A new fuzzy rule based algorithm for estimating software faults in early phase of development

Estimation of reliability and the number of faults present in software in its early development phase, i.e., requirement analysis or design phase is very beneficial for developing reliable software with optimal cost. Software reliability prediction in early phase of development is highly desirable to the stake holders, software developers, managers and end users. Since, the failure data are unavailable in early phase of software development, different reliability relevant software metrics and similar project data are used to develop models for early software fault prediction. The proposed model uses the linguistic values of software metrics in fuzzy inference system to predict the total number of faults present in software in its requirement analysis phase. Considering specific target reliability, weightage of each input software metrics and size of software, an algorithm has been proposed here for developing general fuzzy rule base. For model validation of the proposed model, 20 real software project data have been used here. The linguistic values from four software metrics related to requirement analysis phase have been considered as model inputs. The performance of the proposed model has been compared with two existing early software fault prediction models.     

A bayesian belief network based model for predicting software faults in early phase of software development process

It is always better to have an idea about the future situation of a present work. Prediction of software faults in the early phase of software development life cycle can facilitate to the software personnel to achieve their desired software product. Early prediction is of great importance for optimizing the development cost of a software project. The present study proposes a methodology based on Bayesian belief network, developed to predict total number of faults and to reach a target value of total number of faults during early development phase of software lifecycle. The model has been carried out using the information from similar or earlier version software projects, domain expert’s opinion and the software metrics. Interval type-2 fuzzy logic has been applied for obtaining the conditional probability values in the node probability tables of the belief network. The output pattern corresponding to the total number of faults has been identified by artificial neural network using the input pattern from similar or earlier project data. The proposed Bayesian framework facilitates software personnel to gain the required information about software metrics at early phase for achieving targeted number of software faults. The proposed model has been applied on twenty six software project data. Results have been validated by different statistical comparison criterion. The performance of the proposed approach has been compared with some existing early fault prediction models.     

Investment project evaluation by a decision making methodology based on type-2 fuzzy sets

Although investment projects supported by the state are extremely important in terms of national policy the projects to be transferred from the common public funds brings with it many problems. Highly transparent and comprehensive evaluation model are required to transfer the public resources to the right investment projects. It is necessary to consider many criteria for the evaluation of an investment project. These criteria are generally subjective and extremely difficult to express in numbers. However, using the fuzzy sets provide huge facilities to decision makers in project evaluation process with linguistic variables and measurement challenges. In this study, a new evaluation model for investment projects have been proposed for development agencies operating in Turkey. To address ambiguities and relativities in real world scenarios more conveniently, type-2 fuzzy sets and crisp sets have been simultaneously used. The proposed model for the investment project evaluation problem composed of type-2 fuzzy AHP and type-2 fuzzy TOPSIS methods. The proposed fuzzy MCDM method consists of three phases: (1) identify the criteria to be used in the model, (2) type-2 fuzzy AHP computations, (3) evaluation of investment projects with type-2 fuzzy TOPSIS and determination of the final rank. To perceive proposed model better, an application with real case data have been performed in Middle Black Sea Development Agency in Turkey. As a consequence of this application, it has been observed that the proposed model have proved effective in evaluation of alternatives in multi-criteria group decision making problems in a broader perspective and flexible fashion.     

Reliability growth modeling and optimal release policy under fuzzy environment of an N-version programming system incorporating the effect of fault removal efficiency

Failure of a safety critical system can lead to big losses.Very high software reliability is required for automating the working of systems such as aircraft controller and nuclear reactor controller software systems.Fault-tolerant softwares are used to increase the overall reliability of software systems.Fault tolerance is achieved using the fault-tolerant schemes such as fault recovery (recovery block scheme),fault masking (N-version programming (NVP)) or a combination of both (Hybrid scheme).These softwares incorporate the ability of system survival even on a failure.Many researchers in the field of software engineering have done excellent work to study the reliability of fault-tolerant systems.Most of them consider the stable system reliability.Few attempts have been made in reliability modeling to study the reliability growth for an NVP system.Recently,a model was proposed to analyze the reliability growth of an NVP system incorporating the effect of fault removal efficiency.In this model,a proportion of the number of failures is assumed to be a measure of fault generation while an appropriate measure of fault generation should be the proportion of faults removed.In this paper,we first propose a testing efficiency model incorporating the effect of imperfect fault debugging and error generation.Using this model,a software reliability growth model (SRGM) is developed to model the reliability growth of an NVP system.The proposed model is useful for practical applications and can provide the measures of debugging effectiveness and additional workload or skilled professional required.It is very important for a developer to determine the optimal release time of the software to improve its performance in terms of competition and cost.In this paper,we also formulate the optimal software release time problem for a 3VP system under fuzzy environment and discuss a the fuzzy optimization technique for solving the problem with a numerical illustration.     

