Dynamic Analysis of Customer Demand Based on Intuitionistic Fuzzy Number in Product Planning

To address the fuzziness and variability in determining customer demand importance,a dynamic analysis method based on intuitionistic fuzzy numbers is proposed.First,selected customers use intuitionistic fuzzy numbers to represent the importance of each demand.Then,the preference information is aggregated using customer weights and time period weights through the intuitionistic fuzzy ordered weighted average operator,yielding a dynamic vector of the subjective importance of the demand index.Finally,the feasibility of the proposed method is demonstrated through an application example of a vibrating sorting screen.

Fuzzy finite difference method for heat conduction analysis with uncertain parameters

A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbation method, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems.

Solution and Analysis of the Fuzzy Volterra Integral Equations viaHomotopy Analysis Method

Homotopy Analysis Method(HAM)is semi-analytic method to solve the linear and nonlinear mathematical models which can be used to obtain the approximate solution.The HAM includes an auxiliary parameter,which is an efficient way to examine and analyze the accuracy of linear and nonlinear problems.The main aim of this work is to explore the approximate solutions of fuzzy Volterra integral equations(both linear and nonlinear)with a separable kernel via HAM.This method provides a reliable way to ensure the convergence of the approximation series.A new general form of HAM is presented and analyzed in the fuzzy domain.A qualitative convergence analysis based on the graphical method of a fuzzy HAM is discussed.The solutions sought by the proposed method show that the HAM is easy to implement and computationally quite attractive.Some solutions of fuzzy second kind Volterra integral equations are solved as numerical examples to show the potential of the method.The results also show that HAM provides an easy way to control and modify the convergence area in order to obtain accurate solutions.

Structural Reliability Analysis Method in Fuzzy Environment

In this paper, the fuzzy-set-based structural possibility theory is investigated, and this theory can be used to deal with the subjective uncertainties in the design of engineering structures. Furthermore, a comprehensive model of structural safety assessment, which can merge subjective uncertainties with objective uncertainties, is presented. In this model, the fuzziness of stress-strength inference model, safety margin functions of single or multiple limit-state, structural failure state and the final assessment result are taken into account. This continuous model can be transformed into an equivalent model of probability-based and solved by the present structural reliability analysis method and parallel algorithm. An example is given to show the main idea of the method presented in this paper.

A precise tidal prediction mechanism based on the combination of harmonic analysis and adaptive network-based fuzzy inference system model

An efficient and accurate prediction of a precise tidal level in estuaries and coastal areas is indispensable for the management and decision-making of human activity in the field wok of marine engineering. The variation of the tidal level is a time-varying process. The time-varying factors including interference from the external environment that cause the change of tides are fairly complicated. Furthermore, tidal variations are affected not only by periodic movement of celestial bodies but also by time-varying interference from the external environment. Consequently, for the efficient and precise tidal level prediction, a neuro-fuzzy hybrid technology based on the combination of harmonic analysis and adaptive network-based fuzzy inference system（ANFIS）model is utilized to construct a precise tidal level prediction system, which takes both advantages of the harmonic analysis method and the ANFIS network. The proposed prediction model is composed of two modules： the astronomical tide module caused by celestial bodies’ movement and the non-astronomical tide module caused by various meteorological and other environmental factors. To generate a fuzzy inference system（FIS） structure,three approaches which include grid partition（GP）, fuzzy c-means（FCM） and sub-clustering（SC） are used in the ANFIS network constructing process. Furthermore, to obtain the optimal ANFIS based prediction model, large numbers of simulation experiments are implemented for each FIS generating approach. In this tidal prediction study, the optimal ANFIS model is used to predict the non-astronomical tide module, while the conventional harmonic analysis model is used to predict the astronomical tide module. The final prediction result is performed by combining the estimation outputs of the harmonious analysis model and the optimal ANFIS model. To demonstrate the applicability and capability of the proposed novel prediction model, measured tidal level samples of Fort Pulaski tidal station are selected as the testing database. Simulation and experimental results confirm that the proposed prediction approach can achieve precise predictions for the tidal level with high accuracy, satisfactory convergence and stability.

