Simultaneous Perturbation Stochastic Approximation Algorithm Combined with Neural Network and Fuzzy Simulation

In order to solve three kinds of fuzzy programm model, fuzzy chance-constrained programming mode ng models, i.e. fuzzy expected value and fuzzy dependent-chance programming model, a simultaneous perturbation stochastic approximation algorithm is proposed by integrating neural network with fuzzy simulation. At first, fuzzy simulation is used to generate a set of input-output data. Then a neural network is trained according to the set. Finally, the trained neural network is embedded in simultaneous perturbation stochastic approximation algorithm. Simultaneous perturbation stochastic approximation algorithm is used to search the optimal solution. Two numerical examples are presented to illustrate the effectiveness of the proposed algorithm.

THE FUZZY NUMERICAL VALUE SIMULATION OF NANOMETER ELECTRO-THERMAL IN HOT-WORKING

The fuzzy numerical value analysis method is adopted for the first time, which solves the problem of nanometer electro-thermal in filming process, The key technique is embodied by controlling the time distribution, temperature and press in the filming process. The concrete technique of filming is showed by establishing the fuzzy mumbership function of above three indexes, which improves the precision of the materials of nanometer electro-thermal in hot-working. At the same time, the principles of the fuzzy relationship mapping inversion （FRMI） is put forward, Therefore, the standardization and continuity can be met.

Multiple vehicle routing problem integrated reverse logistics with fuzzy reverse demands

A new type of vehicle routing problem （VRP）, multiple vehicle routing problem integrated reverse logistics （MVRPRL）, is studied. In this problem, there is delivery or pickup （or both） and uncertain features in the demands of the clients. The deliveries of every client as uncertain parameters are expressed as triangular fuzzy numbers. In order to describe MVRPRL, a multi-objective fuzzy programming model with credibility measure theory is constructed. Then the simulationbased tabu search algorithm combining inter-route and intra-route neighborhoods and embedded restarts are designed to solve it. Computational results show that the tabu search algorithm developed is superior to sweep algorithms and that compared with handling each on separate routes, the transportation costs can be reduced by 43% through combining pickups with deliveries.

Distribution Inventory Cost Optimization Under Grey and Fuzzy Uncertainty

The grey fuzzy variable was defined for the two fold uncertain parameters combining grey and fuzziness factors. On the basis of the credibility and chance measure of grey fuzzy variables, the distribution center inventory uncertain programming model was presented. The grey fuzzy simulation technology can generate input-output data for the uncertain functions. The neural network trained from the inputoutput data can approximate the uncertain functions. The designed hybrid intelligent algorithm by embedding the trained neural network into genetic algorithm can optimize the general grey fuzzy programming problems. Finally, one numerical example is provided to illustrate the effectiveness of the model and the hybrid intelligent algorithm.

Study on air formation to ground attack-defends decision making in fuzzy condition

With the development of modern military technology, uncertain decision-making problems become more and more exigent to be solved in military command and control. Based on game theory, and taking air formarion to ground attack-defends campaign as the background, this paper established an opposed dynamic decision-making model. As to the problems in military decision-making in fuzzy condition in uncertainty, this paper put forward a fuzzy-influence-factor, which reflects the fuzzy influence on battle units, and establishes a fuzzy opposed decision-making model in anticipant value and in correlative chance way farther to get strategy equilibrium. It can be seen from the simulating results that the model disposes the fuzzy status in battlefield reasonably, analyzes the fighting results objectively, and offers a powerful decision-making support for military operation. The method is practically and effectively.

Simulating a fuzzy level controller for flotation columns

Level control in flotation columns is an important factor that influences the recovery and the grade of concentrate from the column. A flotation column is a nonlinear, multi-variable problem with changeable parameters that traditional methods have difficulty controlling. We have applied fuzzy control methods to the flotation column and tested the performance of the design by Matlab/Simulink simulation. The simulations show that level control in the flotation column becomes smoother and more rapid with the fuzzy controller. Compared to PID control methods the overshoot in valve position, the adjustment time, and the robustness of the controller are all improved. This indicates that it is suitable to model fuzzy controllers in applications for the study of automatic control of flotation column.

NUMERICAL SIMULATION ALGORITHM FOR RELIABILITY ANALYSIS OF COMPLEX STRUCTURAL SYSTEM BASED ON INTELLIGENT OPTIMIZATION

An efficient importance sampling algorithm is presented to analyze reliability of complex structural system with multiple failure modes and fuzzy-random uncertainties in basic variables and failure modes. In order to improve the sampling efficiency, the simulated annealing algorithm is adopted to optimize the density center of the importance sampling for each failure mode, and results that the more significant contribution the points make to fuzzy failure probability, the higher occurrence possibility the points are sampled. For the system with multiple fuzzy failure modes, a weighted and mixed importance sampling function is constructed. The contribution of each fuzzy failure mode to the system failure probability is represented by the appropriate factors, and the efficiency of sampling is improved furthermore. The variances and the coefficients of variation are derived for the failure probability estimations. Two examples are introduced to illustrate the rationality of the present method. Comparing with the direct Monte-Carlo method, the improved efficiency and the precision of the method are verified by the examples.

