Upon failure discovery, redesign or corrective measures are always implemented to eliminate the defects and improve system reliability in reliability growth management. The Crow-Army Materiel Systems Analysis Activity (AMSAA) model (C-A model) is an effective model candidate in describing cumulative number of faults with respect to reliability growth testing time, in which large amount of recorded failure data are utilized to estimate the parameters in the C-A model. Under small sample size, however, it has been proven difficult to confidently obtain accurate parameter estimators and reliability growth test termination time. In this research, the grey forecasting method, an effective approach in disposing uncertainty especially for scenarios with small sample and poor information, is introduced to fit the limited failure data, predict the next failure time, and extend the original failure dataset. After which, failure dataset is supplemented and parameters in the C-A model are updated. Estimating the reliability metrics at the predicted failure time and comparing with the target requirement, we terminate the reliability growth test, otherwise, continue to predict the failure time with the metabolic grey model. It is shown from two reliability growth cases in the literature that the grey model with first order and one variable (GM(1,1)) possesses a strong data processing ability, makes up for the insufficiencies in circumstance of small sample size, and accelerates the termination time in a reliability growth test.

This paper proposes a new Multiple-criteria decision-making (MCDM) method called MUltiple-TRIangles ScenarioS (MUTRISS) with two scenarios respecting different levels of access to complete information for material selection problems. MUTRISS calculates the areas occupied by alternatives in n-dimensional space, employing analytic geometry and converting each alternative into n-edges forms. The paper applies MUTRISS to three material selection case studies, with Ti-6Al-4V, Material 4, and AISI 4140 Steel- UNS G41400 emerging as the best materials for the three examples with the highest overall scores of 0.036, 4.540 and 0.427 respectively. The results are compared with various MCDM methods through four statistical measures, including relative closeness ratio, robustness analysis, compromise ranking coefficient, and similarity degree. The measures focus on different aspects of MCDM methods in solving problems and their results. The paper concludes that MUTRISS offers a more robust and reliable approach for material selection problems compared to other MCDM methods, with the first scenario of MUTRISS being more reliable than the second scenario. The paper also emphasizes the importance of validating results in material selection problems due to the potential irreversible consequences of selecting the wrong material.

This article presents the$L_1$-gain polynomial fuzzy output-feedback controller design and the stability analysis using the sum-of-squares (SOS) approach for positive polynomial fuzzy-model-based (PPFMB) control systems. The polynomials, positivity, and optimal$L_1$performance make some existing convex methods for general systems inapplicable. To overcome this problem, first, an augmented system of the PPFMB control system is constructed; then, by introducing some constraint conditions and mathematical techniques, nonconvex stability and positivity conditions are skillfully transformed into convex ones simultaneously. In addition, to control the systems flexibly and lower the implementation cost, the imperfect premise matching concept is taken into account for controller design. Besides, the high-degree-polynomial approximation method is adopted to conduct stability and positivity analysis by incorporating the information of membership functions and the boundary information of the state variables. On the basis of the Lyapunov stability theory, the relaxed stability and positivity conditions in terms of the SOS form are obtained. Finally, two simulation examples are presented to verify the feasibility of the theoretical results.

Summary This article investigates the complex relationship between endogenous and exogenous, deterministic and stochastic stimulating factors in public opinion dynamics. An asynchronous multiagent network model is proposed to explore the interaction mechanism between individual opinions and the public opinion in online multiagent network community, including both the micro and the macro patterns of opinion evolution. In addition, based on random network models, a novel algorithm is provided for opinion evolution prediction. The model property analysis and numerical experiments show that the proposed asynchronous multiagent network model can assimilate and explain some interesting phenomena that are observed in the real world. Further case studies with numerical simulation and real‐world applications confirm the feasibility and flexibility of the proposed model in public opinion analysis. The results challenge the common perception that mass media or opinion facilitators play the fundamental role in controlling the development trends of public opinion. This study shows that the formation and evolution of public opinion in the presence of opinion leaders depend also on an individual's emotional inertia and conformity pressures from peers in the same topic group.

