An efficient framework for generating robust adversarial examples

Recent studies show that deep neural networks (DNNs) suffer adversarial examples. That is, attackers can mislead the output of a DNN by adding subtle perturbation to a benign input image. In addition, researchers propose new generation of technologies to produce robust adversarial examples. Robust adversarial examples can consistently fool DNN models under predefined hyperparameter space, which can break through some defenses against adversarial examples or even generate physical adversarial examples against real-world applications. Behind these achievements, expectation over transformation (EOT) algorithm plays as the backbone framework for generating robust adversarial examples. Though EOT framework is powerful, we know little about why such a framework can generate robust adversarial examples. To address this issue, we do the first work to explain the principle behind robust adversarial examples. Then, based on the findings, we point out that traditional EOT framework has a performance problem and propose an adaptive sampling algorithm to overcome such a problem. By modeling the sampling process as classic Coupon Collector Problem, we prove that our new framework reduces the cost from $O\text{◂()▸}\left(n\ast \log \mathrm{}\left(n\right)\right)$ to $O\left(n\right)$, where $n$ denotes the number of sampling points. Under the view of computational complexity, the algorithm is optimal for this problem. The experimental results show that our algorithm can save up to 23% overhead in average. This is significant for black-box attack, where the cost is charged by the amount of queries.     

Efficient secure state estimation against sparse integrity attack for regular linear system

We consider the problem of estimating the state of a time-invariant linear Gaussian system in the presence of integrity attacks. The attacker can compromise $p$ out of $m$ sensors, the set of which is fixed over time and unknown to the system operator, and manipulate the measurements arbitrarily. Under the assumption that the system is regular and system matrix $A$ is non-singular, we propose a secure estimation scheme that is resilient to $p$-sparse attack as long as the system is $2p$-sparse detectable, which achieves the fundamental limit of secure dynamic estimation. In the absence of attack, the proposed estimation coincides with Kalman estimation with a certain probability that can be adjusted to trade-off between performance with and without attack. Furthermore, the detectability condition checking in the designing phase and the estimation computing in the online operating phase are both computationally efficient. Two numerical examples including the IEEE 68 bus test system are provided to corroborate the results and illustrate the performance of the proposed estimator.     

Linguistic Z-number fuzzy soft sets and its application on multiple attribute group decision making problems

In this study, the concept of linguistic Z-number fuzzy soft set ($\text{◂⋅▸}LZnFSS$) is proposed to describe multiple uncertainties in practical decision making problems. $\text{◂⋅▸}LZnFSS$ combines the concepts of fuzzy soft set, linguistic Z-number, and soft set, which could reflect both of the uncertainty in structure and the uncertainty in detailed evaluations. As an initial idea, the set operations on $\text{◂⋅▸}LZnFSSs$ are put forward, the properties of such operations are also discussed. With traditional soft set based decision procedure and fuzzy soft set based decision procedure, a novel linguistic Z-number fuzzy soft set based group decision procedure is developed to solve multiattribute group decision making with linguistic Z-numbers. Wherein an extended technique for order preference by similarity to ideal solution is also developed. Finally, a numerical example is shown to illustrate the practicality and effectiveness of the given method.     

Constructive conditions for consensus of multi-agents under fast switching networks: A time-delay approach

This article studies consensus problem of multi-agent systems under fast switching networks depending on a small parameter . In contrast to the existing methods that are qualitative, we present, for the first time, constructive and quantitative results for finding an upper bound on $\epsilon$ that preserves the consensus and for designing the consensus protocol that includes the designs of continuous-time controller and of sampled-data controller. We first employ a time-delay approach to periodic averaging for continuous-time control of multi-agent systems under fast switching networks leading to a time-delay model where the delay length is equal to $\epsilon$. We construct an appropriate Lyapunov functional for finding sufficient stability conditions in the form of linear matrix inequalities (LMIs). The upper bound on $\epsilon$ that preserves the exponential stability is found from LMIs. Moreover, sufficient conditions on the existence of controller gain are, for the first time, derived for the multi-agent systems under fast switching networks. For the implementation of consensus protocol, we further extend our method to sampled-data consensus of multi-agent systems under fast switching networks where additional Lyapunov functionals are presented to compensate the term due to the sampling. Finally, an example of Caltech multivehicle wireless test bed vehicles is given to illustrate the efficiency of the method.     