FUZZY PRINCIPAL COMPONENT ANALYSIS AND ITS KERNEL-BASED MODEL

Principal Component Analysis(PCA)is one of the most important feature extraction methods,and Kernel Principal Component Analysis(KPCA)is a nonlinear extension of PCA based on kernel methods.In real world,each input data may not be fully assigned to one class and it may partially belong to other classes.Based on the theory of fuzzy sets,this paper presents Fuzzy Principal Component Analysis(FPCA)and its nonlinear extension model,i.e.,Kernel-based Fuzzy Principal Component Analysis(KFPCA).The experimental results indicate that the proposed algorithms have good performances.

AN ANALYSIS OF THE APPLICABILITY OF FUZZY CLUSTERING IN ESTABLISHING AN INDEX FOR THE EVALUATION OF METEOROLOGICAL SERVICE SATISFACTION

An evaluation index is a prerequisite for the scientific evaluation of a public meteorological service.This paper aims to explore a technical method for determining and screening evaluation indicators.Based on public satisfaction survey data obtained in Wafangdian,China in 2010,this study investigates the suitability of fuzzy clustering analysis method in establishing an evaluation index.Through quantitative analysis of multilayer fuzzy clustering of various evaluation indicators,correlation analysis indicates that if the results of clustering were identical for two evaluation indicators in the same sub-evaluation layer,then one indicator could be removed,or the two indicators merged.For evaluation indicators in different sub-evaluation layers,although clustering reveals attribute correlations,these indicators may not be substituted for one another.Analysis of the applicability of the fuzzy clustering method shows that it plays a certain role in the establishment and correction of an evaluation index.

Stability analysis of the simplest Takagi-Sugeno fuzzy control system using circle criterion

A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest T-S fuzzy controller. Besides, this sufficient condition is featured by a graphical interpretation, which makes the condition straightforward to be used. Comparisons are drawn between the performance of the simplest T-S fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this sufficient condition can be applied to both stable and unstable plants.

A New Algorithm for Black-start Zone Partitioning Based on Fuzzy Clustering Analysis

On the process of power system black start after an accident, it can help to optimize the resources allocation and accelerate the recovery process that decomposing the power system into several independent partitions for parallel recovery. On the basis of adequate consideration of fuzziness of black-start zone partitioning, a new algorithm based on fuzzy clustering analysis is presented. Characteristic indexes are extracted fully and accurately. The raw data matrix is made up of the electrical distance between every nodes and blackstart resources. Closure transfer method is utilized to get the dynamic clustering. The availability and feasibility of the proposed algorithm are verified on the New-England 39 bus system at last.

New Configurations of the Fuzzy Fractional Differential Boussinesq Model with Application in Ocean Engineering and Their Analysis in Statistical Theory

The fractional-order Boussinesq equations(FBSQe)are investigated in this work to see if they can effectively improve the situation where the shallow water equation cannot directly handle the dispersion wave.The fuzzy forms of analytical FBSQe solutions are first derived using the Adomian decomposition method.It also occurs on the sea floor as opposed to at the functionality.A set of dynamical partial differential equations(PDEs)in this article exemplify an unconfined aquifer flow implication.Thismethodology can accurately simulate climatological intrinsic waves,so the ripples are spread across a large demographic zone.The Aboodh transform merged with the mechanism of Adomian decomposition is implemented to obtain the fuzzified FBSQe in R,R^(n) and(2nth)-order involving generalized Hukuhara differentiability.According to the system parameter,we classify the qualitative features of the Aboodh transform in the fuzzified Caputo and Atangana-Baleanu-Caputo fractional derivative formulations,which are addressed in detail.The illustrations depict a comparison analysis between the both fractional operators under gH-differentiability,as well as the appropriate attributes for the fractional-order and unpredictability factorsσ∈[0,1].A statistical experiment is conducted between the findings of both fractional derivatives to prevent changing the hypothesis after the results are known.Based on the suggested analyses,hydrodynamic technicians,as irrigation or aquifer quality experts,may be capable of obtaining an appropriate storage intensity amount,including an unpredictability threshold.