This article focuses on the filtering problem and stability analysis for positive Takagi-Sugeno (T-S) fuzzy systems with time delay under L1-induced performance. Due to the importance of estimation of system states but the few filter design results on positive nonlinear systems, it is an attractive and meaningful topic well worth studying. In order to fully exploit and take advantage of the positivity of positive T-S fuzzy systems, many commonly used methods, for instance free-weighting matrix approach and similarity transformation are probably not suitable for positive systems. To address the hard-nut-to-crack problem, an auxiliary variable is introduced so that the augmentation approach can be employed to carry out the positivity and stability analysis of filtering error systems. In addition, another obstacle that cannot be ignored is the existence of nonconvex terms in the stability and positivity conditions. For getting around this barrier, some iterative linear matrix inequality algorithms have been proposed in the literature. However, considering the weakness that these methods cannot guarantee the convergence to a numerical solution and the iterative process is exhaustive, we present an effective matrix decoupling method to convert the nonconvex conditions into convex ones in this article. Furthermore, a linear copositive Lyapunov function, which incorporates the positivity of system states and time delay at the same time is chosen so that the positivity characteristic of filtering error systems can be captured further. However, because of plenty of valuable information of membership functions being ignored, hence, the obtained results are conservative. For the sake of relaxing the conservativeness, the advanced piecewise-linear membership functions approximate method is utilized to facilitate the stability and positivity analysis. Therefore, the relaxed stability and positivity conditions, which are cast as sum of squares (SOS) are obtained and can be solved numerically. Finally, the effectiveness of the designed fuzzy filtering strategy with satisfying L1-induced performance are demonstrated by a simulation example.

In this demo, we present SEBDB, a novel blockchain database that integrates immutability and transparency properties of blockchain with modeling and query ability of relational database. In summary, SEBDB has the following advantages: First, it adopts the linked structure and full replication of data among multiple participants to guarantee immutability and transparency. Second, it introduces the relational model to blockchain without introducing extra overhead, based on which relational queries are supported. SEBDB supports SQL-like language as the general interface to support convenient application development, in which intrinsic operations are re-defined and re-implemented to suit for blockchain platform. Third, it supports rich verifiable queries based on the proposed authenticated index, thin clients can participate in the system regardless of limitations of storage, network, and computing resources. We demonstrate the usability and scalability of SEBDB using a donation system.

Security functions are usually deployed on proprietary hardware, which makes the delivery of security service inflexible and of high cost. Emerging technologies such as software-defined networking and network function virtualization go in the direction of executing functions as software components in virtual machines or containers provisioned in standard hardware resources. They enable network to provide customized security service by deploying Security Service Chain (SSC), which refers to steering flow through multiple security functions in a particular order specified by individual user or application. However, SSC Deployment Problem (SSC-DP) needs to be solved. It is a challenging problem for various reasons, such as the heterogeneity of instances in terms of service capacity and resource demand. In this paper, we propose an SSC-based approach to deliver security service to users without worrying about physical locations of security functions. For SSC-DP, we present a three-phase method to solve it while optimizing network and security resource allocation. The presented method allows network to serve a large number of flows and minimizes the latency seen by flows. Comparative experiments on the fat-tree and Waxman topologies show that our method performs better than other heuristics under a wide range of network conditions.

This research presents a specialised extension to the genetic algorithms (GA) known as the genetic programming (GP) and gene expression programming (GEP) to explore and investigate the outcome of the GEP criteria on the stock market price prediction. The aim of this research is to model and predict short-to-medium term stock value fluctuations in the market via genetically tuned stock market parameters. The technology proposes a fractional adaptive mutation rate Elitism (GEP-FAMR) technique to initiate a balance between varied mutation rates and between varied-fitness chromosomes, thereby improving prediction accuracy and fitness improvement rate. The methodology is evaluated against different dataset and selection methods and showed promising results with a low error-rate in the resultant pattern matching with an overall accuracy of 95.96% for short-term 5-day and 95.35% for medium-term 56-day trading periods.

