust, which has higher classification accuracy and compression ratio, with extremely low computational time.

We present a numerical approximation of Darcy's flow through a porous medium that incorporates networks of fractures with non empty intersection. Our scheme employs PolyDG methods, i.e. discontinuous Galerkin methods on general polygonal and polyhedral (polytopic, for short) grids, featuring elements with edges/faces that may be in arbitrary number (potentially unlimited) and whose measure may be arbitrarily small. Our approach is then very well suited to tame the geometrical complexity featured by most of applications in the computational geoscience field. From the modelling point of view, we adopt a reduction strategy that treats fractures as manifolds of codimension one and we employ the primal version of Darcy's law to describe the flow in both the bulk and in the fracture network. In addition, some physically consistent conditions couple the two problems, allowing for jump of pressure at their interface, and they as well prescribe the behaviour of the fluid along the intersections, imposing pressure continuity and flux conservation. Both the bulk and fracture discretizations are obtained employing the Symmetric Interior Penalty DG method extended to the polytopic setting. The key instrument to obtain a polyDG approximation of the problem in the fracture network is the generalization of the concepts of jump and average at the intersection, so that the contribution from all the fractures is taken into account. We prove the well-posedness of the discrete formulation and perform an error analysis obtaining a priori hp-error estimates. All our theoretical results are validated performing preliminary numerical tests with known analytical solution.

This paper examines the delay range for robust consensus of unstable first-order agents by using proportional (P) and proportional-derivative (PD) control protocols subject to time-varying delays. The maximal delay range is defined by the delay consensus margin (DCM), which is a robustness measure within which consensus can be achieved robustly despite the presence of uncertain and time-varying delays. We apply an Hinf-type small-gain analysis to multi-agent systems, which results in explicit lower bounds on the DCM for both undirected and directed graphs. The results provide sufficient conditions for robust consensus for all time-varying delays that may vary within the range. It is seen that the agent dynamics and the graph connectivity may fundamentally limit the range of tolerable delays. It is also found that the DCM can be increased beyond that achieved by P protocol by incorporating the delay variation rate in the design of the PD control protocol.

We consider the heat equation defined by a generalized measure theoretic Laplacian on $[0,1]$. This equation describes heat diffusion in a bar such that the mass distribution of the bar is given by a non-atomic Borel probabiliy measure $\mu$, where we do not assume the existence of a strictly positive mass density. We show that weak measure convergence implies convergence of the corresponding generalized Laplacians in the strong resolvent sense. We prove that strong semigroup convergence with respect to the uniform norm follows, which implies uniform convergence of solutions to the corresponding heat equations. This provides, for example, an interpretation for the mathematical model of heat diffusion on a bar with gaps in that the solution to the corresponding heat equation behaves approximately like the heat flow on a bar with sufficiently small mass on these gaps., Comment: 22 pages, 1 figure

In the single-machine non-clairvoyant scheduling problem, the goal is to minimize the total completion time of jobs whose processing times are unknown a priori. We revisit this well-studied problem and consider the question of how to effectively use (possibly erroneous) predictions of the processing times. We study this question from ground zero by first asking what constitutes a good prediction; we then propose a new measure to gauge prediction quality and design scheduling algorithms with strong guarantees under this measure. Our approach to derive a prediction error measure based on natural desiderata could find applications for other online problems.

In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established.

