Novel moderate transformation of fuzzy membership function into basic belief assignment

In information fusion,the uncertain information from different sources might be modeled with different theoretical frameworks.When one needs to fuse the uncertain information represented by different uncertainty theories,constructing the transformation between different frameworks is crucial.Various transformations of a Fuzzy Membership Function(FMF)into a Basic Belief Assignment(BBA)have been proposed,where the transformations based on uncertainty maximization and minimization can determine the BBA without preselecting the focal elements.However,these two transformations that based on uncertainty optimization emphasize the extreme cases of uncertainty.To avoid extreme attitudinal bias,a trade-off or moderate BBA with the uncertainty degree between the minimal and maximal ones is more preferred.In this paper,two moderate transformations of an FMF into a trade-off BBA are proposed.One is the weighted average based transformation and the other is the optimization-based transformation with weighting mechanism,where the weighting factor can be user-specified or determined with some prior information.The rationality and effectiveness of our transformations are verified through numerical examples and classification examples.

Insulation and Flame Retardancy Improvement of PBDEs Using 3D-QSAR Model Combined with a Fuzzy Membership Function Method

A three-dimensional quantitative structure-activity relationship(3D-QSAR)model based on the fuzzy membership function method was developed in this study,and then the model was applied to the molecular design of the enhanced comprehensive activities(insulation/flame retardancy)of polybrominated diphenyl ethers(PBDEs)considering their environmental behavior control,to develop environmental-friendly PBDE derivatives with outstanding functionality.Firstly,a fuzzy membership function method was employed to characterize the evaluation values of comprehensive activities of the functional properties of PBDEs based on the 3D-QSAR model.Secondly,a comprehensive activity 3D-QSAR model(CoMFA)of the functional properties of PBDEs was established,which demonstrated robustness and good predictive ability.Thirdly,a molecular modification scheme was designed to enhance the comprehensive activity of the functional properties of PBDEs considering the PBDE homologs BDE-138,BDE-183,and BDE-209 as target molecules.The resulting information indicated that the four PBDE derivatives with significantly enhanced functional properties,such as passing screening for toxicity,bioconcentration,migration,and biodegradability assessments with environmentally friendly results,were successfully designed(43.57%-82.14%enhancement).Finally,the mechanism analysis indicated that the enhanced functional properties of the modified PBDE derivatives were significantly related to the substitution positions and substitution groups of PBDEs.

Energy Price Forecasting Through Novel Fuzzy Type-1 Membership Functions

Electricity price forecasting is a subset of energy and power forecasting that focuses on projecting commercial electricity market present and future prices.Electricity price forecasting have been a critical input to energy corporations’strategic decision-making systems over the last 15 years.Many strategies have been utilized for price forecasting in the past,however Artificial Intelligence Techniques(Fuzzy Logic and ANN)have proven to be more efficient than traditional techniques(Regression and Time Series).Fuzzy logic is an approach that uses membership functions(MF)and fuzzy inference model to forecast future electricity prices.Fuzzy c-means(FCM)is one of the popular clustering approach for generating fuzzy membership functions.However,the fuzzy c-means algorithm is limited to producing only one type of MFs,Gaussian MF.The generation of various fuzzy membership functions is critical since it allows for more efficient and optimal problem solutions.As a result,for the best and most improved results for electricity price forecasting,an approach to generate multiple type-1 fuzzy MFs using FCM algorithm is required.Therefore,the objective of this paper is to propose an approach for generating type-1 fuzzy triangular and trapezoidal MFs using FCM algorithm to overcome the limitations of the FCM algorithm.The approach is used to compute and improve forecasting accuracy for electricity prices,where Australian Energy Market Operator(AEMO)data is used.The results show that the proposed approach of using FCM to generate type-1 fuzzy MFs is effective and can be adopted.