Multi-Objective Evolutionary Algorithms (MOEAs) and transport simulators have been widely utilized to optimise traffic signal timings with multiple objectives. However, traffic simulations require much processing time and need to be called repeatedly in iterations of MOEAs. As a result, traffic signal timing optimisation process is time-consuming. Anytime behaviour of an algorithm indicates its ability to return as good solutions as possible at any time during its implementation. Therefore, anytime behavior is desirable in traffic signal timing optimisation algorithms. In this study, we propose an optimisation strategy (NSGA-II-LS) to improve anytime behaviour based on NSGA-II and local search. To evaluate the validity of the proposed algorithm, the NSGA-II-LS, NSGA-II and MODEA are used to optimize signal durations of an intersection in Andrea Costa scenario. Results of the experiment show that the optimization method proposed in this study has good anytime behaviour in the traffic signal timings optimization problem.

Moving target defense is a revolutionary technology to change the pattern of attack and defense, and end-point information mutation is one of the hotspots belonging to this field. In order to counterpoise the defense benefit of end-point information mutation and service quality of network system, the self-adaptive end-point mutation technique based on adversary strategy awareness is proposed. Directed at the blindness problem of mutation mechanism in the course of defense, adversary strategy awareness based on Sibson entropy algorithm is proposed for guiding the choice of mutation mode by discriminating the scanning attack strategy. Aimed at the low availability problem caused by limited network resource and high mutation overhead, satisfiability modulo theories are used to formally describe the constraints of mutation. Finally, theoretical and experimental analysis shows the ability to resist scanning attack and mutation overhead.

This paper investigates the use of grey theory to enhance the concept of an R-fuzzy set, with regards to the precision of the encapsulating set of returned significance values. The use of lower and upper approximations from rough set theory, allow for an R-fuzzy approach to encapsulate uncertain fuzzy membership values; both collectively generic and individually specific. The authors have previously created a significance measure, which when combined with an R-fuzzy set provides one with a refined approach for expressing complex uncertainty. This pairing of an R-fuzzy set and the significance measure, replicates in part, the high detail of uncertainty representation from a type-2 fuzzy approach, with the relative ease and objectiveness of a type-1 fuzzy approach. As a result, this new research method allows for a practical means for domains where ideally a generalised type-2 fuzzy set is more favourable, but ultimately unfeasible due to the subjectiveness of type-2 fuzzy membership values. This paper focuses on providing a more effective means for the creation of the set which encapsulates the returned degrees of significance. Using grey techniques, rather than the arbitrary configuration of the original work, the result is a high precision set for encapsulation, with the minimal configuration of parameter values. A worked example is used to demonstrate the effectiveness of using grey theory in conjunction with R-fuzzy sets and the significance measure.

In the case that the conclusion of a comparison between the maximum components δikand δjkof decision coefficient vector δiand δjconflicts with that of a full comparison between δiand δjintegrating other components, a clustering dilemma occurs. Here we show a novel method to solve the existing clustering dilemma. We define both the weight vector of grey synthetic measure and the decision coefficient vector with grey synthetic measure at first. Then a novel two-stage decision model with the weight vector of grey synthetic measure and the decision coefficient vector with grey synthetic measure is put forward, and several functional weight vector grey synthetic measures are given. This method can effectively solve the clustering dilemma with maximum values and produce consistent results. At last, a practical evaluation and decision problem of the projects for subjects constructing of a university demonstrates the effectiveness of the proposed novel two stages decision model with grey synthetic measure.

The main aim of this paper is to connect R-fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance of the membership values contained within an R-fuzzy set. The pairing of an R-fuzzy set and the significance measure allows for an intermediary approach to that of a type-2 fuzzy set. By inspecting the returned significance degree of a particular membership value, one is able to ascertain its true significance in relation, relative to other encapsulated membership values. An R-fuzzy set coupled with the proposed significance measure allows for a type-2 fuzzy equivalence, an intermediary, all the while retaining the underlying sentiment of individual and general perspectives, and with the adage of a significantly reduced computational burden. Several human based perception examples are presented, wherein the significance degree is implemented, from which a higher level of detail can be garnered. The results demonstrate that the proposed research method combines the high capacity in uncertainty representation of type-2 fuzzy sets, together with the simplicity and objectiveness of type-1 fuzzy sets. This in turn provides a practical means for problem domains where a type-2 fuzzy set is preferred but difficult to construct due to the subjective type-2 fuzzy membership.

