Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

Fuzzy Henstock-Kurzweil Triple Integral on a Type 1 Quasi-Fuzzy Parallelepipedal Domain

In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.

Proportion Integration Differentiation(PID)Control Strategy of Belt Sander Based on Fuzzy Algorithm

Aiming at solving the problems of response lag and lack of precision and stability in constant grinding force control of industrial robot belts,a constant force control strategy combining fuzzy control and proportion integration differentiation(PID)was proposed by analyzing the signal transmission process and the dynamic characteristics of the grinding mechanism.The simulation results showed that compared with the classical PID control strategy,the system adjustment time was shortened by 98.7%,the overshoot was reduced by 5.1%,and the control error was 0.2%-0.5%when the system was stabilized.The optimized fuzzy control system had fast adjustment speeds,precise force control and stability.The experimental analysis of the surface morphology of the machined blade was carried out by the industrial robot abrasive grinding mechanism,and the correctness of the theoretical analysis and the effectiveness of the control strategy were verified.

Unique Solution of Integral Equations via Intuitionistic Extended Fuzzy b-Metric-Like Spaces

In this manuscript,our goal is to introduce the notion of intuitionistic extended fuzzy b-metric-like spaces.We establish some fixed point theorems in this setting.Also,we plot some graphs of an example of obtained result for better understanding.We use the concepts of continuous triangular norms and continuous triangular conorms in an intuitionistic fuzzy metric-like space.Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions.Triangular conorms are known as dual operations of triangular norms.The obtained results boost the approaches of existing ones in the literature and are supported by some examples and applications.

Integrated classification method of tight sandstone reservoir based on principal component analysise simulated annealing genetic algorithmefuzzy cluster means

In this research,an integrated classification method based on principal component analysis-simulated annealing genetic algorithm-fuzzy cluster means(PCA-SAGA-FCM)was proposed for the unsupervised classification of tight sandstone reservoirs which lack the prior information and core experiments.A variety of evaluation parameters were selected,including lithology characteristic parameters,poro-permeability quality characteristic parameters,engineering quality characteristic parameters,and pore structure characteristic parameters.The PCA was used to reduce the dimension of the evaluation pa-rameters,and the low-dimensional data was used as input.The unsupervised reservoir classification of tight sandstone reservoir was carried out by the SAGA-FCM,the characteristics of reservoir at different categories were analyzed and compared with the lithological profiles.The analysis results of numerical simulation and actual logging data show that:1)compared with FCM algorithm,SAGA-FCM has stronger stability and higher accuracy;2)the proposed method can cluster the reservoir flexibly and effectively according to the degree of membership;3)the results of reservoir integrated classification match well with the lithologic profle,which demonstrates the reliability of the classification method.

Fuzzy Henstock-Kurzweil Triple Integral

In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions for a Henstock triple integral and numerical example is presented in order to show the application and the consequence of the method.

Lebesgues-Stieltjes Integrals of Fuzzy Stochastic Processes with Respect to Finite Variation Processes

Let be a fuzzy stochastic process and be a real valued finite variation process. We define the Lebesgue-Stieltjes integral denoted by for each by using the selection method, which is direct, nature and different from the indirect definition appearing in some references. We shall show that this kind of integral is also measurable, continuous in time t and bounded a.s. under the Hausdorff metric.

On AP-Henstock Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties.

Fuzzy Inventory Model under Selling Price Dependent Demand and Variable Deterioration with Fully Backlogged Shortages

The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.

On Henstock-Stieltjes Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.

模糊数值函数Riemann-Stieltjes积分的相关性质

利用模糊Riemann-Stieltjes积分的定义,讨论了模糊数值函数Riemann-Stieltjes积分序列的2类收敛定理,这些结论对模糊随机积分的研究将起到很重要的作用.

金融保险集团一体化战略的A-FUZZY分析模型及实证研究

随着金融体系深化改革的持续推进,保险业、证券业和银行业的混业经营变得越来越普遍,为了在全球化市场上获得持久竞争优势,金融机构跨行业经营方式也开始向集团化和一体化趋势发展,金融保险集团的一体化成为全球保险业经营体制的最大创新,对于深化金融改革的中国保险行业来说越发重要。文章基于AHP模糊综合量化评价方法构建科学的金融保险集团一体化战略评价模型,采用专家打分数据进行实证分析,发现在一体化战略中组织能力的权重最高,业务创新和资源整合是金融保险集团一体化战略的重要助推器。

模糊Riemann-Stieltjes积分的收敛定理

模糊Riemann-Stieltjes积分是模糊分析中的一类重要的模糊积分,但相应的积分序列的收敛定理尚未见到。将给出模糊数值函数列关于实函数和模糊数值函数关于实函数列的两类模糊Riemann-Stieltjes积分序列的收敛定理。

Robust Fuzzy Tracking Control for Nonlinear Networked Control Systems with Integral Quadratic Constraints

This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.

Selection of the best initial orbital elements of satellite based on fuzzy integration evaluation method

The fuzzy integration evaluation method （FIEM） is studied in order to select the best orbital elements from the multi-group initial orbits determined by a satellite TT＆C （Tracking, Telemetry and Control） center with all kinds of data sources. By employing FIEM together with the experience of TT＆C experts, the index system to evaluate the selection of the best initial orbits is established after the data sources and orbit determination theories are studied. Besides, the concrete steps in employing the method are presented. Moreover, by taking the objects to be evaluated as evaluation experts, the problem of how to generate evaluation matrices is solved. Through practical application, the method to select the best initial orbital elements has been proved to be flexible and effective The originality of the method is to find a new evaluation criterion （comparing the actually tracked orbits） replacing the traditional one （comparing the nominal orbits） for selecting the best orbital elements.