FEW-NNN: A Fuzzy Entropy Weighted Natural Nearest Neighbor Method for Flow-Based Network Traffic Attack Detection

Attacks such as APT usually hide communication data in massive legitimate network traffic, and mining structurally complex and latent relationships among flow-based network traffic to detect attacks has become the focus of many initiatives. Effectively analyzing massive network security data with high dimensions for suspicious flow diagnosis is a huge challenge. In addition, the uneven distribution of network traffic does not fully reflect the differences of class sample features, resulting in the low accuracy of attack detection. To solve these problems, a novel approach called the fuzzy entropy weighted natural nearest neighbor(FEW-NNN) method is proposed to enhance the accuracy and efficiency of flowbased network traffic attack detection. First, the FEW-NNN method uses the Fisher score and deep graph feature learning algorithm to remove unimportant features and reduce the data dimension. Then, according to the proposed natural nearest neighbor searching algorithm(NNN_Searching), the density of data points, each class center and the smallest enclosing sphere radius are determined correspondingly. Finally, a fuzzy entropy weighted KNN classification method based on affinity is proposed, which mainly includes the following three steps: 1、 the feature weights of samples are calculated based on fuzzy entropy values, 2、 the fuzzy memberships of samples are determined based on affinity among samples, and 3、 K-neighbors are selected according to the class-conditional weighted Euclidean distance, the fuzzy membership value of the testing sample is calculated based on the membership of k-neighbors, and then all testing samples are classified according to the fuzzy membership value of the samples belonging to each class;that is, the attack type is determined. The method has been applied to the problem of attack detection and validated based on the famous KDD99 and CICIDS-2017 datasets. From the experimental results shown in this paper, it is observed that the FEW-NNN method improves the accuracy and efficiency of flow-based network traffic attack detection.

Fuzzy smooth support vector machine with different smooth functions

Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm and the Newdon-Armijio （NA） algorithm easily, however the accuracy of sigmoid function is not as good as that of polyno- mial smooth function. Furthermore, the method cannot reduce the influence of outliers or noise in dataset. A fuzzy smooth support vector machine （FSSVM） with fuzzy membership and polynomial smooth functions is introduced into the SVM. The fuzzy member- ship considers the contribution rate of each sample to the optimal separating hyperplane and makes the optimization problem more accurate at the inflection point. Those changes play a positive role on trials. The results of the experiments show that those FSSVMs can obtain a better accuracy and consume the shorter time than SSVM and lagrange support vector machine （LSVM）.

Fuzzy Comprehensive Evaluation for Decision Making of Water Saving Irrigation System

A model of fuzzy comprehensive evaluation for water saving irrigation system (WSIS) decision making is proposed based on establishing an index system affected by six kinds of basic factors including qualitative and quantitative indexes. The object function of WSIS is set up by using the concept of fuzzy membership degree, it is to transform characteristic vector matrix into unify membership matrix and extending the least square method to the least of weighted distance square. The optimum weighted membership degree and the inferior weighted membership degree are used to solve the object function. This method effective solves the problem of classify for fuzzy attributive indexes and the problem of optimum for the set of different attributive indexes. A case study shows that the fuzzy comprehensive evaluation model is reasonable and effective in decision making for water saving irrigation system planning.

Delayed recognition: recent developments and a proposal to study this phenomenon as a fuzzy concept

Purpose： New developments in the study of delayed recognition are discussed.Design/methodology/approach： Based on these new developments a method is proposed to characterize delayed recognition as a fuzzy concept.Findings： A benchmark value of 0.333 corresponding with linear growth is obtained. Moreover, a case is discovered in which an expert found delayed recognition several years before citation analysis could discover this phenomenon. Research limitations： As all citation studies also this one is database dependent.Practical implications： Delayed recognition is turned into a fuzzy concept.Originality/value： The article presents a new way of studying delayed recognition.

Fuzzy Multi-Objective Decision Model of Supplier Selection with Preference Information

Supplier selection is a multi-objective decision problem, which must be considered many objectives, some objectives are qualitative, and others are quantitative. Meanwhile, manufacturer has preference for different suppliers. In this paper, a new multi-objective decision model with preference information of supplier is established. A practical example of supplier selection problem utilizing this model is studied. The result demonstrates the feasibility and effectiveness of the methods proposed in the paper.

A Fuzzy Cluster and Retinex Theory-based Variation Model for Inhomogenous Image Segmentation

A variational inhomogeneous image segmentation model based on fuzzy membership functions and Retinex theory is proposed by introducing the fuzzy membership function.The existence of the solution of the proposed model is proved theoretically.A valid algorithm is designed to make numerical solution of the model under the framework of alternating minimization.The last experimental results show that the model can make segmentation of the real image with intensity inhomogeneity effectively.

