Defuzzification Strategies Research Articles

Design and Simulation of Modified Type-2 Fuzzy Logic Controller for Power System

This Article exhibits the structure of a Modified Type-2 (MT2) Fuzzy Logic (FL) Controller (MT2FLC), direction line programming of development, also performance optimization for different power systems. The implementation of the MT2FLC for control of a power system. New participation capacities were considered in adjusting a domain for an Interval Type-2 (IT2) Fuzzy Logic (FL) System (IT2FLS). Another structure in graphic user interface (GUI) mimicked four controllers: an optimal PID controller, FLC, a Type-1(TIFLC), an Interval Type-2 ((IT2FLC), and the MIT2FLC. Their yields were analysed, different periods of the structure procedure for the fuzzy framework, from beginning depiction to conclusive execution, can be gotten from the altered tool compartment (whose capacity to create complex frameworks and adaptability in broadening the accessible usefulness into working with adjusted type2 fuzzy administrators, phonetic factors, IT2 participation capacities, and defuzzification strategies, just as in assessing the MIT2FLC are its best characteristics). Case study for this work, all the optimization controllers implemented for a Brushless DC (BLDC) Motor with MATLAB Ver.2012a was utilized in the recreation and plan of the entirety of the procedure GUIs. Satisfactory results are obtaining which improve the implementation of the using of MIT2FLC controller as practical solution of power system.

WABL method as a universal defuzzifier in the fuzzy gradient boosting regression model

Gradient Boosting Regression (GBR) models are widely used and can give effective results in regression and classification problems. The main value of the approach proposed in this study is that it allows the GBR algorithm to be used even if the target variables are fuzzy. The defuzzification strategy affects the solutions found. The solutions of the GBR algorithm, depending on various defuzzification strategies, in case the target values are fuzzy numbers, are examined. Techniques have been proposed for calculating fuzzy residuals and loss functions. Definitions and theorems are given to alleviate the computational load on triangular fuzzy numbers. Results of the Fuzzy GBR algorithm were compared on ten popular datasets using COG (Center of Gravity), MOM (Mean of Maxima) and WABL (Weighted Averaging Based on Levels) defuzzification methods. The fuzzy R-squared and the fuzzy RMSE (Root Mean Square Error) scores defined on the basis of fuzzy distance was used to evaluate the results obtained via different defuzzification methods. It has been seen that if the parameters of the WABL method are adjusted appropriately, it gives better results than other defuzzification methods in all data sets, so the WABL can be handled as a universal defuzzifier in the Fuzzy GBR models.

The Stratic Defuzzifier for discretised general type-2 fuzzy sets

Stratification is a feature of the type-reduced set of the general type-2 fuzzy set, from which a new technique for general type-2 defuzzification, Stratic Defuzzification, may be derived. Existing defuzzification strategies are summarised. The stratified structure is described, after which the Stratic Defuzzifier is presented and contrasted experimentally for accuracy and efficiency with both the Exhaustive Method of Defuzzification (to benchmark accuracy) and the α-Planes/Karnik–Mendel Iterative Procedure strategy, employing 5, 11, 21, 51 and 101 α-planes. The Stratic Defuzzifier is shown to be much faster than the Exhaustive Defuzzifier. In fact the Stratic Defuzzifier and the α-Planes/Karnik–Mendel Iterative Procedure Method are comparably speedy; the speed of execution correlates with the number of planes participating in the defuzzification process. The accuracy of the Stratic Defuzzifier is shown to be excellent. It is demonstrated to be more accurate than the α-Planes/Karnik–Mendel Iterative Procedure Method in four of six test cases, regardless of the number of α-planes employed. In one test case, it is less accurate than the α-Planes/Karnik–Mendel Iterative Procedure Method, regardless of the number of α-planes employed. In the remaining test case, the α-Planes/Karnik–Mendel Iterative Procedure Method with 11 α-Planes gives the most accurate result, with the Stratic Defuzzifier coming second.

Robust master planning of a socially responsible supply chain under fuzzy-stochastic uncertainty (A case study of clothing industry)

This paper addresses an integrated physical supply channel, aggregate production, and transportation planning problem through the lens of social sustainability under uncertainty. The three-echelon supply chain network includes multiple suppliers, a manufacturer and multiple distribution centres. Social-related criteria such as workers’ job-security and health (i.e. working conditions) and social investment are contemplated in the supply chain under consideration. In doing so, a chance constraint mixed integer non-linear programming model is built to determine the centralized planning of procurement-production-transportation under fuzzy-stochastic uncertainty over the tactical planning horizon. Moreover, an efficient hybrid solution procedure is developed utilizing convexification and defuzzification strategies. Finally, a real-case study in clothing industry is presented to show the model applicability and the solution procedure efficiency.

Multi-objective mixed integer programming and an application in a pharmaceutical supply chain

Multi-objective integer linear and/or mixed integer linear programming (MOILP/MOMILP) are very useful for many areas of application as any model that incorporates discrete phenomena requires the consideration of integer variables. However, the research on the methods for the general multi-objective integer/mixed integer model has been scant when compared to multi-objective linear programming with continuous variables. In this paper, an MOMILP is proposed, which integrates various conflicting objectives. We give importance to the imprecise nature of some of the critical factors used in the modelling that can influence the effectiveness of the model. The uncertainty and the hesitation arising from estimating such imprecise parameters are represented by intuitionistic fuzzy numbers. The MOMILP model with intuitionistic fuzzy parameters is first converted into a crisp MOMILP model, using appropriate defuzzification strategies. Thereafter, the MOMILP is transformed into a single objective problem to yield a compromise solution with an acceptable degree of satisfaction, using suitable scalarisation techniques such as the gamma-connective technique and the minimum bounded sum operator technique. The proposed solution method is applied to several test problems and a multi-objective pharmaceutical supply chain management model with self generated random data.

