Rock burst laws in deep mines based on combined model of membership function and dominance-based rough set

Rock bursts are spontaneous, violent fracture of rock that can occur in deep mines, and the likelihood of rock bursts occurring increases as depth of the mine increases. Rock bursts are also affected by the compressive strength, tensile strength, tangential strength, elastic energy index, etc. of rock, and the relationship between these factors and rock bursts in deep mines is difficult to analyze from quantitative point. Typical rock burst instances as a sample set were collected, and membership function was introduced to process the discrete values of these factors with the discrete factors as condition attributes and rock burst situations as decision attributes. Dominance-based rough set theory was used to generate preference rules of rock burst, and eventually rock burst laws analysis in deep mines with preference relation was taken. The results show that this model for rock burst laws analysis in deep mines is more reasonable and feasible, and the prediction results are more scientific.

Rough function model and rough membership function

Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.

New Methods of Fitting the Membership Function of Oceanic Water Masses

After reviewing the analytical theories of T S curve, some methods of T S relationship, and fuzzy sets for studying water masses, new methods of fitting the membership function of oceanic water masses are presented based on the characteristics of T S curve family of oceanic water masses. The membership functions of oceanic Subsurface Water Mass with high salinity and Intermediate Water Mass with low salinity are fitted and discussed using the new methods. The proposed methods are useful in analyzing the mixing and modifying processes of these water masses, especially in tracing their sources. The principles and formulae of the new methods and examples are given.

INVESTIGATION ON MAKING MEMBERSHIP FUNCTION OF WATER MASS FROM MIXING MODIFIED PROCESS

A water mass in the sea area under investigation is defined as a fuzzy subset in the discourse universe. Possible forms of membership function of water masses in the mixing modified process are discussed with the mixing theory for conservative concentration of sea water. It may provide bases for making membership functions. Results in this paper may be extended and applied to shallow water. Examples and discussion are given in this paper.

Research on Method R_w for Discrete Membership Functions

In this paper, a number of concepts related to continuous membership function (CMFs) advanced in [2] are extended to discrete membership functions (DMFs) in the light of the characteristics of DMFs so that fuzzy reasoning method R. based upon CMFs suits the case of DMFs.

Describing Fuzzy Membership Function and Detecting the Outlier by Using Five Number Summary of Data

One of the most important activities in data science is defining a membership function in fuzzy system. Although there are few ways to describe membership function like artificial neural networks, genetic algorithms etc.;they are very complex and time consuming. On the other hand, the presence of outlier in a data set produces deceptive results in the modeling. So it is important to detect and eliminate them to prevent their negative effect on the modeling. This paper describes a new and simple way of constructing fuzzy membership function by using five-number summary of a data set. Five states membership function can be created in this new method. At the same time, if there is any outlier in the data set, it can be detected with the help of this method. Usually box plot is used to identify the outliers of a data set. So along with the new approach, the box plot has also been drawn so that it is understood that the results obtained in the new method are accurate. Several real life examples and their analysis have been discussed with graph to demonstrate the potential of the proposed method. The results obtained show that the proposed method has given good results. In the case of outlier, the proposed method and the box plot method have shown similar results. Primary advantage of this new procedure is that it is not as expensive as neural networks, and genetic algorithms.

集对模糊联系数构建与因素影响重要性分析

为研究系统及其在因素影响下的安全性特征,必须考虑各方面的数据模糊性和不确定性。因此需要一种能同时表示系统及数据模糊性和不确定性的方法,为此提出了一种结合模糊数学隶属函数和集对分析联系数的方法。首先,论述了两者的等效关系;然后,通过将各模糊语义分级中隶属函数的积分与总积分的比值作为该语义对应集对联系数的系数,建立单因素集对模糊联系数;使用同、异、反三状态逻辑真值表将单因素集对模糊联系数耦合形成多因素集对模糊联系数;最后,提出使用单因素集对模糊联系数的系统安全因素影响分析方法。通过两因素五级语义划分以系统安全为目标构建了集对模糊类联系数,并分析了两因素对系统安全影响的程度和排序。研究表明,将模糊数学隶属函数与集对分析联系数关联起来能同时描述数据的模糊性和不确定性,具有较好的研究性质和前景。

New Approaches to the Prognosis and Diagnosis of Breast Cancer Using Fuzzy Expert Systems

