MATHEMATICAL EXPECTATION ABOUT DISCRETE RANDOM VARIABLE WITH INTERVAL PROBABILITY OR FUZZY PROBABILITY

The character and an algorithm about DRVIP（ discrete random variable with interval probability） and the secured kind DRVFP （discrete random variable with crisp event-fuzzy probability） are researched. Using the fuzzy resolution theorem, the solving mathematical expectation of a DRVFP can be translated into solving mathematical expectation of a series of RVIP. It is obvious that solving mathematical expectation of a DRVIP is a typical linear programming problem. A very functional calculating formula for solving mathematical expectation of DRVIP was obtained by using the Dantzig＇s simplex method. The example indicates that the result obtained by using the functional calculating formula fits together completely with the result obtained by using the linear programming method, but the process using the formula deduced is simpler.

An Efficient Content-Based Image Retrieval System Using kNN and Fuzzy Mathematical Algorithm

The implementation of content-based image retrieval(CBIR)mainly depends on two key technologies:image feature extraction and image feature matching.In this paper,we extract the color features based on Global Color Histogram(GCH)and texture features based on Gray Level Co-occurrence Matrix(GLCM).In order to obtain the effective and representative features of the image,we adopt the fuzzy mathematical algorithm in the process of color feature extraction and texture feature extraction respectively.And we combine the fuzzy color feature vector with the fuzzy texture feature vector to form the comprehensive fuzzy feature vector of the image according to a certain way.Image feature matching mainly depends on the similarity between two image feature vectors.In this paper,we propose a novel similarity measure method based on k-Nearest Neighbors(kNN)and fuzzy mathematical algorithm(SBkNNF).Finding out the k nearest neighborhood images of the query image from the image data set according to an appropriate similarity measure method.Using the k similarity values between the query image and its k neighborhood images to constitute the new k-dimensional fuzzy feature vector corresponding to the query image.And using the k similarity values between the retrieved image and the k neighborhood images of the query image to constitute the new k-dimensional fuzzy feature vector corresponding to the retrieved image.Calculating the similarity between the two kdimensional fuzzy feature vector according to a certain fuzzy similarity algorithm to measure the similarity between the query image and the retrieved image.Extensive experiments are carried out on three data sets:WANG data set,Corel-5k data set and Corel-10k data set.The experimental results show that the outperforming retrieval performance of our proposed CBIR system with the other CBIR systems.

FUZZY MATHEMATICAL EVALUATION FOR MASONRY STRUCTURE BUILDINGS' DAMAGE GRADE CAUSED BY COAL MINING

Coal mining under buildings certainly causes surface movement and deformation, therefore, it brings about deformation even fracture for buildings. It is an important task to evaluate correcly the buildings’ damage grabe caused by coal mining. Fuzzy comprehensive evaluation,considering some factors of buildings’ fracture, has been applied to analyze the masonry structure buildings’ damage grade affer coal mining in this paper. It provides a scientific basis for buildings’reidercement before mining and maintenance or compensation after mining.

Geological Environmental Adaptability of Qingdao Rural Urbanization Based on Fuzzy Mathematical Method

Fuzzy mathematics comprehensive evaluation method is used to evaluate the geological environment suitability of rural urbanization in Qingdao City,China.A total of 5 first-level evaluation factors are selected,including environmental geological condition,geological resources,engineering geological condition,geological disaster and environmental geological problem,and human engineering activity.And there are 27 second-level evaluation factors,such as topography,land type and vegetation,nature reserve,water source protection area,groundwater quality division,and major engineering project.Qingdao City is divided into four districts of suitable area,relatively suitable area,moderately suitable area and relatively unsuitable area of ecological environment.And their characteristics are introduced.Suggestions for the developing direction of urban construction are put forward.Region of Laoshan District lying to the west of the Shilaoren is suitable to set up high-rise building;west Hongshiya may establish a waste landfill site;Jiaozhou Bay,the downstream of Dagu River,and Jihongtan Reservoir should be built as the key geological environment protection area and water source protection area.And the north Hongdao should be strictly monitored in order to control the expansion of urban construction to Jihongtan Reservoir.Mocheng District and the area north of it,Jiaozhou District and the area east of it are the ideal urban construction development areas in Qingdao City in the future.

