Linguistic IF-THEN Rules Research Articles

Combination of linguistic Z-numbers and IF-THEN rules based on rectangular coordinate system

There is a growing body of literature that recognises the importance of Z-numbers proposed by Prof Zadeh. However, due to the complicated structure and short presentation time, many unknowns about Z-numbers still exist. To fill these gaps, this study aims to make use of rectangular coordinate system to express linguistic Z-numbers. Simultaneously, this study sets out to design a score function to quantify the information contained in different Z-numbers. Subsequently, distance measure and similarity measure are also presented from the perspective of coordinate system. Besides, linguistic discrete Z-numbers and belief rule base (BRB) model are combined to construct a novel reasoning model on the basis of implication operators. To verify the validity of the proposed method, three representative examples of epidemic level assessment, multicriteria group decision-making (MCGDM), and network security assessment are employed. The comparison with other widely used methods are performed to further demonstrate the superiority of the proposed method.

Redundancy criteria for linguistic fuzzy rules

The elimination of redundant rules in a given system is considered to be an important step towards its simplicity, clarity, and comprehensibility. In this paper, we return to the problem of redundancies in systems of linguistic fuzzy IF-THEN rules based on the perception-based logical deduction inference method. We generalize the existing criteria for detecting redundant rules in these systems to general ones, and elaborate a new algorithm for an automatic search and deletion of redundant linguistic fuzzy rules. The criteria are provided in a theoretically formulated form with full proofs. Furthermore, we present the final algorithm and demonstrative examples that show the positive impact of the new algorithm.

Quarterly sales analysis using linguistic fuzzy logic with weather data

Reliable estimation of customer demand for products and services constitutes a key aspect of financial planning in every company. When estimating future sales, as a proxy to demand, in addition to pure economic quantities, a large selection of (exogenous) variables specific to a given product can be considered. Potential impact of weather conditions on sales has been known for very long time, though the research using weather data has been mostly focused on energy sector. As concerns retail, several authors have started to analyze this issue only recently. This paper proposes a novel approach studying (quarterly) sales using weather data and is inspired by fuzzy natural logic. The method is based on modeling the influence of average temperatures on sales by fuzzy linguistic IF-THEN rules. The proposed methodology is applied to real data of quarterly ice-cream sales and compared with a standard approach. The results are promising especially when monthly average temperatures are considered.

Multiobjective Automated Type-2 Parsimonious Learning Machine to Forecast Time-Varying Stock Indices Online

Real-time forecasting of the financial time-series data is challenging for many machine learning (ML) algorithms. First, many ML models operate offline, where they need a batch of data, which may not be available during training. Besides, due to a fixed architecture of the majority of the offline-based ML models, they suffer to deal with the uncertain nature of financial time-series data. In contrast, online learning mode evolving-structured ML models could be promising for financial time-series forecasting. For real-time deployment of such models, low memory demand is a must. Besides, the model’s explainability plays a crucial role in forecasting financial time-series. Considering all the requirements, a rule-based autonomous neuro-fuzzy learning algorithm called the parsimonious learning machine (PALM) is proposed here to forecast time-varying stock indices. To provide efficient automation of the proposed algorithm by maintaining the model explainability in terms of limited number linguistic IF-THEN rules, two popular multiobjective evolutionary algorithms (MEAs), such as a real-coded genetic algorithm (GA) and a self-adaptive differential evolution (DE) algorithm are utilized here. In addition, fuzzy type-2 variants of PALMs’ are considered here due to better uncertainty handling capacity than their type-1 counterparts. To evaluate the proposed algorithm’s performance, the closing stock price of fifteen (15) different stock market indices are predicted here. From the results, it is observed that the MEA-based PALMs are performing better than the state-of-the-art benchmark online ML models and providing a rule-based explainable model to the end-user.

