Implementation of a microcontroller-based simplified FITA-FIS model

The paper describes basic approach to building a general purpose MISO-FITA (multiple inputs single output rule based system) fuzzy logic inference system. It is also discussed classic and simplified models of the inference systems and some optimization methods of its architecture. The fuzzy engine of the proposed system is based on simplified Mamdani’s fuzzy inference model. It has been implemented on the sample platform based on ARMv7 Cortex-M4 microcontroller. The performance of the fuzzy inference system, defined as a time to obtain an output crisp inference result, is higher or comparable to another software and hardware solutions. For proposed system it even takes 10 μs.     

A fuzzy reasoning design for fault detection and diagnosis of a computer-controlled system

A fuzzy reasoning and verification Petri nets (FRVPNs) model is established for an error detection and diagnosis mechanism applied to a complex fault-tolerant PC-controlled system. The inference accuracy can be improved through the hierarchical design of a two-level fuzzy rule decision tree and a Petri nets technique to transform the fuzzy rule into the FRVPNs model. Several simulation examples of the assumed failure events were carried out by using the FRVPNs and the Mamdani fuzzy method with MATLAB tools. The reasoning performance of the developed FRVPNs was verified by comparing the inference outcome to that of the Mamdani method. Both methods result in the same conclusions. Thus, the present study demonstrates that the proposed FRVPNs model is able to achieve the purpose of reasoning, and furthermore, determining of the failure event of the monitored application program.     

基于模糊线性化预测模型的HVAC系统温度控制

针对暖通空调（HVAC）系统难以控制的问题,提出一种基于max-product推理的Mamdani模糊模型预测控制策略．首先利用一步模糊预测模型的结构分析得到其解析表达式,获得系统在k＋1时刻的线性化预测模型;然后基于模糊线性化模型进行模型预测控制器设计．对HVAC系统的仿真和实验结果表明,该算法是一种跟踪性能好且鲁棒性强的有效控制算法．     

Neural computing models for prediction of permeability coefficient of coarse-grained soils

Correlations are very significant from the earliest days; in some cases, it is essential as it is difficult to measure the amount directly, and in other cases it is desirable to ascertain the results with other tests through correlations. Soft computing techniques are now being used as alternate statistical tool, and new techniques such as artificial neural networks, fuzzy inference systems, genetic algorithms, and their hybrids were employed for developing the predictive models to estimate the needed parameters, in the recent years. Determination of permeability coefficient (k) of soils is very important for the definition of hydraulic conductivity and is difficult, expensive, time-consuming, and involves destructive tests. In this paper, use of some soft computing techniques such as ANNs (MLP, RBF, etc.) and ANFIS (adaptive neuro-fuzzy inference system) for prediction of permeability of coarse-grained soils was described and compared. As a result of this paper, it was obtained that the all constructed soft computing models exhibited high performance for predicting k. In order to predict the permeability coefficient, ANN models having three inputs, one output were applied successfully and exhibited reliable predictions. However, all four different algorithms of ANN have almost the same prediction capability, and accuracy of MLP was relatively higher than RBF models. The ANFIS model for prediction of permeability coefficient revealed the most reliable prediction when compared with the ANN models, and the use of soft computing techniques will provide new approaches and methodologies in prediction of some parameters in soil mechanics.     

A variable spread fuzzy linear regression model with higher explanatory power and forecasting accuracy

Fuzzy regression models have been applied to operational research (OR) applications such as forecasting. Some of previous studies on fuzzy regression analysis obtain crisp regression coefficients for eliminating the problem of increasing spreads for the estimated fuzzy responses as the magnitude of the independent variable increases; however, they still cannot cope with the situation of decreasing or variable spreads. This paper proposes a three-phase method to construct the fuzzy regression model with variable spreads to resolve this problem. In the first phase, on the basis of the extension principle, the membership functions of the least-squares estimates of regression coefficients are constructed to conserve completely the fuzziness of observations. In the second phase, then they are defuzzified by the center of gravity method to obtain crisp regression coefficients. In the third phase, the error terms of the proposed model are determined by setting each estimated spread equals its corresponding observed spread. Furthermore, the Mamdani fuzzy inference system is adopted for improving the accuracy of its forecasts. Compared to the previous studies, the results from five examples and an application example of Japanese house prices show that the proposed fuzzy linear regression model has higher explanatory power and forecasting performance.     