Breast cancer remains a significant global health challenge, necessitating effective early detection and prognosis to enhance patient outcomes. Current diagnostic methods, including mammography and MRI, suffer from limitations such as uncertainty and imprecise data, leading to late-stage diagnoses. To address this, various expert systems have been developed, but many rely on type-1 fuzzy logic and lack mobile-based applications for data collection and feedback to healthcare practitioners. This research investigates the development of an Enhanced Mobile-based Fuzzy Expert system (EMFES) for breast cancer pre-growth prognosis. The study explores the use of type-2 fuzzy logic to enhance accuracy and model uncertainty effectively. Additionally, it evaluates the advantages of employing the python programming language over java for implementation and considers specific risk factors for data collection. The research aims to dynamically generate fuzzy rules, adapting to evolving breast cancer research and patient data. Key research questions focus on the comparative effectiveness of type-2 fuzzy logic, the handling of uncertainty and imprecise data, the integration of mobile-based features, the choice of programming language, and the creation of dynamic fuzzy rules. Furthermore, the study examines the differences between the Mamdani Inference System and the Sugeno Fuzzy Inference method and explores challenges and opportunities in deploying the EMFES on mobile devices. The research identifies a critical gap in existing breast cancer diagnostic systems, emphasizing the need for a comprehensive, mobile-enabled, and adaptable solution by developing an EMFES that leverages Type-2 fuzzy logic, the Sugeno Inference Algorithm, Python Programming, and dynamic fuzzy rule generation. This study seeks to enhance early breast cancer detection and ultimately reduce breast cancer-related mortality.

适应电压支撑下的光伏发电机组最大功率点控制技术

常规的光伏发电机组最大功率点控制技术,在机械功率的调整上,缺少对适应电压支撑的考虑,导致最大功率点控制效果不好。基于此,提出适应电压支撑下的光伏发电机组最大功率点控制技术。使用功率信号反馈法,检测光伏发电机组的功率,将光伏发电机组的固有功率,作为主要参数。根据发电机组运行状态点的变化,对光伏发电机组功率进行跟踪,以光伏发电机组功率跟踪结果为基础,在适应电压支撑下,通过双输入单输出的结构,调节机械功率,导入调节后的机械功率,将其作为最大功率点控制的基础数据。按照隶属函数,对控制器参数进行实时调整,从而完成对光伏发电机组最大功率点控制。结果表明,在使用本文设计的方法进行控制后,光伏发电机组的最大功率振幅有效降低,控制效果较好,具有较好应用价值。

基于五元引力减法集对势的溃坝环境影响评价

分析水库溃坝风险的综合影响,诊断识别溃坝环境影响的脆弱性指标。在集对分析原理的基础上,通过改进五元隶属度函数的构造方式,结合五元引力减法集对势及级别特征值,构建了基于五元引力减法集对势的溃坝环境影响评价模型,应用于沙河集水库并进行分析和论证。结果表明,该模型在水库溃坝环境影响中评价结果相比其他评价方法更为合理可靠,且评价结果是一实数值,具有一定的精确性。对评价指标进行诊断识别,其中河道形态、植被覆盖、土壤环境、污染工业4个评价指标是影响沙河集水库溃坝环境评价结果的主要因素。五元引力减法集对势的溃坝环境影响评价模型可为水库溃坝环境影响评价提供一种新的思路。

Traffic Flow Data Forecasting Based on Interval Type-2 Fuzzy Sets Theory

This paper proposes a long-term forecasting scheme and implementation method based on the interval type-2 fuzzy sets theory for traffic flow data. The type-2 fuzzy sets have advantages in modeling uncertainties because their membership functions are fuzzy. The scheme includes traffic flow data preprocessing module, type-2 fuzzification operation module and long-term traffic flow data forecasting output module, in which the Interval Approach acts as the core algorithm. The central limit theorem is adopted to convert point data of mass traffic flow in some time range into interval data of the same time range (also called confidence interval data) which is being used as the input of interval approach. The confidence interval data retain the uncertainty and randomness of traffic flow, meanwhile reduce the influence of noise from the detection data. The proposed scheme gets not only the traffic flow forecasting result but also can show the possible range of traffic flow variation with high precision using upper and lower limit forecasting result. The effectiveness of the proposed scheme is verified using the actual sample application. © 2014 Chinese Association of Automation.

Modelling spatial vagueness based on type-2 fuzzy set

The modelling and formal characterization of spatial vagueness plays an increasingly important role in the imple- mentation of Geographic Information System (GIS). The concepts involved in spatial objects of GIS have been investigated and acknowledged as being vague and ambiguous. Models and methods which describe and handle fuzzy or vague (rather than crisp or determinate) spatial objects, will be more necessary in GIS. This paper proposes a new method for modelling spatial vagueness based on type-2 fuzzy set, which is distinguished from the traditional type-1 fuzzy methods and more suitable for describing and implementing the vague concepts and objects in GIS.

A NEW UNSUPERVISED CLASSIFICATION ALGORITHM FOR POLARIMETRIC SAR IMAGES BASED ON FUZZY SET THEORY

In this letter, a new method is proposed for unsupervised classification of terrain types and man-made objects using POLarimetric Synthetic Aperture Radar (POLSAR) data. This technique is a combi-nation of the usage of polarimetric information of SAR images and the unsupervised classification method based on fuzzy set theory. Image quantization and image enhancement are used to preprocess the POLSAR data. Then the polarimetric information and Fuzzy C-Means (FCM) clustering algorithm are used to classify the preprocessed images. The advantages of this algorithm are the automated classification, its high classifica-tion accuracy, fast convergence and high stability. The effectiveness of this algorithm is demonstrated by ex-periments using SIR-C/X-SAR (Spaceborne Imaging Radar-C/X-band Synthetic Aperture Radar) data.