基于模糊理论的软件项目调度算法

针对软件项目调度问题中信息的不确定性及资源分配的特殊性需要,提出了一种基于模糊理论的软件项目调度算法FSSA。该算法采用模糊数表示任务的工期并应用遗传算法产生任务的调度序列。实验结果表明,FSSA算法能在很短的时间内得到理想的结果,有一定的应用价值。     

Convenient T-S fuzzy model with enhanced performance using a novel swarm intelligent fuzzy clustering technique

To automatically extract T-S fuzzy models with enhanced performance from data is an interesting and important issue for fuzzy system modeling. In this paper, a novel methodology is proposed for this issue based on a three-step procedure. Firstly, the idea of variable length genotypes is introduced to the artificial bee colony (ABC) algorithm to derive a so-called Variable string length Artificial Bee Colony (VABC) algorithm. The VABC algorithm can be used to solve a kind of optimization problems where the length of the optimal solutions is not known as a priori. Secondly, fuzzy clustering without knowing cluster number as a priori is viewed as such kind of optimization problem. Thus, a novel version of Fuzzy C-Means clustering technique (VABC-FCM), holding powerful global search ability, is proposed based on the VABC algorithm. Use of VABC allows the encoding of variable cluster number. This makes VABC-FCM not require a priori specification of the cluster number. Finally, the proposed VABC-FCM algorithm is used to extract T-S fuzzy model from data. Such VABC-FCM based convenient T-S fuzzy model extraction methodology does not require a specification of rule number as a priori. Some artificial data sets are applied to validate the performance of the convenient T-S fuzzy model. The experimental results show that the proposed convenient T-S fuzzy model has low approximation error and high prediction accuracy with appreciate rule number. Moreover, the convenient T-S fuzzy model is used to model the characteristics of superheated steam temperature in power plant, and the results suggest the powerful performance of the proposed method.     

间歇性风电并网能源调度综合模糊评价系统设计

针对传统风电并网能源调度评价系统设计评估准确率低、系统响应时间慢的不足,提出基于综合模糊理论的能源调度评价系统设计。给出了模糊评价系统的硬件架构与软件实现流程,依托于数据输入管理模块、编辑查询模块、模糊评价模块与数据输入模块构建了可变模糊评价模型,并分别确定出两级的指标评价体系、权重指标和模糊隶属度矩阵;基于模糊算子和模型参数确定出综合评价向量矩阵,实现对并网能源调度方案的精确评价。算例分析结果表明,提出评价系统的平均偏差率可以控制到0.131%,显著优于传统能源调度评价系统。     

A fuzzy logic based approach for phase-wise software defects prediction using software metrics

ContextThe software defect prediction during software development has recently attracted the attention of many researchers. The software defect density indicator prediction in each phase of software development life cycle (SDLC) is desirable for developing a reliable software product. Software defect prediction at the end of testing phase may not be more beneficial because the changes need to be performed in the previous phases of SDLC may require huge amount of money and effort to be spent in order to achieve target software quality. Therefore, phase-wise software defect density indicator prediction model is of great importance.ObjectiveIn this paper, a fuzzy logic based phase-wise software defect prediction model is proposed using the top most reliability relevant metrics of the each phase of the SDLC.MethodIn the proposed model, defect density indicator in requirement analysis, design, coding and testing phase is predicted using nine software metrics of these four phases. The defect density indicator metric predicted at the end of the each phase is also taken as an input to the next phase. Software metrics are assessed in linguistic terms and fuzzy inference system has been employed to develop the model.ResultsThe predictive accuracy of the proposed model is validated using twenty real software project data. Validation results are satisfactory. Measures based on the mean magnitude of relative error and balanced mean magnitude of relative error decrease significantly as the software project size increases.ConclusionIn this paper, a fuzzy logic based model is proposed for predicting software defect density indicator at each phase of the SDLC. The predicted defects of twenty different software projects are found very near to the actual defects detected during testing. The predicted defect density indicators are very helpful to analyze the defect severity in different artifacts of SDLC of a software project.     