In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons., 12 pages

High-dimensional multivariate systems often lack closed-form solutions and are therefore resolved using simulation. Random Orthogonal Matrix (ROM) simulation is a state-of-the-art method that has gained popularity in this context because certain simulation errors are completely removed (Ledermann, Alexander, and Ledermann, 2011). Specifically, every sample generated with ROM simulation exactly matches a target mean and covariance matrix. A simple extension can also target a scalar measure of skewness or kurtosis. However, targeting non-scalar measures of higher moments is much more complex. The problem of targetting exact Kollo skewness has already been considered, but the algorithm proceeds via time-consuming trial-and-error which can be very slow. Moreover, the algorithm often fails completely. Furthermore, it produces simulations with very long periods of inactivity which are inappropriate for most real-world applications. This paper provides an in-depth theoretical analysis of a much quicker ROM simulation extension which always succeeds to target Kollo skewness exactly. It also derives new results on Kollo skewness in concatenated samples and applies them to produce realistic simulations for many applications, especially those in finance. Our first contribution is to establish necessary and sufficient conditions for Kollo skewness targeting to be possible. Then we introduce two novel methods, one for speeding up the algorithm and another for improving the statistical properties of the simulated data. We illustrate several new theoretical results with some extensive numerical analysis and we apply the algorithm using some real data drawn from two different multivariate systems of financial returns.

The centroid is one of the most important methods for type–reduction of Type–2 fuzzy sets/numbers and it is also a popular expectation measure, but available methods to compute it are iterative/algorithmic which is an important issue for real–world implementations. This paper presents some theoretical results about the Chebyshev integral inequality for a class of Interval Type–2 fuzzy numbers which leads to obtain non–iterative closed forms of the centroid and its bounds for Type–1 and interval Type–2 fuzzy numbers (by extension). An analysis of the obtained results and a comparison to four well known type–reduction methods: the Karnik–Mendel, Yager Index, Mitchell and Nie–Tan methods are provided where the experimental evidence shows that the proposed method is equivalent to the K–M algorithms.

In this work, we are interested in a class of Bi-directional associative memory neural networks (BAMNNs) with hybrid time-varying delays and D operator. We establish some sufficient conditions to guarantee the existence and global exponential stability of measure-pseudo almost periodic solutions of the considered BAMNNs, using contraction mapping principle, exponential dichotomy theory, differential inequality techniques, and the properties of the measure-pseudo almost periodic functions. A numerical example along with a graphical illustration are presented to support the effectiveness and fasibility of the obtained results. The results in this paper are original and complement the previous outcomes.

Similarity measures have been widely used in applications dealing with reasoning, classification and information retrieval. In this paper, we first propose three new Interval Type-2 Fuzzy Similarity measures (IT-2 FSMs) as a dual concept of some semi-metric distances between Intuitionistic Fuzzy Sets (IFSs). We also prove that the extended IT-2 FSMs satisfy many common properties (i.e. reflexivity, transivity, symmetry and overlapping). Experiments are carried out on a variety of datasets including UCI Learning Machine and real data. Comparative studies between the proposed IT-2 FSMs and the other well-known existing similarity measures (Gorzalczany, Bustince, Mitchell, Zeng and Li as well as VSM and Jaccard) are performed. Obviously, the best results are obtained with the IT-2 FSMs being resilient to the high levels of uncertainty noise. We also prove that our IT-2 FSMs can overcome the drawbacks of some existing similarity measures based on the accuracy rate measure. In addition, the proposed IT-2 FSMs are joined with Fuzzy cmeans algorithm as a clustering method and the proposed system is compared against the existing clustering algorithms (Type- 1 Fuzzy k-means, Type-1 and Type-2 Fuzzy c-means, Cluster Forest, Bagged Clustering, Evidence Accumulation and Random Projection). Relying on the clustering quality parameters R and C (equivalent to the standard classification accuracy), the advanced IT-2FSMs show higher classification accuracy of about 86% which outperforms nearly the other classifiers.

We investigate modeling and control of probabilistic fuzzy discrete event systems (PFDES). PFDES is a new type of fuzzy discrete event systems. It allows the use of probabilities to describe the chances of occurrences of different events. Our new model for PFDES consists of a fuzzy automaton and a crisp automaton that specifies what sequences of events can occur and their probabilities of occurrences. Based on the new model, optimal control is designed using an on-line and limited lookahead method. Control is calculated one step at a time, after an occurrence of an event. At each step, a lookahead window of $N$ events is constructed. The performance measures for all states in the window are determined, which is a function of fuzzy states. Control is calculated to maximize the expected performance measure after the occurrences of $N$ events. To reduce computational complexity, a “dynamic-programming” approach is proposed. We prove that the control obtained is optimal. Examples are given in the paper to illustrate the results.