Integrated guidance and control of guided projectile with multiple constraints based on fuzzy adaptive and dynamic surface

Based on fuzzy adaptive and dynamic surface(FADS),an integrated guidance and control(IGC)approach was proposed for large caliber naval gun guided projectile,which was robust to target maneuver,canard dynamic characteristics,and multiple constraints,such as impact angle,limited measurement of line of sight(LOS)angle rate and nonlinear saturation of canard deflection.Initially,a strict feedback cascade model of IGC in longitudinal plane was established,and extended state observer(ESO)was designed to estimate LOS angle rate and uncertain disturbances with unknown boundary inside and outside of system,including aerodynamic parameters perturbation,target maneuver and model errors.Secondly,aiming at zeroing LOS angle tracking error and LOS angle rate in finite time,a nonsingular terminal sliding mode(NTSM)was designed with adaptive exponential reaching law.Furthermore,combining with dynamic surface,which prevented the complex differential of virtual control laws,the fuzzy adaptive systems were designed to approximate observation errors of uncertain disturbances and to reduce chatter of control law.Finally,the adaptive Nussbaum gain function was introduced to compensate nonlinear saturation of canard deflection.The LOS angle tracking error and LOS angle rate were convergent in finite time and whole system states were uniform ultimately bounded,rigorously proven by Lyapunov stability theory.Hardware-in-the-loop simulation(HILS)and digital simulation experiments both showed FADS provided guided projectile with good guidance performance while striking targets with different maneuvering forms.

Integrated evaluation system under randomness and fuzziness for groundwater contamination risk assessment in a little town, Central China

An integrated evaluation system under randomness and fuzziness was developed in this work to systematically assess the risk of groundwater contamination in a little town, Central China. In this system, randomness of the parameters and the fuzziness of the risk were considered simultaneously, and the exceeding standard probability of contamination and human health risk due to the contamination were integrated. The contamination risk was defined as a combination of "vulnerability" and "hazard". To calculate the value of "vulnerability", pollutant concentration was simulated by MODFLOW with random input variables and a new modified health risk assessment(MRA) model was established to analyze the level of "hazard". The limit concentration based on environmental-guideline and health risk due to manganese were systematically examined to obtain the general risk levels through a fuzzy rule base. The "vulnerability" and "hazard" were divided into five categories of "high", "medium-high", "medium", "low-medium" and "low", respectively. Then, "vulnerability" and "hazard" were firstly combined by integrated evaluation. Compared with the other two scenarios under deterministic methods, the risk obtained in the proposed system is higher. This research illustrated that ignoring of uncertainties in evaluation process might underestimate the risk level.

Emotional inference by means of Choquet integral and λ-fuzzy measurement in consideration of ambiguity of human mentality

Research on human emotions has started to address psychological aspects of human nature and has advanced to the point of designing various models that represent them quantitatively and systematically. Based on the findings, a method is suggested for emotional space formation and emotional inference that enhance the quality and maximize the reality of emotion-based personalized services. In consideration of the subjective tendencies of individuals, AHP was adopted for the quantitative evaluation of human emotions, based on which an emotional space remodeling method is suggested in reference to the emotional model of Thayer and Plutchik, which takes into account personal emotions. In addition, Sugeno fuzzy inference, fuzzy measures, and Choquet integral were adopted for emotional inference in the remodeled personalized emotional space model. Its performance was evaluated through an experiment. Fourteen cases were analyzed with 4.0 and higher evaluation value of emotions inferred, for the evaluation of emotional similarity, through the case studies of 17 kinds of emotional inference methods. Matching results per inference method in ten cases accounting for 71% are confirmed. It is also found that the remaining two cases are inferred as adjoining emotion in the same section. In this manner, the similarity of inference results is verified.

Research and application of sidewall stability predic-tion method based on analytic hierarchy process and fuzzy integrative evaluation method

As a difficult problem, sidewall instability has been beset drilling workers all the time. Not only does it cause huge economic losses, but also it determines the success or failure of drilling engineering. Due to complex relationship between various factors which influence sidewall stability, it hasn’t been found a widely applied method to predicate sidewall stability so far. Therefore, in order to formulate corresponding measures to ensure successful drilling, searching for a kind of better method to forecast sidewall stability before drilling becomes an imperative and significant topic for drilling engineering. On the basis of traditional sidewall stability analytical method, we have put forward the Fuzzy Comprehensive Evaluation Method to forecast sidewall stability regulation using physico-chemical performance parameters of the clay mineral. This method has been improved by introducing the Analytic Hierarchy Process (AHP) and the Maximum Subjection Principle in the application process. After introducing Analytic Hierarchy Process to identify weight, and Maximum Subjection Principle to obtain evaluation results, it has reduced the influence of human factors and enhanced the accuracy of the fuzzy evaluation results. The application in Hailaer Area indicates that this method can predict sidewall stability of gas-oil well with high credibility and strong practicability.

An Equivalent Condition for （K） Integrability of Fuzzy-valued Mappings

In this paper, we first discuss the relationship between the McShane integral and Pettis integral for vector-valued functions. Then by using the embedding theorems for the fuzzy number space E^1, we give a new equivalent condition for （K） integrabihty of a fuzzy set-valued mapping F ： [a, b] → E^1.