软件可靠度的模糊故障树评定方法

软件可靠性的定量评价是软件可靠性工程的关键问题之一,采用故障树方法对软件进行定性和定量分析,提出了两类情况下对影响软件可靠性的主次因素划分及其模糊权重的计算方法。在此基础上,建立多级模糊评价模型,提出了增广和聚合算法,并给出了软件可靠度算式。选择某型航空装备软件进行了测试实例分析,实验结果表明了该方法评价结构的合理性与评价算法的有效性,适用于软件质量及开发过程控制的工程实践。     

采样点个数对T-S模糊建模精度的影响

在模糊建模中所取的采样点个数会对辨识出的模型精度产生影响,在只给出有限个数据采样点且数据分布不能人为控制的情况下怎样选取最优的采样点个数是模糊辨识中要解决的问题之一.通过采样点个数变化的模糊辨识算法来研究模糊建模中采样点个数对模型描述性能的影响.基于T S模糊模型,采用对称三角形模糊划分和“网格对角线法”提取模糊规则,通过对DISO系统和Mackey Glass 无序时间序列进行建模,给出模糊模型训练性能指标和检验性能指标随采样点个数增加的变化趋势曲线.     

A hybrid model based on differential fuzzy logic relationships and imperialist competitive algorithm for stock market forecasting

In this study, a new kind of fuzzy set in fuzzy time series’ field is introduced. It works as a trend estimator to be appropriate for fuzzy time series forecasting by reconnoitering trend of data appropriately. First, the historical data are fuzzified into differential fuzzy sets, and then differential fuzzy relationships are calculated. Second, differential fuzzy logic groups are established by grouping differential fuzzy relationships. Finally, in the defuzzification step, the forecasts are calculated. However, for increasing the accuracy of the models, an evolutionary algorithm, namely imperialist competitive algorithm is injected, to train the model. A massive stock data from four main stock databases have been selected for model validation. The final project, has shown that outperformed its counterparts in term of accuracy.     

Interval type-2 fuzzy inverse controller design in nonlinear IMC structure

In the recent years it has been demonstrated that type-2 fuzzy logic systems are more effective in modeling and control of complex nonlinear systems compared to type-1 fuzzy logic systems. An inverse controller based on type-2 fuzzy model can be proposed since inverse model controllers provide an efficient way to control nonlinear processes. Even though various fuzzy inversion methods have been devised for type-1 fuzzy logic systems up to now, there does not exist any method for type-2 fuzzy logic systems. In this study, a systematic method has been proposed to form the inverse of the interval type-2 Takagi-Sugeno fuzzy model based on a pure analytical method. The calculation of inverse model is done based on simple manipulations of the antecedent and consequence parts of the fuzzy model. Moreover, the type-2 fuzzy model and its inverse as the primary controller are embedded into a nonlinear internal model control structure to provide an effective and robust control performance. Finally, the proposed control scheme has been implemented on an experimental pH neutralization process where the beneficial sides are shown clearly.     

Finding multiple possible critical paths using fuzzy PERT

Program evaluation and review techniques (PERT) is an efficient tool for large project management. In actual project control decisions, PERT has successfully been applied to business management, industry production, project scheduling control, logistics support, etc. However, classical PERT requires a crisp duration time representation for each activity. This requirement is often difficult for the decision-makers due to the fact that they usually can not estimate these values precisely. In recent years, some fuzzy PERT methods have been proposed based on fuzzy set theory for project management. However, there is a drawback in the existing fuzzy PERT methods, i.e., sometimes they maybe cannot find a critical path in a fuzzy project network. In this paper, we propose a fuzzy PERT algorithm to find multiple possible critical paths in a fuzzy project network, where the duration time of each activity in a fuzzy project network is represented by a fuzzy number. The proposed algorithm can overcome the drawback of the existing fuzzy PERT methods.     

Applying fuzzy neural network to estimate software development effort

The ability to accurately and consistently estimate software development efforts is required by the project managers in planning and conducting software development activities. Since software effort drivers are vague and uncertain, software effort estimates, especially in the early stages of the development life cycle, are prone to a certain degree of estimation errors. A software effort estimation model which adopts a fuzzy inference method provides a solution to fit the uncertain and vague properties of software effort drivers. The present paper proposes a fuzzy neural network (FNN) approach for embedding artificial neural network into fuzzy inference processes in order to derive the software effort estimates. Artificial neural network is utilized to determine the significant fuzzy rules in fuzzy inference processes. We demonstrated our approach by using the 63 historical project data in the well-known COCOMO model. Empirical results showed that applying FNN for software effort estimates resulted in slightly smaller mean magnitude of relative error (MMRE) and probability of a project having a relative error of less than or equal to 0.25 (Pred(0.25)) as compared with the results obtained by just using artificial neural network and the original model. The proposed model can also provide objective fuzzy effort estimation rule sets by adopting the learning mechanism of the artificial neural network.     