In complicated product industry such as aircraft manufacturing, an assembly model contains abundant engineering information for use in design, manufacture, and maintenance. Assembly retrieval can be used to find relevant models for knowledge reuse. However, an assembly with rotatable joints may have many poses, which brings difficulty to assembly retrieval, since there is no pose principle for assembly design. Therefore, focused on rotatable joints in assembly, a skeleton-based descriptor for pose-free assembly retrieval is proposed. The centroid points of part surfaces and contact faces in an assembly are extracted to construct a spatial-contact skeleton. The skeleton-based distance is proposed to measure the distance between two surface points, which is invariant to the rotatable joints. The distribution of skeleton distances between two parts is used to describe the pair. Considering a part paired with all other parts in the assembly, the set of part pairs is used to represent a part, and the modified Hausdorff distance is used to measure the dissimilarity between parts for assembly retrieval. Experiments are conducted to compare the accuracy of the proposed descriptor to holistic and structureless descriptors. The proposed method is shown to retrieve assemblies with similar parts and structures regardless of their rotatable joints.

Corporate boards, experts panels, parliaments, cabinets, and even nations all take important decisions as a group. Selecting an efficient decision rule to aggregate individual opinions is paramount to the decision quality of these groups. In our experiment we measure revealed preferences over and efficiency of several important decision rules. Our results show that: (1) the efficiency of the theoretically optimal rule is not as robust as simple majority voting, and efficiency rankings in the lab can differ from theory; (2) participation constraints often hinder implementation of more efficient mechanisms; (3) these constraints are relaxed if the less efficient mechanism is risky; (4) participation preferences appear to be driven by realized rather than theoretic payoffs of the decision rules. These findings highlight the difficulty of relying on theory alone to predict what mechanism is better and acceptable to the participants in practice.

We show that the classification performance of graph convolutional networks (GCNs) is related to the alignment between features, graph, and ground truth, which we quantify using a subspace alignment measure (SAM) corresponding to the Frobenius norm of the matrix of pairwise chordal distances between three subspaces associated with features, graph, and ground truth. The proposed measure is based on the principal angles between subspaces and has both spectral and geometrical interpretations. We showcase the relationship between the SAM and the classification performance through the study of limiting cases of GCNs and systematic randomizations of both features and graph structure applied to a constructive example and several examples of citation networks of different origins. The analysis also reveals the relative importance of the graph and features for classification purposes., Comment: Published in IEEE Transactions on Neural Networks and Learning Systems; Date of Publication: 11 January 2021

The consideration of social influence in solving group decision making (GDM) problems has caused widespread concern in recent years. In most cases, the interaction of experts and the association efforts of alternatives are often not to be ignored in the actual decision-making environment, especially for those situations with incomplete information in the process of opinion changes. In this study, a novel measure-based GDM model is proposed to more comprehensively consider such a factor. Also, a positive cooperation-first principle (PCFP) is proposed as a guide for situations with incomplete information. One of the main advantages of the proposed model is that the estimation of missing fuzzy preference relations (FPR) is completed according to the modeling results of peer interactions, which makes the preference evolution results more reliable. With the utilization of the fuzzy measure framework, the Shapley function and interaction indicator, originated from the cooperative game theory (CGT), are also introduced to extract the interaction features. After several iterations, the global opinion can be eventually obtained via the social influence network (SIN) technique. Furthermore, it is also demonstrated that the evolution of individual opinions converges to the ultimate collective opinion. A case study of supplier selection with the proposed model is implemented to illustrate its practicality and effectiveness. Related comparisons and discussion regarding related methods are also mentioned.