Kernel method-based fuzzy clustering algorithm

The fuzzy C-means clustering algorithm(FCM) to the fuzzy kernel C-means clustering algorithm(FKCM) to effectively perform cluster analysis on the diversiform structures are extended, such as non-hyperspherical data, data with noise, data with mixture of heterogeneous cluster prototypes, asymmetric data, etc. Based on the Mercer kernel, FKCM clustering algorithm is derived from FCM algorithm united with kernel method. The results of experiments with the synthetic and real data show that the FKCM clustering algorithm is universality and can effectively unsupervised analyze datasets with variform structures in contrast to FCM algorithm. It is can be imagined that kernel-based clustering algorithm is one of important research direction of fuzzy clustering analysis.

Evaluation of Farmland Drainage Water Quality by Fuzzy–Gray Combination Method

The complex relationships between indicators and water conditions cause fuzzy and gray uncertainties in evaluation of water quality. Compared to conventional single-factor evaluation methods, the combination evaluation method can consider these two uncertainties to produce more objective and reasonable evaluation results. In this paper, we propose a combination evaluation method with two main parts:(1) the use of fuzzy comprehensive evaluation and gray correlation analysis as submodels with which to consider the fuzzy and gray uncertainties and(2) the establishment of a combination model based on minimum bias squares. In addition, using this method, we evaluate the water quality of a ditch in a typical rice–wheat system of Yixing city in the Taihu Lake Basin during three rainfall events. The results show that the ditch water quality is not good and we found the chemical oxygen demand to be the key indicator that affects water quality most significantly. The proposed combination evaluation method is more accurate and practical than single-factor evaluation methods in that it considers the uncertainties of fuzziness and grayness.

Multiple Criteria Analysis for Energy Storage Selection

In view of the current and predictable energy shortage and environmental concerns, the exploitation of renewable energy sources offers great potential to meet increasing energy demands and to decrease depend- ence on fossil fuels. However, introducing these sources will be more attractive provided they operate in conjunction with energy storage systems (ESS). Furthermore, effective energy storage management is essential to achieve a balance between power quality, efficiency, costs and environmental constraints. This paper presents a method based on the analytic hierarchy process and fuzzy multi-rules and multi-sets. By exploiting a multiple criteria analysis, the proposed methods evaluate the operation of storage energy systems such as: pumped hydro and compressed air energy storage, H2, flywheel, super-capacitors and lithium-ion storage as well as NaS advanced batteries and VRB flow battery. The main objective of the study is to find the most appropriate ESS consistent with a power quality priority. Several parameters are used for the investigation: efficiency, load management, technical maturity, costs, environmental impact and power quality.

Harmoniousness analysis of total amount control of water use

Based on the fundamental principles of total amount control of water use, the harmony theory was used in this study to develop a concept of the degree of harmony of total amount control of water use. Based on this concept, the harmoniousness of total amount control of water use was analyzed in terms of the supply and demand of water resources, water resources management, water use benefits, and water-saving level. An evaluation index system of the degree of harmony of total amount control of water use was established, and a method for calculation of the degree of harmony of total amount control of water use was developed based on the analytic hierarchy process （AHP） and fuzzy comprehensive analysis （FCA） methods. The new evaluation index system was applied to a certain area in Jiangsu Province, China. The degree of harmony of total amount control of water use over this area was calculated for different years. Results indicate that the evaluation index system and calculation method proposed in this study are feasible, and such a harmoniousness analysis can provide scientific references for the strict water resources management system that will be implemented in China in the near future.