QUICK-RESPONSE FUZZY-CONTROLLED INDUCTION MOTOR DRIVE

High performance motor drives require high accuracy, fast response, wide range of control, robustness and immunity from the effect of parameter variations. Three phase motors have a complex and highly nonlinear mathematical model associated with interactive parameters. This makes designing a conventional controller for such a system is a hard task. Researchers are paying more attention to fuzzy logic controllers (FLCs) since they can be employed to control complex or nonlinear systems even without knowing their mathematical model. The main task of this paper is to design and implement an FLC for indirect field orientated control of a three phase induction motor drive. The proposed controller is a proportional-derivative (PD) FLC. It uses the speed and its derivative as input and the electromagnetic torque as output. The input and output are coupled with simple linguistic if-then rules. The spread of each input and output is adjusted using a gain block to achieve the best performance in a trial-and-error process. Also, an incremental counter is attached to the output of the controller to yield the desired electromagnetic torque. The design was implemented and tested using MATLAB/SIMULINK. Finally, the simulation results and figures were presented.

Achieving More Stringent Levels of Comfort via an Adaptive Fuzzy Controller Optimized by the Gravitational Search Algorithm for a Half-Body Car Model

An optimal adaptive fuzzy controller is designed to achieve more stringent levels of comfort for a half-body car model. This aim will be fulfilled by reducing road disturbances and decreasing the acceleration of the body. The proposed controller consists of two adaptive fuzzy controllers with two fuzzy systems. Each one has two inputs, one output and twenty five linguistic fuzzy IF-THEN rules. Every input has five Gaussian membership functions and uses the product inference engine, singleton fuzzifier and the centre average defuzzifier. In order to determine the optimal parameters for the Adaptive Fuzzy Controller (AFC), the Gravitational Search Algorithm (GSA) is applied. The relative displacement between spring mass and tire, along with the acceleration of the body, are the two objective functions being applied in the optimization algorithm. The results illustrate the superiority of the proposed optimal adaptive fuzzy controller in comparison with traditional controllers.

Fuzzy – PI controller to control the velocity parameter of Induction Motor

The major application of Induction motor includes the usage of the same in industries because of its high robustness, reliability, low cost, highefficiency and good self-starting capability. Even though it has the above mentioned advantages, it also have some limitations: (1) the standard motor is not a true constant-speed machine, itsfull-load slip varies less than 1 % (in high-horsepower motors).And (2) it is not inherently capable of providing variable-speedoperation. In order to solve the above mentioned problem smart motor controls and variable speed controllers are used. Motor applications involve non linearity features, which can be controlled by Fuzzy logic controller as it is capable of handling those features with high efficiency and it act similar to human operator.This paper presents individuality of the plant modelling. The fuzzy logic controller (FLC)trusts on a set of linguistic if-then rules, a rule-based Mamdani for closed loop Induction Motor model. Themotor model is designed and membership functions are chosenaccording to the parameters of the motor model. Simulation results contains non linearity in induction motor model. A conventional PI controller iscompared practically to fuzzy logic controller using Simulink.

Fuzzy information system for condition based maintenance of gearbox

Gearbox is an inseparable part of any rotating machinery today. Gearbox transfers speed and torque from one shaft to another. Hence, correct diagnosis of gearbox faults is an important and critical task for maintenance operators. But, due to nonlinear, time-varying behavior and imprecise measuremen t information of the systems it is difficult to deal with gearbox failures with precise mathematical equations. Human operators with the aid of their practical experience can handle these complex situations, with only a set of imprecise linguistic if-then rules and imprecise system state. The purpose of this study is to provide a correct and timely diagnosis of gearbox failures in the context of condition based maintenance. The diagnosis is performed by knowledge acquisition through a fuzzy rule-based inference system which could approximate human reasoning. The proposed approach is tested and applied to an experimental data emanating from a gearbox system.

ECG Prediction Based on Classification via Neural Networks and Linguistic Fuzzy Logic Forecaster.