An intelligent approach to predict unconfined compressive strength of rock surrounding access tunnels in longwall coal mining

Unconfined compressive strength (UCS) of rocks is one of the most important parameters in rock engineering, engineering geology, and mining projects. In the laboratory determination of UCS, high-quality samples are necessary; in which preparing of core samples has several limits, as it is difficult, expensive, and time-consuming. For this, development of predictive models to determine the UCS of rocks seems to be an attractive research. In this study, an intelligent approach based on the Mamdani fuzzy model was utilized to predict UCS of rock surrounding access tunnels in longwall coal mining. To approve the capability of this approach, the obtained results are compared to the results of statistical model. A database containing 93 rock sample records, ranging from weak to very strong rock types, was used to develop and test the models. For the evaluation of models performance, determination coefficient (R ²), root mean square error, and variance account for indices were used. Based on this comparison, it was concluded that performance of fuzzy model is considerably better than statistical model. Also, the fuzzy model results indicate very close agreement for the UCS with the laboratory measurements. Furthermore, the fuzzy model sensitivity analysis shows that Schmidt hardness and porosity are the most and least effective parameters on the UCS, respectively.     

A Highly Accurate Model-Free Motion Control System with a Mamdani Fuzzy Feedback Controller combined with a TSK Fuzzy Feed-forward Controller

In this paper, a new intelligent robot motion control architecture – a highly accurate model-free fuzzy motion control- is proposed in order to achieve improved robot motion accuracy and dynamic performance. Its architecture combines a Mamdani fuzzy proportional (P) and a conventional integral (I) plus derivative (D) controller for the feedback part of the system, and a Takagi-Sugeno-Kang fuzzy controller for the feed-forward, nonlinear part. The fuzzy P + ID controller improves the performance of the nonlinear system, and the TSK fuzzy controller uses a TSK fuzzy inference system based on extended subtractive- clustering method which integrates information on joint angular displacement, velocity and acceleration for torque identification. The advantage of this kind of model-free control is that it uses the information directly from the input/output of the nonlinear system, without any complex robot model computation, in order to decrease the control system’s sensitivity to any dynamical uncertainty. Furthermore, parametric search for clustering parameters in extended subtractive clustering secures the high accuracy of the system identification. Consequently, this proposed model-free fuzzy motion control benefits from the advantages of two kinds of fuzzy system. It not only incorporates flexible design, good performance and simple conception but also ensures precise motion control and great robustness. Comparisons with other intelligent models and results from numerical studies on a 4-bar planar parallel mechanism show the effectiveness and competitiveness of the proposed control.     

Several non-linear models in estimating air-overpressure resulting from mine blasting

This research presents several non-linear models including empirical, artificial neural network (ANN), fuzzy system and adaptive neuro-fuzzy inference system (ANFIS) to estimate air-overpressure (AOp) resulting from mine blasting. For this purpose, Miduk copper mine, Iran was investigated and results of 77 blasting works were recorded to be utilized for AOp prediction. In the modeling procedure of this study, results of distance from the blast-face and maximum charge per delay were considered as predictors. After constructing the non-linear models, several performance prediction indices, i.e. root mean squared error (RMSE), variance account for (VAF), and coefficient of determination (R ²) and total ranking method are examined to choose the best predictive models and evaluation of the obtained results. It is obtained that the ANFIS model is superior to other utilized techniques in terms of R ², RMSE, VAF and ranking herein. As an example, RMSE values of 5.628, 3.937, 3.619 and 2.329 were obtained for testing datasets of empirical, ANN, fuzzy and ANFIS models, respectively, which indicate higher performance capacity of the ANFIS technique to estimate AOp compared to other implemented methods.     

Structure and stability analysis of general Mamdani fuzzy dynamic models

Mamdani fuzzy models have always been used as black‐box models. Their structures in relation to the conventional model structures are unknown. Moreover, there exist no theoretical methods for rigorously judging model stability and validity. I attempt to provide solutions to these issues for a general class of fuzzy models. They use arbitrary continuous input fuzzy sets, arbitrary fuzzy rules, arbitrary inference methods, Zadeh or product fuzzy logic AND operator, singleton output fuzzy sets, and the centroid defuzzifier. I first show that the fuzzy models belong to the NARX (nonlinear autoregressive with the extra input) model structure, which is one of the most important and widely used structures in classical modeling. I then divide the NARX model structure into three nonlinear types and investigate how the settings of the fuzzy model components, especially input fuzzy sets, dictate the relations between the fuzzy models and these types. I have found that the fuzzy models become type‐2 models if and only if the input fuzzy sets are linear or piecewise linear (e.g., trapezoidal or triangular), becoming type 3 if and only if at least one input fuzzy set is nonlinear. I have also developed an algorithm to transfer type‐2 fuzzy models into type‐1 models as far as their input–output relationships are concerned, which have some important properties not shared by the type‐2 models. Furthermore, a necessary and sufficient condition has been derived for a part of the general fuzzy models to be linear ARX models. I have established a necessary and sufficient condition for judging local stability of type‐1 and type‐2 fuzzy models. It can be used for model validation and control system design. Three numeric examples are provided. Our new findings provide a theoretical foundation for Mamdani fuzzy modeling and make it more consistent with the conventional modeling theory. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 103–125, 2005.     