Numerical investigation on MHD Jeffery-Hamel nanofluid flow with different nanoparticles using fuzzy extension of generalized dual parametric homotopy algorithm

This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual parametric homotopy algorithm.The nanofluids have been formulated to enhance the thermophysical characteristics of fluids,including thermal diffusivity,conductivity,convective heat transfer coefficients and viscosity.Due to the presence of distinct nanofluids,a change in the value of volume fraction occurs that influences the velocity profiles of the flow.The short value of nanoparticles volume fraction is considered an uncertain parameter and represented in a triangular fuzzy number range among[0.0,0.1,0.2].A novel generalized dual parametric homotopy algorithm with fuzzy extension is used here to study the fuzzy velocities at various channel positions.Finally,the effectiveness of the proposed approach has been demonstrated through a comparison with the available results in the crisp case.

Application of entropy-based fuzzy matter-element analysis in seepage monitoring of RCC dam

Taking account of the fuzzy results of the seepage monitoring analysis of roller compacted concrete(RCC)dam and uncertainties of the individual indicator evaluation,the fuzzy matter-element model of seepage monitoring of RCC dam analysis has been established with the use of the fuzzy matter-element analysis theory and the concept of euclid approach degree.The use of entropy theory can calculate the weighting factor through the disorder utility values of the information reflected by the data itself,which can effectively avoid the problems of weight distribution and uncertainties of subjective judgments of the seepage monitoring analysis of roller compacted concrete dam.And further the example shows that the analysis of entropy-based fuzzy matter-element analysis model of the seepage monitoring of roller compacted concrete dam is in accordance with the actual situation,which verifies the effectiveness of the method.

一种SPA集转化Fuzzy集的新方法

结合SPA集,Vague集及Fuzzy集理论分析,在此基础上提出了一种基于SPA集向Fuzzy集转化的新方法,给出了SPA集转化Fuzzy集的相关准则及证明。通过示例验证了该算法的有效性与合理性。

矿井安全性综合评价的AHP—Fuzzy数学模型及其应用

针对目前煤矿安全状况方面存在的问题， 以矿井安全性为研究对象， 建立了矿井安全性综合评价的指标体系。运用层次分析法和模糊数学方法， 建立了矿井安全性综合评价的ＡＨＰ—Ｆｕｚｚｙ 数学模型， 给出了具体的综合评价方法并应用于煤矿实际， 取得了令人满意的效果。

一种基于Fuzzy聚类分析的疾病预测诊断模型

使用模糊聚类分析的方法,在医学上建立了疾病预测诊断模型,并将其应用于临床疾病诊断。通过实例检验表明,该方法具有良好的实际应用前景。

Water quality evaluation based on improved fuzzy matter-element method

For natural water, method of water quality evaluation based on improved fuzzy matter-element evaluation method is presented. Two important parts are improved, the weights determining and fuzzy membership functions. The coefficient of variation of each indicator is used to determine the weight instead of traditional calculating superscales method. On the other hand, fuzzy matter-elements are constructed, and normal membership degrees are used instead of traditional trapezoidal ones. The composite fuzzy matter-elements with associated coefficient are constructed through associated transformation. The levels of natural water quality are determined according to the principle of maximum correlation. The improved fuzzy matter-element evaluation method is applied to evaluate water quality of the Luokou mainstream estuary at the first ten weeks in 2011 with the coefficient of variatiola method determining the weights. Water quality of Luokou mainstream estuary is dropping from level I to level II. The results of the improved evaluation method are basically the same as the official water quality. The variation coefficient method can reduce the workload, and overcome the adverse effects from abnormal values, compared with the traditional calculating superscales method. The results of improved fuzzy matter- element evaluation method are more credible than the ones of the traditional evaluation method. The improved evaluation method can use information of monitoring data more scientifically and comprehensively, and broaden a new evaluation method for water quality assessment.