The paper deals with ECG prediction based on neural networks classification of different types of time courses of ECG signals. The main objective is to recognise normal cycles and arrhythmias and perform further diagnosis. We proposed two detection systems that have been created with usage of neural networks. The experimental part makes it possible to load ECG signals, preprocess them, and classify them into given classes. Outputs from the classifiers carry a predictive character. All experimental results from both of the proposed classifiers are mutually compared in the conclusion. We also experimented with the new method of time series transparent prediction based on fuzzy transform with linguistic IF-THEN rules. Preliminary results show interesting results based on the unique capability of this approach bringing natural language interpretation of particular prediction, that is, the properties of time series.

Fuzzy logic system based prediction effort: A case study on the effects of tire parameters on contact area and contact pressure

Various methodologies of artificial intelligence have been recently used for estimating performance parameters of soil working machines and off-road vehicles. Due to nonlinear and stochastic features of soil–wheel interactions, application of knowledge-based Mamdani max–min fuzzy expert system for estimation of contact area and contact pressure is described in this paper. Fuzzy logic model was constructed by use of the experience of contact area and contact pressure utilizing data obtained from series of experimentations in soil bin facility and a single-wheel tester. Two paramount tire parameters: wheel load and tire inflation pressure are the input variables for our model, each has five membership functions. As a fundamental aspect of the fuzzy logic based prediction systems, a set of fuzzy if-then rules were used in accordance with fuzzy logic principles. 25 linguistic if-then rules were included to develop a complicated highly intelligent predicting model based on Centroid method at defuzzification stage. The model performance was assessed on the basis of several statistical quality criteria. Mean relative error lower than 10%, satisfactory scattering around unity-slope line (T), and high coefficient of determination, R2, were obtained by the fuzzy logic model proposed in this study.

OPTIMUM FUZZY MODEL FOR SINGLE INPUT SINGLE OUTPUT DATA SYSTEM

Fuzzy and intelligent modelling is one of the powerful features of the intelligent system that overcame classical modelling. In this paper, a methodology is proposed to develop the optimum fuzzy model of single input-single output data; the data could be a model of physical system or a statistical data. The methodology used was to develop two models. The first one is based on Mamdani as inference mechanism, with aggregation type AND and defuzzification method the centre of gravity (CoG). The second model is based on Takagi-Sugeno inference mechanism, the aggregation type and defuzzification method are AND and CoG, respectively. Presuming that each input crisp excites all input membership functions (MFs); the linguistic input-output MFs, IF-THEN rules, fuzzification and defuzzification are converted to a single highly non-linear equation. Afterwards, the least square method, which was implemented in Matlab, is used as an optimization technique to fit the data. Finally, the proposed algorithm is applied and tested on some non-linear functions.

A fuzzy inference system for pump failure diagnosis to improve maintenance process: The case of a petrochemical industry

Pump operating problems may be either hydraulic or mechanical and there is interdependence between the failure diagnoses of these two categories. Consequently, a correct diagnosis of a pump failure needs to consider many symptoms and hydraulic or mechanical causes. But, due to nonlinear, time-varying behavior and imprecise measurement information of the systems it is difficult to deal with pumps failures with precise mathematical equations, while human operators with the aid of their practical experience can handle these complex situations, with only a set of imprecise linguistic if-then rules and imprecise system state, but this procedure is time consuming and needs the knowledge of human experts and experienced maintenance personnel. The purpose of this study is to provide a correct and timely diagnosis mechanism of pump failures by knowledge acquisition through a fuzzy rule-based inference system which could approximate human reasoning. The proposed fuzzy inference system by: (1) reduction of human error, (2) reduction of repair time (3) creation of expert knowledge which could be used for training (4) reduction of unnecessary expenditures for upgrades and finally, (5) reduction of maintenance costs, will improve the maintenance process. The novelty of this work is the knowledge acquisition (the extraction of linguistic rules) through the interactive impact of the critical failure modes on the both hydraulic and mechanical operating parameters including flow rate, discharge pressure, NPSHR (Net Positive Suction Head Required), BHP (Brake Horse Power), efficiency, vibration and temperature. The proposed approach is tested and applied to a petrochemical industry.