Exponential stability of time-delay systems with flexible delayed impulse

The problem of exponential stability for time-delay systems with flexible delayed impulse control is investigated. Unlike the conventional Razumikhin-type inequality, variable parameter based on the flexible impulsive gain is introduced. Sufficient conditions for exponential stability are developed for a class of time-delay systems, for which the size of delay is not limited by impulsive intervals. A flexible impulse control scheme is developed by utilizing the flexible impulsive gain and time-varying delays. When the system is disturbed by the impulse interferences, both the impulse gain and impulse delay can be adjusted accordingly to make the system exponential stable. The effectiveness of the present results is illustrated by two numerical examples and an application.     

A self-stabilizing distributed algorithm for the bounded lattice domination problems under the distance-2 model

The domination problem is one of the fundamental graph problems, and there are many variations. In this article, we propose a new problem called the minus -domination problem where , and are integers such that , , and . The problem is to assign a value from for each vertex in a graph such that the local summation of values is greater than or equal to . We also propose a framework named the bounded lattice domination for a class of domination problems, including the minus -domination problem. Then, we present a self-stabilizing distributed algorithm under the distance-2 model for the bounded lattice domination. Here, self-stabilization is a class of fault-tolerant distributed algorithms that tolerate transient faults. The time complexity for convergence is $$, where $$ is the number of processes in a network if the cardinality of the domain of process values is finite and constant. Otherwise, the time complexity for convergence is $$.     

Weighted power means of q-rung orthopair fuzzy information and their applications in multiattribute decision making

Weighted power means with weights and exponents serving as their parameters are generalizations of arithmetic means. Taking into account decision makers' flexibility in decision making, each attribute value is usually expressed by a $q$-rung orthopair fuzzy value ($q$-ROFV, $q\ge 1$), where the former indicates the support for membership, the latter support against membership, and the sum of their $q$th powers is bounded by one. In this paper, we propose the weighted power means of $q$-rung orthopair fuzzy values to enrich and flourish aggregations on $q$-ROFVs. First, the $q$-rung orthopair fuzzy weighted power mean operator is presented, and its boundedness is precisely characterized in terms of the power exponent. Then, the $q$-rung orthopair fuzzy ordered weighted power mean operator is introduced, and some of its fundamental properties are investigated in detail. Finally, a novel multiattribute decision making method is explored based on developed operators under the $q$-rung orthopair fuzzy environment. A numerical example is given to illustrate the feasibility and validity of the proposed approach, and it is shown that the power exponent is an index suggesting the degree of the optimism of decision makers.     

Novel admissibility and robust stabilization conditions for fractional-order singular systems with polytopic uncertainties

This paper considers the issues of the admissibility and robust stabilization of fractional-order singular systems with polytopic uncertainties and fractional-order and . Firstly, the novel admissibility conditions for nominal fractional-order singular systems are proposed with no conservatism and without any equalities or nonstrict inequalities. Secondly, the robust admissibility conditions for fractional-order singular systems with polytopic uncertainties are given based on the admissibility conditions for nominal fractional-order singular systems. Thirdly, to make the uncertain fractional-order singular systems robustly admissible, the methods of designing the static output feedback controllers are obtained with wider application scope, which are direct, concise, and more relaxed compared with the existing results. All the results are proposed in terms of linear matrix inequalities. Finally, three illustrative examples are given to demonstrate the effectiveness of the results.     

Differential calculus of interval-valued q-rung orthopair fuzzy functions and their applications

The interval-valued q-rung orthopair fuzzy set (IVq-ROFS) provides an extension of Yager's q-rung orthopair fuzzy set (q-ROFS), where membership and nonmembership degrees are subsets of the closed interval $\left[0,1\right]$. In such a situation, it is more superior for decision makers to provide their judgments by intervals instead of crisp numbers due to the uncertainty and vagueness in real life. In this paper, we study the calculus theories of IVq-ROFS from the microscopic. In particular, we first introduce the elementary arithmetic of interval-valued q-rung orthopair fuzzy values (IVq-ROFVs), including addition, multiplication, and their inverse. They are the basis for analysis and calculation throughout the work. In addition, we discuss and prove in detail the operation properties and aggregation operators of IVq-ROFVs. Then, we introduce the concept of interval-valued q-rung orthopair fuzzy functions (IVq-ROFFs), which is the main research object of this paper. After that, we further discuss the continuity, derivatives and differentials of IVq-ROFFs. We also find that the derivatives of IVq-ROFFs are closely related to elasticity, which is an important concept in economics. Finally, we provide some application examples to verify the feasibility and effectiveness of the derived results.