Research on trend prediction of component stock in fuzzy time series based on deep forest

With the continuous development of machine learning and the increasing complexity of financial data analysis,it is more popular to use models in the field of machine learning to solve the hot and difficult problems in the financial industry.To improve the effectiveness of stock trend prediction and solve the problems in time series data processing,this paper combines the fuzzy affiliation function with stock-related technical indicators to obtain nominal data that can widely reflect the constituent stocks in the case of time series changes by analysing the S&P 500 index.Meanwhile,in order to optimise the current machine learning algorithm in which the setting and adjustment of hyperparameters rely too much on empirical knowledge,this paper combines the deep forest model to train the stock data separately.The experimental results show that(1)the accuracy of the extreme random forest and the accuracy of the multi-grain cascade forest are both higher than that of the gated recurrent unit(GRU)model when the un-fuzzy index-adjusted dataset is used as features for input,(2)the accuracy of the extreme random forest and the accuracy of the multigranular cascade forest are improved by using the fuzzy index-adjusted dataset as features for input,(3)the accuracy of the fuzzy index-adjusted dataset as features for inputting the extreme random forest is improved by 18.89% compared to that of the un-fuzzy index-adjusted dataset as features for inputting the extreme random forest and(4)the average accuracy of the fuzzy index-adjusted dataset as features for inputting multi-grain cascade forest increased by 5.67%.

Fuzzy stochastic damage mechanics(FSDM) based on fuzzy auto-adaptive control theory

In order to fully interpret and describe damage mechanics, the origin and development of fuzzy stochastic damage mechanics were introduced based on the analysis of the harmony of damage, probability, and fuzzy membership in the interval of [0,1]. In a complete normed linear space, it was proven that a generalized damage field can be simulated through β probability distribution. Three kinds of fuzzy behaviors of damage variables were formulated and explained through analysis of the generalized uncertainty of damage variables and the establishment of a fuzzy functional expression. Corresponding fuzzy mapping distributions, namely, the half-depressed distribution, swing distribution, and combined swing distribution, which can simulate varying fuzzy evolution in diverse stochastic damage situations, were set up. Furthermore, through demonstration of the generalized probabilistic characteristics of damage variables, the cumulative distribution function and probability density function of fuzzy stochastic damage variables, which show β probability distribution, were modified according to the expansion principle. The three-dimensional fuzzy stochastic damage mechanical behaviors of the Longtan rolled-concrete dam were examined with the self-developed fuzzy stochastic damage finite element program. The statistical correlation and non-normality of random field parameters were considered comprehensively in the fuzzy stochastic damage model described in this paper. The results show that an initial damage field based on the comprehensive statistical evaluation helps to avoid many difficulties in the establishment of experiments and numerical algorithms for damage mechanics analysis.

Assessment of drought hazard,vulnerability and risk in Iran using GIS techniques

The drought has enormous adverse effects on agriculture,water resources and environment,and causes damages around the world.Drought risk assessment and prioritization of drought management can help decision makers and planners to manage the adverse effects of drought.This paper aims to determine the risk of drought in Iran.At the first stage,standardized precipitation index(SPI)was calculated for the period 1981–2016.Then the probability map of different drought classes or drought hazard probability map were prepared.After that the indicator-based vulnerability assessment method was used to determine the drought vulnerability index.Five indices including climate,topography,waterway density,land use and groundwater resources were chosen as the most critical factors of drought in Iran and followed by the analytical hierarchy process questionnaire,the weights of each index were obtained based on expert opinions.Fuzzy membership maps of each index and sub-index were prepared using ArcGIS software.The drought vulnerability map of Iran was plotted using these weights and maps of each indicator.Finally,the drought risk map of Iran was provided by multiplying drought hazard and vulnerability maps.According to the 43-completed questionnaires by experts,climate index has the highest vulnerability to drought.Climate does not have an important role in drought hazard index,but it is the most crucial factor to classified drought vulnerability index.The results showed that central,northeast,southeast and west parts of Iran are at high risks of drought.There are regions with different risks in Iran due to unusual weather and climatic conditions.We realized that the climate and the groundwater situation is almost the same in the central,east and south parts of Iran,because the land use plays a crucial role in the drought vulnerability and risk in these areas.The drought risk decreases from the center of Iran to the southwest and northwest.