Fully Automated RF/Microwave Filter Tuning by Extracting Human Experience Using Fuzzy Controllers

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The paper introduces modeling of human experience by linguistic if-then rules in terms of fuzzy logic controllers for tuning RF/Microwave filters. The approach could be used for any circuit or system tuning problem that involves human expert information provided that the expert information could be described in terms of linguistic if-then rules. The tuning approach is both theoretically and practically illustrated in this paper. The tuning is done in two stages both taking advantage of fuzzy controllers. The first stage uses the phase response of the filter, while the second stage uses the magnitude response of the filter for adjustment of the tuning screws. A fully automated experimental setup is implemented by high resolution motors with flexible leads to make the tuning possible. 3-pole and 7-pole Chebyshev waveguide filters are used to demonstrate the concept. The measured results prove the validity of the method. </para>

A Fuzzy Decision Tree for Fault Classification

In plant accident management, the control room operators are required to identify the causes of the accident, based on the different patterns of evolution of the monitored process variables thereby developing. This task is often quite challenging, given the large number of process parameters monitored and the intense emotional states under which it is performed. To aid the operators, various techniques of fault classification have been engineered. An important requirement for their practical application is the physical interpretability of the relationships among the process variables underpinning the fault classification. In this view, the present work propounds a fuzzy approach to fault classification, which relies on fuzzy if-then rules inferred from the clustering of available preclassified signal data, which are then organized in a logical and transparent decision tree structure. The advantages offered by the proposed approach are precisely that a transparent fault classification model is mined out of the signal data and that the underlying physical relationships among the process variables are easily interpretable as linguistic if-then rules that can be explicitly visualized in the decision tree structure. The approach is applied to a case study regarding the classification of simulated faults in the feedwater system of a boiling water reactor.

Design and Real Time Implementation of a Fuzzy Tuned H∞ Estimator in a Low Cost AHRS

In this paper a Fuzzy Tuned extended H∞ (FTH∞) estimator is designed and implemented in an Attitude Heading Reference System (AHRS), which is specialized to vehicular applications. In AHRS, 3-axis accelerometers are allotted to measure the earth's gravity field vector and then to update the roll and pitch angles obtained from gyros’ dynamic. Therefore, the AHRS on an accelerated vehicle will be affected by large disturbances. Additionally, in ground vehicles, the measurements of 3-axis magnetometers are corrupted by both soft and hard iron time varying disturbances. The FTH∞ estimator is an extended H∞*** filter in which only noise and attenuation bounds are tuned based on fuzzy linguistic if-then rules. The mentioned features make the estimator more reliable and suitable for hardware implementation. FTH∞ estimator relies on a consistent fuzzy combination of two change detection tests; namely, likelihood ratio and averaged norm error. Real-time implementation of new attitude-heading estimator is performed on a TMS320VC5416 Digital Signal Processor (DSP). Incorporating this powerful and small size DSP with micro electro mechanical inertial and resistive magnetic sensors leads to a low cost, small size and low power consumption AHRS. Performance of the AHRS was evaluated in Monte Carlo simulations of vehicle's attitude-headings. The FTH∞ estimator results in a superior performance compared to that of the extended H∞ estimator in simulation and real tests.

Interaction analysis for MIMO nonlinear systems based on a fuzzy basis function network model

This paper describes an interaction analysis method for a general multi-input multi-output (MIMO) nonlinear system based on its fuzzy rule-based model. Most real-world multivariable systems are nonlinear, complex and time varying. The multiple system input–output variables interact and sometime even fight against each other, causing significant challenges for system control and optimization. Especially in many practical applications, the accurate quantitative system model is not available or difficult to obtain, which subsequently makes it impossible to analyze the system multivariable interaction characteristics. In this paper, the nonlinear MIMO system is first modeled by fuzzy basis function networks (FBFN) based on a set of linguistic IF–THEN rules or data. The multivariable interaction property is analyzed locally around the operating point based on the relative gain Array (RGA), which is systematically formulated using the system steady-state gain values. Two simulation examples of chemical distillation columns illustrate the system interaction degree obtained by the proposed method is in a sufficient accuracy compared with the result calculated from the system explicit mathematical model, which indicates the applicability of the proposed method as an alternative way to derive the system multivariable interaction when the system mathematical model is not available.