Bi-matrix Games with Fuzzy Strategies and Fuzzy Payoffs and Their Mathematical Programming Equivalents

A fuzzy bi-matrix game（FBG）,namely a two-person non-zero-sum game with fuzzy strategies and fuzzy payoffs is proposed.We have defined and analyzed the optimal strategies of this FBG,and shown that it can be transformed into a corresponding fuzzy mathematical programming issue,for which a ranking function approach can be applied.In addition,optimal strategies of FBG for both Player I and Player II can be gotten.

Pseudo-Semi-Overlap Functions-Based Fuzzy Rough Sets Applied to Image Edge Extraction

As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and further extended for applications in image edge extraction. Firstly, a new clustering function, the pseudo-semi-overlap function, is introduced by eliminating the symmetry and right continuity present in the overlap function. The relaxed nature of this function enhances its applicability in image edge extraction. Secondly, the definitions of (I, PSO)-fuzzy rough sets are provided, using (I, PSO)-fuzzy rough sets, a pair of new fuzzy mathematical morphological operators (IPSOFMM operators) is proposed. Finally, by combining the fuzzy C-means algorithm and IPSOFMM operators, a novel image edge extraction algorithm (FCM-IPSO algorithm) is proposed and implemented. Compared to existing algorithms, the FCM-IPSO algorithm exhibits more image edges and a 73.81% decrease in the noise introduction rate. The outstanding performance of (I, PSO)-fuzzy rough sets in image edge extraction demonstrates their practical application value.

基于AHP-Fuzzy-TOPSIS帕鲁特金矿不同中段开采方法对比优化选择

随着井下开采不断向大埋深作业,通风、安全、排水等作业环境日益复杂,不同采矿方法的选择对矿山的可持续发展显得尤为重要。本文以帕鲁特金矿的开采技术条件为基础,针对4种采矿方法(崩落法、上向分层充填采矿法、分段空场嗣后充填法、梯段空场干式充填法),选取包括生产能力、采切比、损失率、贫化率、作业成本(含充填)、通风条件、生产组织和安全条件8个评价指标,运用AHP-Fuzzy-TOPSIS(层次分析-模糊数学-逼近理想解的排序法)分析模型,计算了2292 m、2050 m和1930 m三个较有代表性的中段的贴合度,并对结果进行了分析,与矿山实际生产情况贴合,验证了该方法的可行性。研究成果为下一步1930 m中段采矿方法的选择提供了理论依据,同时为其他矿井在不同生产阶段最优采矿方法选择提供了一定的借鉴意义。

A STUDY ON THE CARTOGRAPHIC FUZZY MATRIX MODEL AND MATHEMATICAL EXPRESSIONS OF CARTOGRAPHIC TERMS

On the basis of the research of the cartographic modelsmade by the authors some years ago,this paper further studies theestablishment of cartographic fuzzy matrix to make the concepts incartography e.g.,selection,deletion,mapping generalization andimage tranformation,into some precise mathematical expressions.

Ecological Suitability Evaluation on Agricultural Land in Western Jilin Province Based on Fuzzy Mathematics

[Objective] This study was to evaluate the ecological suitability of agricultural land in western Jilin Province, with the aim to provide basis for the effective application of agricultural resources and the structural adjustment of land use. [Method] The evaluation index system was constructed based on fuzzy mathematic method according to the principles of systematic, dominant, effectiveness and feasibility; based on law of tolerance, reasonable evaluation criteria were determined according to the ecological amplitude of crops; based on GIS processing, the initial data completed the mathematical operation by using the VBA program in Excel. [Result] The area of agricultural land grade I was 5 512 km2, grade II of 25 985 km2, grade Ill of 7 907 km2, and area of land not suitable for agriculture was 6 312 km2. According to the evaluation results, the key areas for land use adjustment were Zhenlai County, Da＇an County, Tongyu County and western Changling County. The directions of land use adjustment included improving irrigation and drainage conditions, governing land salinization and conversion of cropland to forest and grassland. [Conclusion] This study provided basis for the effective application of agricultural resources and ecological environment construction in western Jilin Province.