Fuzzy models to predict consumer ratings for biscuits based ondigital image features

Fuzzy models to recognize consumer preferences were developed as part of an automated inspection system for biscuits. Digital images were used to estimate the physical features of chocolate chip cookies including size, shape, baked dough color, and fraction of top surface area that was chocolate chips. Polls were conducted to determine consumer ratings of cookies. Four fuzzy models were developed to predict consumer ratings based on three of the features. There was substantial variation in consumer ratings in terms of individual opinions, as well as poll-to-poll differences. Parameters for the inference system, including fuzzy values for cookie features and consumer ratings, were defined based on the judgment and statistical analysis of data from the calibration polls. The two fuzzy models that gave satisfactory estimates of average consumer ratings are: the Mamdani inference system based on eight fuzzy values for consumer ratings; and the Sugeno inference system developed using the adaptive neurofuzzy inference system algorithm     

Parameter Identification of Recurrent Fuzzy Systems With Fuzzy Finite-State Automata Representation

This paper presents the identification of nonlinear dynamical systems by recurrent fuzzy system (RFS) models. Two types of RFS models are discussed: the Takagi-Sugeno-Kang (TSK) type and the linguistic or Mamdani type. Both models are equivalent and the latter model may be represented by a fuzzy finite-state automaton (FFA). An identification procedure is proposed based on a standard general purpose genetic algorithm (GA). First, the TSK rule parameters are estimated and, in a second step, the TSK model is converted into an equivalent linguistic model. The parameter identification is evaluated in some benchmark problems for nonlinear system identification described in literature. The results show that RFS models achieve good numerical performance while keeping the interpretability of the actual system dynamics.     

Constitutive models describing the influence of the geometry of partially-spanning joints on jointed rock mass strength: Regression and fuzzy logic analysis of experimental data

Using existing experimental data from Uniaxial Compressive Strength (UCS) testing, constitutive models were produced to describe the influence of joint geometry (joint location, trace length and orientation) on the UCS of rock containing partially-spanning joints. Separate approaches were used to develop two models: a multivariable regression model, and a fuzzy inference system model. Comparison of model predictions to the experimental data demonstrates that both models are capable of accurately describing the UCS of jointed rock with partially-spanning joints using information relating to joint geometry. However, according to the statistical evaluation methods used for performance evaluation, the multivariable regression model was significantly more accurate. Analysis of predictions made by the fuzzy inference system model showed that it was capable of resolving certain peculiarities in the influence of partially-spanning joint orientation on the compressive strength of rock that, from rock mechanics and fracture mechanics theory, should be expected. The multivariable regression model, whilst more accurate, did not recognise these peculiarities. Due to the additional insight that can be gleaned from the fuzzy inference system modelling, we recommend the use of the fuzzy inference system constitutive model in combination with the multivariable regression model.     

Forest fire detection: A fuzzy system approach based on overlap indices

It is well known that a powerful method to tackle diverse problems with lack of knowledge and/or uncertainty are Fuzzy Logic Systems (FLSs). In the literature, there exist different fuzzy inference mechanisms based on fuzzy variables and fuzzy rules to obtain a solution. In this work we introduce a generalization of the inference algorithm proposed by Mamdani, by using overlap functions and overlap indices. A challenging issue is the selection of most suitable overlap expressions for each problem. For this aim, we propose to use the convex combination of several ones. In this way, the conclusions obtained by our FLSs avoid the bad results obtained by an inadequate overlap expression. We test our proposal on a real problem of forest fire detection using a wireless sensor network.     

Environmental comprehensive assessment of agricultural systems at the farm level using fuzzy logic: A case study in cane farms in Iran

Development of a fuzzy inference model is a complex multi-step process in which we encounter a large number of parameters such as type and number of membership functions, fuzzy operators, defuzzification and implication methods and etc. There is currently very little literature on the topic of the best selection of parameters for development of expert based inference models. In this study we developed a fuzzy rule based model, which uses available farm management data as required inputs, for the environmental assessment of farming systems. We also tried to make an analysis on the efficiency of current mathematical parameters in the development of our fuzzy model. Finally, in a practical example we demonstrate the applicability of the developed model for improvement of environmental status of the cane farming in Iran.A Mamdani fuzzy inference model with two inference engines was developed to combine five basic input indexes, which were selected as indicators of farms environmental status based on the experts' interview and scientific knowledge. To validate the developed model, we inserted several cycles of analysis using graphical and global sensitivity methods on the model and compared the model outcomes with experts' viewpoints. Using these analysis methods, we also evaluated the effects of changes in operators, membership function shape and defuzzification methods, on the model outcomes and their sensitivities.In this study, fuzzy inference emerged as a suitable, uncomplicated and effective tool for development of environmental assessment models. Totally, performance of one parameter was highly influenced by other parameters. For the selection of one parameter its interaction with other parameters had to be considered. Type, shape and the number of membership functions were from the most effective parameters for development of the model and significantly influenced the other factors. Case study results showed that environmental indexes of sugarcane production can enhance between 37 and 59% using simple improving strategies.     