A gray model with a time varying weighted generating operator is put forward in order to fully extract information concealed in recent data. This model increases the weight of new data and reduces the influence of some possible data fluctuation. The relationship between the sample size and the error from the inverse time varying weighted generating operator is discussed. Compared with traditional gray forecasting models, the results of the practical numerical examples demonstrate that this new model performs well in forecasting problems with limited data, and provides reliable and acceptable accuracy for future prediction.

This paper presents a newly created significance measure based on a variation of Bayes' theorem, one which quantifies the significance of any value contained within an R-fuzzy set. An R-fuzzy set is a relatively new concept and an extension to fuzzy sets. By utilising the lower and upper approximations from rough set theory, an R-fuzzy approach allows for uncertain fuzzy membership values to be encapsulated. The membership values associated with the lower approximation are regarded as absolute truths, whereas the values associated with the upper approximation maybe be the result of a single voter, or the vast majority, but definitely not all. By making use of the significance measure one can inspect each and every encapsulated membership value. The significance value itself is a coefficient, this value will indicate how strongly it was agreed upon by the populace for a specific R-fuzzy descriptor. There has been no recent effort made in order to make sense of the significance of any of the values contained within an R-fuzzy set, hence the motivation for this paper. Also presented is a worked example, demonstrating the coupling together of an R-fuzzy approach and the significance measure.

Stock market prediction is of immense interest to trading companies and buyers due to high profit margins. Therefore, precise prediction of the measure of increase or decrease of stock prices also plays an important role in buying/selling activities. This research presents a specialised extension to the genetic algorithms (GA) known as the genetic programming (GP) and gene expression programming (GEP) to explore and investigate the outcome of the GEP criteria on the stock market price prediction. The research presented in this paper aims at the modelling and prediction of short-to-medium term stock value fluctuations in the market via genetically tuned stock market parameters. The technique uses hierarchically defined GP and GEP techniques to tune algebraic functions representing the fittest equation for stock market activities. The proposed methodology is evaluated against five well-known stock market companies with each having its own trading circumstances during the past 20+ years. The proposed GEP/GP methodologies were evaluated based on variable window/population sizes, selection methods, and Elitism, Rank and Roulette selection methods. The Elitism-based approach showed promising results with a low error-rate in the resultant pattern matching with an overall accuracy of 93.46% for short-term 5-day and 92.105 for medium-term 56-day trading periods.

To determine the ordered weighted averaging (OWA) weights, the latent information function is developed to analyze the likelihood of occurrence for the preference value. The more likelihood a preference value is, the bigger the weight is, and vice versa. The proposed model is further extended to the situation where the preference value is an interval number by introducing a new method for interval number comparison. An example of energy technology evaluation is provided to demonstrate that the proposed approach is reasonable and simple.

The aim of this paper is to distinguish between some of the more intrinsic differences that exist between grey system theory (GST) and fuzzy system theory (FST). There are several aspects of both paradigms that are closely related, it is precisely these close relations that will often result in a misunderstanding or misinterpretation. The subtly of the differences in some cases are difficult to perceive, hence why a definitive explanation is needed. This paper discusses the divergences and similarities between the interval-valued fuzzy set and grey set, interval and grey number; for both the standard and the generalised interpretation. A preference based analysis example is also put forward to demonstrate the alternative in perspectives that each approach adopts. It is believed that a better understanding of the differences will ultimately allow for a greater understanding of the ideology and mantras that the concepts themselves are built upon. By proxy, describing the divergences will also put forward the similarities. We believe that by providing an overview of the facets that each approach employs where confusion may arise, a thorough and more detailed explanation is the result. This paper places particular emphasis on grey system theory, describing the more intrinsic differences that sets it apart from the more established paradigm of fuzzy system theory.