Big Data Audit of Banks Based on Fuzzy Set Theory to Evaluate Risk Level

The arrival of big data era has brought new opportunities and challenges to the development of various industries in China.The explosive growth of commercial bank data has brought great pressure on internal audit.The key audit of key products limited to key business areas can no longer meet the needs.It is difficult to find abnormal and exceptional risks only by sampling analysis and static analysis.Exploring the organic integration and business processing methods between big data and bank internal audit,Internal audit work can protect the stable and sustainable development of banks under the new situation.Therefore,based on fuzzy set theory,this paper determines the membership degree of audit data through membership function,and judges the risk level of audit data,and builds a risk level evaluation system.The main features of this paper are as follows.First,it analyzes the necessity of transformation of the bank auditing in the big data environment.The second is to combine the determination of the membership function in the fuzzy set theory with the bank audit analysis,and use the model to calculate the corresponding parameters,thus establishing a risk level assessment system.The third is to propose audit risk assessment recommendations,hoping to help bank audit risk management in the big data environment.There are some shortcomings in this paper.First,the amount of data acquired is not large enough.Second,due to the lack of author’knowledge,there are still some deficiencies in the analysis of audit risk of commercial banks.

DISCUSSION OF SOME CONCEPTIONS OF A WATER MASS BASED ON THE THEORY OF FUZZY SETS

The fundamental principle for differentiating water masses is a strict consideration of their relative "interior homogeneity" and obvious "exterior differences" with others in characteristics. The conceptions of water type, water mass and water system are dealt with on the basis of the theory of fuzzy sets. A proposal to apply the theory of fuzzy sets to define the water mass and its core, independent area, boundary and mixing area is put forward.As an example, the membership function of the surface water masses in the Yellow Sea and East China Sea in August, 1979, are considered. Their cores, independent areas, boundaries, mixing areas and the approximation degrees between different water masses are calculated respectively. The water masses are ranged according to their fuzzy degrees.

A novel vague set approach for selective contrast enhancement of mammograms using multiresolution

The proposed algorithm introduces a novel vague set approach to develop a selective but robust, flexible and intelligent contrast enhancement technique for mammograms. Wavelet based filtering analysis can produce Low Frequency (LF) and High Frequency (HF) subbands of the original input images. The extremely small size microcalcifications become visible under multiresolution techniques. LF subband is then fuzzified by conventional fuzzy c-means clustering (FCM) algorithm with justified number of clusters. HF components, representing the narrow protrusions and other fine details are also fuzzified by FCM with justified number of clusters. Vague set approach captures the hesitancies and uncertainties of truly affected masses/other breast abnormalities with normal glandular tissues. After highlighting the masses/microcalcifications accurately, both LF and HF subbands are transformed back to the original resolution by inverse wavelet transform. The results show that the proposed method can successfully enhance the selected regions of mammograms and provide better contrast images for visual interpretation.

Modeling Multisource-heterogeneous Information Based on Random Set and Fuzzy Set Theory

This paper presents a new idea, named as modeling multisensor-heterogeneous information, to incorporate the fuzzy logic methodologies with mulitsensor-multitarget system under the framework of random set theory. Firstly, based on strong random set and weak random set, the unified form to describe both data (unambiguous information) and fuzzy evidence (uncertain information) is introduced. Secondly, according to signatures of fuzzy evidence, two Bayesian-markov nonlinear measurement models are proposed to fuse effectively data and fuzzy evidence. Thirdly, by use of "the models-based signature-matching scheme", the operation of the statistics of fuzzy evidence defined as random set can be translated into that of the membership functions of relative point state variables. These works are the basis to construct qualitative measurement models and to fuse data and fuzzy evidence.

Commonsense Reasoning and Nonmonotonic Aggregation Connectives on Fuzzy Sets

Commonsense representation and manipulation based on fuzzy logic is a new research field which handles the incompleteness, error-tolerability (allow exceptions) and uncertainty associated with commonsense knowledge. In this paper, we introduce a pair of nonmonotonic aggregation connectives on fuzzy sets-soft intersection and soft union, in the light of Zadeh’s fuzzy set theory. Some important features of the nonmonotonic connectives are also discussed.

区间值犹豫模糊集群决策模型及其应用

为了更好地解决区间值犹豫模糊集(IVHFS)群决策问题,利用平面向量建立了一种可以从多个角度判定方案优劣的群决策模型.首先,在IVHFS中定义了区间值隶属度的中位数、区间值隶属度的清晰度,并以此通过构造平面向量来刻画IVHFS.其次,通过利用平面向量簇刻画IVHFS建立了区间值犹豫模糊元(IVHFE)的外部固定函数模型和内部稳定函数模型,给出比较2个IVHFE大小的准则和计算二者距离的方法,并根据所有方案的外部固定函数值和内部稳定函数值分别计算了测评准则的外部权重和内部权重(依据外部权重与内部权重的相离程度值来确定测评准则的综合权重).再次,通过利用参数调整方案的外部固定函数值与内部稳定函数值的比例计算了各个方案的综合决策值.最后,利用数值算例验证了本文方法的可行性.