If approximating nonlinear areas, then consider fuzzy systems

The fuzzy system is a knowledge-based system consisting of linguistic if-then rules. This article will focus on the Takagi-Sugeno (TS) type models. A novel approach of INFUMO has been applied in fault detection. The INFUMO was derived using the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> -norm function approximation. The majority of papers focus on the construction of the so-called residual generator, a comparator of the process and the process-model output that creates a residual signal

Fuzzy Miner

We study the problem of classification as this is presented in the context of data mining. Among the various approaches that are investigated, we focus on the use of Fuzzy Logic for pattern classification, due to its close relation to human thinking. More specifically, this paper presents a heuristic fuzzy method for the classification of numerical data, followed by the design and the implementation of its corresponding tool (Fuzzy Miner). The initial idea comes from the fact that fuzzy systems are universal approximators of any real continuous function. Such an approximation method coming from the domain of fuzzy control is appropriately adjusted into pattern classification and an “adaptive” procedure is proposed for deriving highly accurate linguistic if-then rules. Extensive simulation tests are performed to demonstrate the performance of Fuzzy Miner, while a comparison with a neuro-fuzzy classifier of the area is taking place in order to contradict the methodologies and the corresponding outcomes. Finally, new research directions in the context of Fuzzy Miner are identified, and ideas for its improvement are formulated.

Industrial application of fuzzy control in bioprocesses.

In a bioprocess, for example a fermentation process, many biological reactions are always working in intracellular space and the control of such a process is very complicated. Bioprocesses have therefore been controlled by the judgment of the experts who are the skilled operators and have much experience in the control of such processes. Such experience is normally described in terms of linguistic IF-THEN rules. Fuzzy inference is a powerful tool for incorporating linguistic rules into computer control of such processes. Fuzzy control is divided into two types--direct fuzzy control of process variables, for example sugar feed rate and fermentation temperature, and indirect control via phase recognition. In bioprocess control the experts decide the value of controllable process variables such as sugar feed rate or temperature as output data from several state variables as input data. Fuzzy control is regarded as a computational algorithm in which the causal relationship between input and output data are incorporated. In Japan fuzzy control has already been applied to practical industrial processes such as production of pravastatin precursor and vitamin B2 and to the Japanese sake mashing process; these examples are reviewed. In addition, an advanced control tool developed from a study on fuzzy control, fuzzy neural networks (FNN), are introduced. FNN can involve complicated causality between input and output data in a network model. FNN have been proven to be applicable to a research in biomedicine, for example modeling of the complicated causality between electroencephalogram or gene expression profiling data and prognostic prediction. Successful results on this research will be also explained.

Fuzzy control of bioprocess in Japan

Process control of bioprocess has been carried out by the judgment of the experts, who are the skilled operators and have lots of experiences for the control of the process. In almost all cases, those experiences are described linguistic IF-THEN rules. Fussy inference is one of the powerful tools to incorporate the linguistic rules to the computer for process control. Fuzzy control are divided into two types; one is the direct fuzzy control of process variables such as sugar feed rate in fed-batch culture and fermentation temperature in batch operation. The other is the indirect control of bioprocess, in which at first the phase recognition is carried out by fuzzy inference and the control strategies constructed in each phase are used for the control of process variables. In Japan, the fuzzy control has already been applied to practical industrial productions, such as pravastatin precursor, vitamin B2, and Japanese sake mashing process. In this review, these industrial approaches of fuzzy control are introduced.