Innovation and industrial outputs of China's High-tech industries are interacted, and a loop model is used to describe this relation. Based on this, grey relational analysis is applied to measure this relation. And the results show the bidirectional positive relationship.

In the literature, there is a presumption that a grey set and an interval-valued fuzzy set are equivalent. This presumption ignores the existence of discrete components in a grey number. In this paper, new measurements of uncertainties of grey numbers and grey sets, consisting of both absolute and relative uncertainties, are defined to give a comprehensive representation of uncertainties in a grey number and a grey set. Some simple examples are provided to illustrate that the proposed uncertainty measurement can give an effective representation of both absolute and relative uncertainties in a grey number and a grey set. The relationships between grey sets and interval-valued fuzzy sets are also analyzed from the point of view of the proposed uncertainty representation. The analysis demonstrates that grey sets and interval-valued fuzzy sets provide different but overlapping models for uncertainty representation in sets.

Grey system theory has many facets, one of which is the so-called GM(1,1) model, used for predicting and forecasting. This paper proposes a novel way of improving the overall relative accuracy of the new-information grey model, and the metabolic grey model, and also by improving the filter value accuracy. By incorporating a weight sequence that is populated by a genetic algorithm to minimize the error of the simulated values. The least square parameters (-a) and b, can then be scaled by the values contained in the weight sequence, until a satisfactory result is obtained. If a high level of accuracy can be attained for the simulation values of the model, and also for the filter value, it will ultimately allow for greater forecasting ability.

The present interval arithmetic often results in unnecessary diameter expansions in interval operations. To solve this problem, this paper defines a new operation of intervals using their algebraic representations. On the basis of algebraic interval representations, the arithmetic operations are investigated and formulated. Then, the capability of the proposed operation methods in solving unnecessary diameter expansions is analyzed. An application of the proposed model to a typical game problem is provided in the end to demonstrate the feasibility of the proposed model.

A systematic carding on the research of grey incidence analysis modeling has been made in this paper. The grey incidence analysis models developed from the models based on incidence coefficients of each point in the sequences in early days to the generalized grey incidence analysis models based on integral or overall perspective. It evolved from the grey incidence analysis models which measure similarity based on nearness into the models which consider similarity and nearness respectively. The objects of the research advanced from the analysis of relationship among curves to that among curved surfaces, and further to the analysis of relationship in three-dimensional space and even the relationship among super surfaces in n-dimensional space. The problems remained to be studied in this field are clarified too. Several research approaches of grey incidence analysis modeling are clearly revealed.

This research proposes a new model for constructing decision trees using interval-valued fuzzy membership values employing on look-ahead based fuzzy decision tree induction and interval-valued fuzzy sets. Most existing fuzzy decision trees do not consider the uncertainty associated with their membership values. However, precise values of fuzzy membership values are not always possible. In this paper, we represent fuzzy membership values as intervals to model uncertainty and employ the look-ahead based fuzzy decision tree induction method and Hamming distance of interval-valued fuzzy sets to construct decision trees. An example is given to demonstrate the effectiveness of the approach.

Among various methods in protein function prediction, rough set has recently been applied to prediction of protein structural classes. However, this was a blind application on a single but small data set of high homology, which did not consider investigation of various parameters in the rough set. The aim of this paper is therefore to study rough set in the area through comprehensive and consistent analysis and then to present a practical strategy in the rough set-based protein function prediction. To achieve this aim, three different data sets were considered: the first data set for prediction of six main enzyme classes, and other two for prediction of structural classes. Boolean reasoning, Entropy scaling and Equal frequency binning were used for discretization along with two methods for producing reducts and rules, genetic and Johnson's algorithms. It can be seen that the predictive accuracies were poor for the enzyme dataset whereas it performed better at prediction of the protein structural classes. It is also observed that the dataset with low homology produced poor accuracies than the dataset with high homology. Furthermore, various parameters and methods used in the rough set were sensitive to the problems in the area, as well as the data sets of low and high homology and different number of the features. The results appear to indicate that the equal frequency-based approach combined with genetic algorithm yields higher prediction. However, other methods such as Boolean reasoning with the genetic algorithm are also found to be promising. Further investigation will provide a practical strategy that can be used in the rough set-based protein function prediction as well as other areas of Bioinformatics.