一种改进的可能模糊聚类算法*

通过分析FCM、PCM、IPCM和PFCM等流行的聚类算法和它们在噪声环境下所面临的问题,提出一种概率模糊聚类新算法（SWPFCM）,该算法结合样本加权和一种适用于噪音环境下的初始化聚类中心的方法,可以有效地消除噪声对聚类结果的影响。实验表明,SWPFCM算法具有处理大量噪声数据的能力,但对于没有噪声或噪声很少时,效果不明显,当目标样本集中出现噪声时,使用SWPFCM算法聚类将会得到满意的聚类结果。     

基于项目模糊相似度的协同过滤推荐算法

针对传统协同过滤算法中评分和标签存在的模糊性问题进行了研究,利用梯形模糊数描述评分与满意度的映射关系,在考虑评分稀疏性的基础上构建了一种新的梯形模糊评分模型以判断基于模糊评分的相似度,分析标签与项目的隶属度,构建模糊项目标签矩阵以衡量基于标签隶属度的相似度,最终采用改进的评分预测策略进行评分估计。在MovieLens数据集上的实验结果显示,所提算法在抑制项目冷启动、缓解模糊性和稀疏性问题的同时,提高了预测精度,表明了该算法的有效性。     

Application of fuzzy sets to multi-objective project management decisions

In real-world project management (PM) decision problems, input data and/or related parameters are frequently imprecise/fuzzy over the planning horizon owing to incomplete or unavailable information, and the decision maker (DM) generally faces a fuzzy multi-objective PM decision problem in uncertain environments. This work focuses on the application of fuzzy sets to solve fuzzy multi-objective PM decision problems. The proposed possibilistic linear programming (PLP) approach attempts to simultaneously minimise total project costs and completion time with reference to direct costs, indirect costs, relevant activities times and costs, and budget constraints. An industrial case illustrates the feasibility of applying the proposed PLP approach to practical PM decisions. The main advantage of the proposed approach is that the DM may adjust the search direction during the solution procedure, until the efficient solution satisfies the DM's preferences and is considered to be the preferred satisfactory solution. In particular, computational methodology developed in this work can easily be extended to any other situations and can handle the realistic PM decision problems with simplified triangular possibility distributions.     

ARMA(p,q) type high order fuzzy time series forecast method based on fuzzy logic relations

Within classic time series approaches, a time series model can be studied under 3 groups, namely AR (autoregressive model), MA (moving averages model) and ARMA (autoregressive moving averages model). On the other hand, solutions are based mostly on fuzzy AR time series models in the fuzzy time series literature. However, just a few fuzzy ARMA time series models have proposed until now. Fuzzy AR time series models have been divided into two groups named first order and high order models in the literature, highlighting the impact of model degree on forecast performance. However, model structure has been disregarded in these fuzzy AR models. Therefore, it is necessary to eliminate the model specification error arising from not utilizing of MA variables in the fuzzy time series approaches. For this reason, a new high order fuzzy ARMA(p,q) time series solution algorithm based on fuzzy logic group relations including fuzzy MA variables along with fuzzy AR variables has been proposed in this study. The main purpose of this article is to show that the forecast performance can be significantly improved when the deficiency of not utilizing MA variables. The other aim is also to show that the proposed method is better than the other fuzzy ARMA time series models in the literature from the point of forecast performance. Therefore, the new proposed method has been compared regarding forecast performance against some methods commonly used in literature by applying them on gold prices in Turkey, Istanbul Stock Exchange (IMKB) and the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX).     

Polynomial regression interval-valued fuzzy systems

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system (FLS). In order to make the type-2 FLS reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and probability type reduce reasoning method for the interval-valued FLS are developed. We have implemented the proposed non-linear (polynomial regression) statistical interval-valued type-2 FLS to perform smart washing machine control. The results show that our quadratic statistical method is more robust to design a reliable type-2 FLS and also can be extend to polynomial model.     

Neuro fuzzy schemes for fault detection in power transformer

This paper proposes fuzzy system and neural network approaches to identify the incipient faults in the power transformer using dissolved gas analysis (DGA) method. Using the IEC/IEEE DGA criteria and the gas concentration values as references the fuzzy diagnosis system and neural network are built. The proposed systems are verified using practical data collected from Electricity Board. The fuzzy system is tested with triangular, trapezoidal and Gaussian membership functions and its effectiveness is analyzed through simulation in terms of accuracy in identifying the transformer faults. The proposed Back propagation network is verified to overcome the drawbacks of conventional methods. The proposed schemes are simulated and tested in the software environment. The simulation results are presented.