一种基于模糊测度的自动多门限图象分割

在模糊特征域上提出一种基于模糊隶属度、模糊测度的图象自动门限分割方法，提出了X及X的分割应满足的条件．实践证明，该方法和其它方法相比较，效果较好．

基于灰色模糊综合评判的高压断路器状态评估

针对高压断路器状态评估因素具有模糊性和灰色性的特点,将灰色模糊理论应用到高压断路器的状态评估中。基于试点工程,建立考虑高压断路器运行机理的递阶层次评估模型;采用层次分析法计算各层次评估因素权重集的模部,结合信息充裕程度及专家经验,确定相应评估因素权重集的灰部;综合定性分析与定量分析,以隶属度描述评估因素与状态等级间的模糊关系,并引入点灰度描述模糊关系的不可信程度,建立灰色模糊判别矩阵,进而对高压断路器运行状态进行综合评估。实际算例表明,所提模型能够客观有效地评估高压断路器的状态。

FUZZY SATISFYING INTERACTIVE MULTIOBJECTIVE THERMAL POWER DISPATCH： SWT APPROACH

In multiobjective optimization, trade-off analysis plays an important role in determining most preferred solution. This paper presents an explicit interactive trade-off analysis based on the surrogate worth trade-off function to determine the best compromised solution. In the multiobjective framework thermal power dispatch problem is undertaken in which four objectives viz. cost, NOx emission, SOx emission and COx emission are minimized simultaneously. The interactive process is implemented using a weighting method by regulating the relative weights of objectives in systematic manner. Hence the weighting method facilitates to simulate the trade-offrelation between the conflicting objectives in non-inferior domain. Exploiting fuzzy decision making theory to access the indifference band, interaction with the decision maker is obtained via surrogate worth trade-off （SWT） functions of the objectives. The surrogate worth trade-off functions are constructed in the functional space and then transformed into the decision space, so the surrogate worth trade-off functions of objectives relate the decision maker＇s preferences to non-inferior solutions through optimal weight patterns. The optimal solution of thermal power dispatch problem is obtained by considering real and reactive power losses. Decoupled load flow analysis is performed to find the transmission losses. The validity of the proposed method is demonstrated on 11-bus, 17-lines IEEE system, comprising of three generators.

Kernel Density Estimation Based Multiphase Fuzzy Region Competition Method for Texture Image Segmentation

In this paper,we propose a multiphase fuzzy region competition model for texture image segmentation.In the functional,each region is represented by a fuzzy membership function and a probability density function that is estimated by a nonparametric kernel density estimation.The overall algorithm is very efficient as both the fuzzy membership function and the probability density function can be implemented easily.We apply the proposed method to synthetic and natural texture images,and synthetic aperture radar images.Our experimental results have shown that the proposed method is competitive with the other state-of-the-art segmentation methods.

A COMPUTATIONAL METHOD FOR FUZZY TIME SERIES FORECASTING BASED ON DIFFERENCE PARAMETERS

Present study proposes a method for fuzzy time series forecasting based on difference parameters.The developed method has been presented in a form of simple computational algorithm.It utilizes various difference parameters being implemented on current state for forecasting the next state values to accommodate the possible vagueness in the data in an efficient way.The developed model has been simulated on the historical student enrollments data of University of Alabama and the obtained forecasted values have been compared with the existing methods to show its superiority.Further,the developed model has also been implemented in forecasting the movement of market prices of share of State Bank of India(SBI)at Bombay Stock Exchange(BSE),India.

PRODUCTS RECOMMENDATIONS USING EMOTIONAL INFORMATION

Kutani-ware is a famous traditional craft which is so significant not only from the economic perspective, but also from the cultural viewpoint. It had a prosperous time in the last decades; however it has been shrinking recently due to the changes of lifestyle or the appearance of more functional products. Compared with the function, the brand image and style of products have become much more important in purchasing; ＂moreover, technology is no longer the sole driving force in the development of products. As the spread of marketing appealing to consumers＇ emotion, many methods treating human＇s feeling have been developed and applied in many fields. Since human＇s emotion has both linear and non-linear characteristics, and it is changing by every moment, a method which fits better is essential. This paper develops a new evaluation model by comparing statistical, fuzzy and pseudo-fuzzy approaches based-on an emotional evaluation database to find a better approach for recommendation of products.