Fault Diagnosis for Non-linear System Based On Adaptive Fuzzy System

Although lots of valuable results for fault diagnosis based on model have been achieved in linear system, it is difficult to apply these results to non-linear system due to the difficulty of modeling the non-linear system by analysis. Adaptive Fuzzy system provides a way for solving this problem because it can approximate any non-linear system at any accuracy. The key for adaptive Fuzzy system to solve problem is its learning ability, so the authors present a learning algorithm for Adaptive fuzzy system, which can build the system's model by learning from the measurement data as well as experience knowledge with high accuracy. Furthermore, the experiment using the learning algorithm to model a servo-mechanism and to construct the fault diagnosis system based on the model is carried out, the results is very good.

A New Paradigm for Simulating and Forecasting China's Economic Growth in the Medium and Long Term

Taking the system philosophy of human-earth relationship as the theoretical axis,and under the three-dimensional goals of economic growth,social development,and protection of the ecological environment,this paper constructs the supporting system of China’s economic development.On this basis,guided by the basic principles of system theory and system dynamics,and combined with the theories of other related disciplines,we constructed an economic geography-system dynamics(EG-SD)integrated forecasting model to simulate and quantitatively forecast China’s economic growth in the medium and long term.China’s economic growth will be affected by quantifiable and unquantifiable factors.If the main unquantifiable factors are not taken into account in the simulation and prediction of China’s economic growth in the medium and long term,the accuracy and objectivity of the prediction results will be diminished.Therefore,based on situation analysis(Strengths,Weaknesses,Opportunities,and Threats,SWOT),we combined scenario analysis with the Delphi method,and established a qualitative prediction simulation model(referred to as the S-D compound prediction model)to make up for the shortcomings associated with quantitative simulation predictions.EG-SD and S-D are organically combined to construct a simulation and prediction paradigm of China’s economic growth in the medium and long term.This paradigm not only realizes the integration of various forecasting methods and the combination of qualitative and quantitative measures,but also realizes the organic combination of unquantifiable and quantifiable elements by innovatively introducing fuzzy simulation of system dynamics,which renders the simulation and prediction results more objective and accurate.

FUZZY MODEL FOR TWO-DIMENSIONAL RIVER WATER QUALITY SIMULATION UNDER SUDDEN POLLUTANTS DISCHARGED

Based on the fuzziness and impreciseness of water environmental system, the fuzzy arithmetic was used to simulate the fuzzy and imprecise relations in modeling river water quality. By defining the parameters of water quality model as symmetrical triangular fuzzy numbers, a two-dimensional fuzzy water quality model for sudden pollutant discharge is established. From the fuzzy model, the pollutant concentrations, corresponding to the specified confidence level of a, can be obtained by means of the a-cut technique and arithmetic operations of triangular fuzzy numbers. Study results reveal that it is feasible in theory and reliable on calculation applying triangular fuzzy numbers to the simulation of river water quality.

Parameter design and performance analysis of zero inertia continuously variable transmission system

In order to solve the problem of weak power performance of vehicle equipped with continuously variable transmission(CVT) system working under transient operating conditions, a new CVT equipped with planetary gear mechanism and flywheel was researched, a design method of transmission parameter optimization was proposed, and the comprehensive matching control strategy was established for the new transmission system. Fuzzy controllers for throttle opening and CVT speed ratio were designed, and power performance and fuel economy of both vehicles respectively equipped with conventional CVT system and new transmission system wrere compared and analyzed by simulation. The results show that power performance and fuel economy of the vehicle equipped with new transmission system are better than that equipped with conventional CVT, thus the rationality of the parameter design method and control algorithm are verified.

Fuzzy Economic Order Quantity Inventory Models Without Backordering

In economic order quantity models without backordering, both the stock cost of each unit quantity and the order cost of each cycle are characterized as independent fuzzy variables rather than fuzzy numbers as in previous studies. Based on an expected value criterion or a credibility criterion, a fuzzy expected value model and a fuzzy dependent chance programming （DCP） model are constructed. The purpose of the fuzzy expected value model is to find the optimal order quantity such that the fuzzy expected value of the total cost is minimal. The fuzzy DCP model is used to find the optimal order quantity for maximizing the credibility of an event such that the total cost in the planning periods does not exceed a certain budget level. Fuzzy simulations are designed to calculate the expected value of the fuzzy objective function and the credibility of each fuzzy event. A particle swarm optimization （PSO） algorithm based on a fuzzy simulation is designed, by integrating the fuzzy simulation and the PSO algorithm. Finally, a numerical example is given to illustrate the feasibility and validity of the proposed algorithm.