Improvements to the fuzzy mathematics comprehensive quantitative method for evaluating fault sealing

Fuzzy mathematics is an important means to quantitatively evaluate the properties of fault sealing in petroleum reservoirs.To accurately study fault sealing,the comprehensive quantitative evaluation method of fuzzy mathematics is improved based on a previous study.First,the single-factor membership degree is determined using the dynamic clustering method,then a single-factor evaluation matrix is constructed using a continuous grading function,and finally,the probability distribution of the evaluation grade in a fuzzy evaluation matrix is analyzed.In this study,taking the F1 fault located in the northeastern Chepaizi Bulge as an example,the sealing properties of faults in different strata are quantitatively evaluated using both an improved and an un-improved comprehensive fuzzy mathematics quantitative evaluation method.Based on current oil and gas distribution,it is found that our evaluation results before and after improvement are significantly different.For faults in＂best＂and＂poorest＂intervals,our evaluation results are consistent with oil and gas distribution.However,for the faults in＂good＂or＂poor＂intervals,our evaluation is not completelyconsistent with oil and gas distribution.The improved evaluation results reflect the overall and local sealing properties of target zones and embody the nonuniformity of fault sealing,indicating the improved method is more suitable for evaluating fault sealing under complicated conditions.

Evaluation on Ecological Risks of Soil Heavy Metals in a Certain Area of Sichuan by Improved Fuzzy Mathematics Method

Taking a certain area in Sichuan Province as the object of this study, this paper adopts fuzzy mathematics method to make an evaluation on ecological risks of heavy metal in soil of this area. On calculation of factors’ weights, the traditional method of giving weight according to pollutants’ concentrations fails to consider the toxicity of heavy metals, and can’t reflect their actual ecological effect. With reference to the toxicity coefficient in potential ecological risk index evaluation, this article revises the traditional fuzzy mathematics evaluation model and puts forward a new method to calculate factors’ weight by incorporating toxicity levels in weight setting. The results of this study indicate: surface soil of this area was good in general, with 91.2% samples belonging to the first level, 7.77% samples belonging to the second level, and only 1.03% belonging to the third level. Compared with the results of the evaluation method of the reality content of soil, soil quality is better than the results of the quantitative evaluation, and is closer to the actual local conditions.

Oil Tea Soup Formula Optimization Based on Orthogonal Test and Fuzzy Mathematics Sensory Evaluation

The aim of this study is to optimize the formula of oil soup, which was one of traditional food of Guangxi province, south China. Tea leaves, bone soup, beans and other minor ingredients in the formula of oil tea soup are selected as the research objects. The sensory evaluation factors such as flavor, taste, color, aroma were selected to optimize the formula of oil tea soup based on orthogonal test and fuzzy mathematics comprehensive evaluation. The results showed the most important factor that affected the quality of the oil tea soup was tea leaves content, followed by the proportion of bone soup, minor ingredient and beans content. The study indicated that the optimal recipe ofoil tea soup was as follow： 0.6% tea, 0.4% beans, and 0.5% other ingredients. The ratio of material to solution of bone soup was 1：5.

Optimal design of structural parameters for shield cutterhead based on fuzzy mathematics and multi-objective genetic algorithm

In order to improve the strength and stiffness of shield cutterhead, the method of fuzzy mathematics theory in combination with the finite element analysis is adopted. An optimal design model of structural parameters for shield cutterhead is formulated,based on the complex engineering technical requirements. In the model, as the objective function of the model is a composite function of the strength and stiffness, the response surface method is applied to formulate the approximate function of objective function in order to reduce the solution scale of optimal problem. A multi-objective genetic algorithm is used to solve the cutterhead structure design problem and the change rule of the stress-strain with various structural parameters as well as their optimal values were researched under specific geological conditions. The results show that compared with original cutterhead structure scheme, the obtained optimal scheme of the cutterhead structure can greatly improve the strength and stiffness of the cutterhead, which can be seen from the reduction of its maximum equivalent stress by 21.2%, that of its maximum deformation by 0.75%, and that of its mass by 1.04%.