Over the last seven years we have seen an exponential increase in the number of Bioinformatics databases available. These databases are becoming increasingly specialised and are often only known by a small community of users. This paper describes the implementation of a novel meta-database. Rather than simply displaying a list of databases that are available this project has used graphical data in the form of a family tree to show how the databases are related to one another. A general level of relatedness is described using fuzzy sets, this relationship compares every database against all the other databases to see how related they are. It facilitates an automatic construction of the tree when new databases are added.

Most existing distances between intuitionistic fuzzy sets are defined in linear plane representations in 2D or 3D space. Here, we define a new interpretation of intuitionistic fuzzy sets as a restricted spherical surface in 3D space. A new spherical distance for intuitionistic fuzzy sets is introduced. We prove that the spherical distance is different from those existing distances in that it is nonlinear with respect to the change of the corresponding fuzzy membership degrees. © 2009 Wiley Periodicals, Inc.

This paper defines a new parameter for describing the uncertainty of rough sets. Different from the roughness of a rough set, a global roughness measures the uncertainty of rough sets with respect to the entire information system. This is essential especially for a special rough set - boundary rough sets.We give the definition of global roughness of approximation and boundary rough sets, and analyse their properties. Some examples are also provided to show the complementary features of global roughness and roughness of rough sets.

Grey numbers can be represented as their kernels and associated degrees of greyness. Therefore, the operation between kernels of grey numbers has significance in the application of grey numbers. This paper investigates the operations of grey numbers using their kernels and degrees of greyness and provides conditions for the application of real number operations to their kernels.

Aircraft noise is influenced by many complex factors and it is difficult to devise an accurate mathematical model to simulate it with respect to operations at an airport. This paper presents an investigation in simulating airport noise using artificial neural networks. The results show that it is possible to establish a simple neural network model with monitored data for a specific airport and specific aircraft under local conditions.

Combining both intervals and discrete sets of numbers, this paper presents a definition for an extended grey number model representing both continuous and discrete grey numbers. Based on the new definition, the operation properties and degree of greyness are investigated and a new formula for arithmetic operations of grey numbers is derived.

Roughness is an important indicator for the uncertainty of a rough set. This paper analyses the roughness bounds for set-oriented rough set operations. A bound of the roughness of the union between two set-oriented rough sets could be determined by the roughness of the two operand set-oriented sets. In most cases, a bound could also be found for a difference set between two set-oriented rough sets. However, the roughness of the operand sets can not uniquely bound the roughness of their intersection set. The results presented here show that a bound of the set operation can be determined from their operand's roughnesses under some operations. We provide an example to show the derived bounds from operand's roughness.

It is a common understanding in neural network research and applications that a network with fewer redundant nodes is more reliable. This paper argues that a redundant network structure approach improves the learning process of neural networks. This redundant structure is shown to be free from extra parameters and hence does not introduce additional uncertainty. Using a small partition problem, the training results of standard BP networks are compared with those networks with a redundant structure. The comparison shows that a redundant structure does not necessarily always have a negative effect, and as a result it is possible to help a neural network obtain better performance.

This paper presents a new method for explaining the reasoning results of a trained neural network. The method considers the most significant attribute first under the guidance of a relative strength of effect analysis and eliminates irrelevant points. Following the adaptive search in the dynamic state space, a set of relevant points are extracted and form the basis of the explanation of the neural network reasoning. Combining a relative strength of effect analysis with the relevant points, a case based explanation approach is put forward. As an illustration, an experiment with a small data set on the relationship between weather conditions and play decisions is presented to demonstrate the utility of the proposed approach.