Multi-item fuzzy inventory model for deteriorating items in multi-outlet under single management

Multi-item inventory model with stock-dependent demand is developed in fuzzy environment.Items are deteriorated in constant rate and are sold from different outlets in the city under single management.Due to the impreciseness of different parameters,objectives as well as constraints are imprecise in nature.As optimization of fuzzy objectives as well as fuzzy constraints are not well defined,the model is formulated as a multi-objective chance constrained programming problem where optimistic/pessimistic return of the objectives with some degree of possibility/necessity are optimized and constraints are satisfied with some degree of necessity.The model is solved via Multi-Objective Genetic Algorithm(MOGA)when crisp equivalent of the problem is available.In other cases,fuzzy simulation process is proposed to check the constraints as well as to determine the optimistic/pessimistic return of the objectives.The model is illustrated with some numerical examples.

Fuzzy Programming Models for Vendor Selection Problem in a Supply Chain

This paper characterizes quality, budget, and demand as fuzzy variables in a fuzzy vendor selection expected value model and a fuzzy vendor selection chance-constrained programming model, to maximize the total quality level. The two models have distinct advantages over existing methods for selecting vendors in fuzzy environments. A genetic algorithm based on fuzzy simulations is designed to solve these two models. Numerical examples show the effectiveness of the algorithm.

FUZZY EPQ INVENTORY MODELS WITH BACKORDER

This paper considers the economic production quantity （EPQ） problem with backorder in which the setup cost, the holding cost and the backorder cost are characterized as fuzzy variables, respectively. Following expected value criterion and chance constrained criterion, a fuzzy expected value model （EVM） and a chance constrained programming （CCP） model are constructed. Then fuzzy simulations are employed to estimate the expected value of fuzzy variable and c^-level minimal average cost. In order to solve the CCP model, a particle swarm optimization （PSO） algorithm based on the fuzzy simulation is designed. Finally, the effectiveness of PSO algorithm based on the fuzzy simulation is illustrated by a numerical example.

Maintenance Policy for Multi-Component System with Fuzzy Lifetimes

The application of possibility theory to maintenance policies is proposed in this paper. The lifetime of a component is modeled as a fuzzy variable. Two types of replacement policies-block replacement and age replacement with fuzzy lifetimes are investigated. The theorems show that the long-run average fuzzy reward per unit time in both policies is just the expected cost per unit of time. In order to solve the proposed models, a hybrid intelligent algorithm is employed. Finally, numerical examples are provided for the sake of illustration.

Fuzzy Resource-Constrained Project Scheduling Problem for Software Development

This paper presents a new method to solve the resource-constrained project scheduling problem for software development. In this method,activity duration times are described as fuzzy variables and resource-constrained software project scheduling problems are described as fuzzy programming models. First,how to model the software project scheduling problem under the fuzzy environment conditions is proposed. Second,in order to satisfy the different requirements of decision-making,two novel fuzzy project scheduling models,expected cost model and credibility maximization model,are suggested. Third,a hybrid intelligent algorithm integrated by genetic algorithm and fuzzy simulation is designed to solve the above two fuzzy programming models. Numerical experiments illustrate the effectiveness of the hybrid intelligent algorithm.

Adaptive Fuzzy Torque Control of Passive Torque Servo Systems Based on Small Gain Theorem and Input-to-state Stability

Passive torque servo system （PTSS） simulates aerodynamic load and exerts the load on actuation system, but PTSS endures position coupling disturbance from active motion of actuation system, and this inherent disturbance is called extra torque. The most important issue for PTSS controller design is how to eliminate the influence of extra torque. Using backstepping technique, adaptive fuzzy torque control （AFTC） algorithm is proposed for PTSS in this paper, which reflects the essential characteristics of PTSS and guarantees transient tracking performance as well as final tracking accuracy. Takagi-Sugeno （T-S） fuzzy logic system is utilized to compensate parametric uncertainties and unstructured uncertainties. The output velocity of actuator identified model is introduced into AFTC aiming to eliminate extra torque. The closed-loop stability is studied using small gain theorem and the control system is proved to be semiglobally uniformly ultimately bounded. The proposed AFTC algorithm is applied to an electric load simulator （ELS）, and the comparative experimental results indicate that AFTC controller is effective for PTSS.