Fuzzy Interpolation and Extrapolation: A Practical Approach

Fuzzy interpolation does not only help to reduce the complexity of fuzzy models, but also makes inference in sparse rule-based systems possible. It has been successfully applied to systems control, but limited work exists for its applications to tasks like prediction and classification. Almost all fuzzy interpolation techniques in the literature make strong assumptions that there are two closest adjacent rules available to the observation, and that such rules must flank the observation for each attribute. Also, some interpolation approaches cannot handle fuzzy sets whose membership functions involve vertical slopes. To avoid such limitations and develop a more practical approach, this paper extends the work of Huang and Shen. The result enables both interpolation and extrapolation which involve multiple fuzzy rules, with each rule consisting of multiple antecedents. Two realistic applications, namely truck backer-upper control and computer activity prediction, are provided in this paper to demonstrate the utility of the extended approach. Experiment-based comparisons to the most commonly used Mamdani fuzzy reasoning mechanism, and to other existing fuzzy interpolation techniques are given to show the significance and potential of this research.     

直觉F推理与普通F推理的比较研究

直觉F推理克服了普通F推理在不确定性信息的描述、推理结果可信性等方面存在的局限性。在介绍普通F推理直觉化扩展的基础上,首先分析了两类推理算法的相互转化问题,指出普通F推理是直觉F推理的一种特例,当直觉指数为0时二者可相互转化。其次,比较了两类算法的还原性,分析表明Zadeh型、Mamdani型、Larsen型直觉F推理算法与其对应的普通F推理算法具有相同的还原性。最后,通过实例研究了直觉F推理算法在推理结果精度、可信性上的优势,从而较普通F推理更适用于智能控制与决策。     

A Cascaded Fuzzy Inference System for Indian river water quality prediction

Now-a-days, Fuzzy Inference System (FIS) is considered as an effective tool for solution of many complex engineering systems when ambiguity and uncertainly is associated with the systems. Mamdani and Takagi, Sugeno and Kang (TSK) models poses simplicity in modeling but their system performance prediction capability is severely affected as complexity of the problem increases. In a multi-input, multi-output situation where a system consists of many subsystems and different outputs are desired from each subsystem, an improved version of FIS must be adopted rather than developing FIS for each subsystem. When dealing with such a system, it is prudent to use cascading systems rather than developing models for individual systems. To this end, a new Cascaded Mamdani Fuzzy Inference System is proposed in this paper and its performance is evaluated with the help of prediction of Indian River water quality index (WQI). In general, WQI value is a dimensionless number ranging from 0 to 100 (best quality) and plays an important role in evaluating the water quality of rivers. The proposed model is designed to predict WQI for five rivers in India. The cascaded fuzzy system simplifies and speeds up the computation of WQI as compared to the currently existing standards. In this paper, the proposed model is compared with three International water quality criteria and it is found that the designed model results in accurate prediction.     

泛蕴涵推理机及其应用

本文提出模糊系统中基于泛逻辑的泛蕴涵推理机,给出其在描绘函数图形时的应用,同时比较了它与Mamdani型和Lasen型两种模糊系统在描绘函数图形时的误差。分析和比较表明,在相同规则下含有泛蕴涵推理机的模糊系统产生的误差最低。     

Estimation of elastic constant of rocks using an ANFIS approach

The engineering properties of the rocks have the most vital role in planning of rock excavation and construction for optimum utilization of earth resources with greater safety and least damage to surroundings. The design and construction of structure is influenced by physico-mechanical properties of rock mass. Young's modulus provides insight about the magnitude and characteristic of the rock mass deformation due to change in stress field. The determination of the Young's modulus in laboratory is very time consuming and costly. Therefore, basic rock properties like point load, density and water absorption have been used to predict the Young's modulus. Point load, density and water absorption can be easily determined in field as well as laboratory and are pertinent properties to characterize a rock mass. The artificial neural network (ANN), fuzzy inference system (FIS) and neuro fuzzy are promising techniques which have proven to be very reliable in recent years. In, present study, neuro fuzzy system is applied to predict the rock Young's modulus to overcome the limitation of ANN and fuzzy logic. Total 85 dataset were used for training the network and 10 dataset for testing and validation of network rules. The network performance indices correlation coefficient, mean absolute percentage error (MAPE), root mean square error (RMSE), and variance account for (VAF) are found to be 0.6643, 7.583, 6.799, and 91.95 respectively, which endow with high performance of predictive neuro-fuzzy system to make use for prediction of complex rock parameter.