The evaluation of mine geology disasters based on fuzzy mathematics and grey theory

Mine geology disasters include mine water, mine solid waste, apron and slide, ground collapse sink and underground fracture, etc.. The subject was studied in many ways, and fuzzy mathematics was usually used. It may assure the result and distinguish the dangerous rank of different areas. But it has two defects： The first is the result is not very exact, especially the border; The second is it is short of quantity. Fuzzy mathematics and grey theory were used in order to solve the problem. Firstly, mathematical model was constructed by using grey theory, so as to evaluate and forecast the dangerous rank of mining geology disaster in different areas. Then different areas were analyzed and divided by fuzzy mathematics. By doing these, similitude rules are not only studied but also differences are discriminated. Through the practice it can be known that the result is more accurate than before.

The Application of Fuzzy Mathematic in Fabrics Feel Valuation

This paper not only introduce fuzzy mathematic method into the evaluation of fabrics’ style and put forward a new comprehensive fuzzy method on the fabric’s evaluate, but also develop a set of software to set automatic valuation of fabric’s style, “the intelligent system evaluation of fabric”. The system quoted the expert system principle.

Application of Fuzzy Mathematics to the Evaluation of Drinking Water Quality in Wuhan

The quality of raw water from major water plants in Wuhan was evaluated by using Fuzzy synthetic evaluation model.It is suggested to select the alternative synthetic evaluation model when the first Fuzzy synthetic model failed in order to increase accuracy.

The Program Application on the Relative Method of Fuzzy Mathematics

The method of fuzzy mathematics for simultaneous assessment of time and intensity of earthquake hazards has been studied.This method is based on fundamental statistical indices of regional seismicity.Applying the retrieval method of fuzzy information,we can classify the time and intensity into several intervals and classes of seismic activity,then the possible time interval of large earthquakes with magnitude of M≥Ms can be estimated in a given region.Based on the preceding idea,an FRPP program is constructed.For the automatic data processing when this method is used,it is very important to design the statistical process of each index decomposition so that the program could be fit to a different sample discussed.There are some functions in the FRPP program.The man-made impact on results is reduced to the minimum as far as possible.Computation time is saved.There is a menu on which time interval,index,intensity class,and output data all can be selected.The catalog input that can be displayed on the

基于Fuzzy-TOPSIS的金矿床采矿方法优选

针对工程地质条件为复杂隐伏大型金矿床簸箕田金矿,通过数学模糊法对其采矿方法优选。首先,在初选的四种采矿方法基础上,使用逼近理想解的排序法对其指标量化,建立矩阵计算的正理想解的欧氏距离,从而得出根据贴合度确定四种采矿方法最终的优劣顺序;其次,通过数值模拟,对得到的最大应力场分布及塑性区分布分析,得到初选四种采矿方法的优劣顺序。结果表明,上向进路充填采矿法是簸箕田金矿最优采矿方法,为簸箕田金矿采矿方法选择提供了参考,也为贵州地区同类型复杂黄金矿床的开采积累了经验。

Summary of Application of Fuzzy Mathematics in Construction Project Management

Construction project management is an important aspect of civil engineering construction. How to use scientific and efficient methods to effectively manage construction projects is the focus of construction project development under the current situation. This article discusses the application of fuzzy mathematics in construction project management. The study found that in the process of construction project management, it was found that a single fuzzy mathematical method was difficult to adapt to the current complex and changeable construction projects. Combining fuzzy mathematics with other management methods and computer applications can better simplify complex things, reduce human subjectivity, increase calculation speed, and achieve a combination of qualitative and quantitative research;selection of optimization schemes and risk assessment, etc. All have a good effect, and can better deal with possible or uncertain things and emergencies in the process of project management. At the same time, combining fuzzy mathematics with heuristic algorithms or meta-heuristic algorithms can make research more objective, improve management efficiency and calculation speed.

A Mathematical Theory of Big Data

This article presents a cardinality approach to big data,a fuzzy logic-based approach to big data,a similarity-based approach to big data,and a logical approach to the marketing strategy of social networking services.All these together constitute a mathematical theory of big data.This article also examines databases with infinite attributes.The research results reveal that relativity and infinity are two characteristics of big data.The relativity of big data is based on the theory of fuzzy sets.The relativity of big data leads to the continuum from small data to big data,big data-driven small data analytics to become statistical significance.The infinity of big data is based on the calculus and cardinality theory.The infinity of big data leads to the infinite similarity of big data.The proposed theory in this article might facilitate the mathematical research and development of big data,big data analytics,big data computing,and data science with applications in intelligent business analytics and business intelligence.