Feasibility Study on Intelligent Evaluation of Marine Traffic Congestion Degree for Restricted Water Using Fuzzy Expert System with AIS Report

In this paper we investigate the modification of feasibility study on Intelligent Evaluation Marine Traffic Congestion Degree for Restricted Water Area which has now become one of the numerous challenging factors to improve the safety of navigation. However, the observation of marine traffic using Fuzzy Expert with the aid of AIS acquired knowledge from the collected data enable the congestion degree to be visualize and possible to estimate Restricted Water Area base on traffic congestion degree with main flow velocity. The formation, aggregation, and decomposition of rules explained fuzzy mathematical tools and the calculus of IF-THEN rules provides a most useful paradigm for the automation and implementation of an extensive body of human knowledge. Therefore, the clarification includes a discussion of fuzzification and defuzzification strategies, the definition of fuzzy implication and an analysis of fuzzy reasoning mechanism. Now IMO is trying to standardize criterion of Universal AIS. As you know AIS is now studied and has been studied in many advanced country as a tools to exchange information in both ship-to-ship and ship-to-shore in congested waterways. The intention of standardization is to improve safety of VTS management and to support effective navigation of ships.

Performance Study of PID and Fuzzy Controllers for Position Control of 6 DOF arm Manipulator with Various Defuzzification Strategies

Today’s arm manipulators are more and more demanding in terms of productivity. Conventional controllers are not always able to provide good and accurate results. To complete a position movement of the manipulator’s end-effector, a set of joint angles of manipulator first required to be converted to the position coordinates by using the forward kinematics method, and each joint rotation is executed using a servomotor feedback control. The kinematic model has been validated using MATLAB® robotics toolbox. An end-effector based 6 degree of freedom (6-DOF) platform is proposed in this work which uses DC servomotor for actuation of the three revolute joints. PID controller is used as a reference benchmark. And FLC controller with different defuzzification strategies was employed. Results were compared in terms of time response criteria. Simulation results using MATLAB are demonstrated that PID has superior performance in terms of transient parameters. In Steady state response, both PID and FLC manage to converge to the desired output but in terms of overshot FLC is outperformed.

On type-reduction of type-2 fuzzy sets: A review

As an undetachable module of type-2 (T2) fuzzy computations and reasoning, type-reduction methods play an important role in various fuzzy disciplines including fuzzy logic systems and fuzzy clustering. Importance of type-reduction techniques lies in the fact that they are the main tools for collecting the entire inherent vagueness of the data. Therefore, type-reduction methods form the output of type-2 fuzzy sets (T2 FSs) as the representative of the entire uncertainty in a given space. Hence, their accuracy, precision, and performance speed is of much interest. This paper, presents a comprehensive review on various type-reduction and defuzzification strategies for general and interval type-2 fuzzy sets and systems. It is tried to analyze the existing approaches from different point of views accompanied by extensive comparisons on different features of type-reduction methods to facilitate further research studies by the fuzzy community.

Performance evaluation of industrial enterprises via fuzzy inference system approach: a case study

The aim of this study is not only to give self-contained and methodological steps of data mining with its areas of applications, but also to provide a compact source of reference for the researchers who want to use data mining and fuzzy inference in their area of work. We construct a fuzzy inference system to predict the profit of the major 500 industrial enterprises of Turkey. For this aim, we use most of the data mining tools. First, we use fuzzy $$c$$ c -means clustering algorithm and obtain the linguistic terms of the variables. Having used decision tree technique, fuzzy rules are revealed. Eventually, we compare various defuzzification strategies to obtain crisp prediction values of our fuzzy inference system. We can conclude that the prediction results of the smallest of maxima defuzzification strategy-based fuzzy inference system has circa 40 % smaller sum square error than that of classical regression model.

Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set

The work reported in this paper addresses the challenge of the efficient and accurate defuzzification of discretised interval type-2 fuzzy sets. The exhaustive method of defuzzification for type-2 fuzzy sets is extremely slow, owing to its enormous computational complexity. Several approximate methods have been devised in response to this bottleneck. In this paper we survey four alternative strategies for defuzzifying an interval type-2 fuzzy set: (1) The Karnik–Mendel Iterative Procedure, (2) the Wu–Mendel Approximation, (3) the Greenfield–Chiclana Collapsing Defuzzifier, and (4) the Nie–Tan Method.We evaluated the different methods experimentally for accuracy, by means of a comparative study using six representative test sets with varied characteristics, using the exhaustive method as the standard. A preliminary ranking of the methods was achieved using a multi-criteria decision making methodology based on the assignment of weights according to performance. The ranking produced, in order of decreasing accuracy, is (1) the Collapsing Defuzzifier, (2) the Nie–Tan Method, (3) the Karnik–Mendel Iterative Procedure, and (4) the Wu–Mendel Approximation.Following that, a more rigorous analysis was undertaken by means of the Wilcoxon Nonparametric Test, in order to validate the preliminary test conclusions. It was found that there was no evidence of a significant difference between the accuracy of the Collapsing and Nie–Tan Methods, and between that of the Karnik–Mendel Iterative Procedure and the Wu–Mendel Approximation. However, there was evidence to suggest that the collapsing and Nie–Tan Methods are more accurate than the Karnik–Mendel Iterative Procedure and the Wu–Mendel Approximation.In relation to efficiency, each method’s computational complexity was analysed, resulting in a ranking (from least computationally complex to most computationally complex) as follows: (1) the Nie–Tan Method, (2) the Karnik–Mendel Iterative Procedure (lowest complexity possible), (3) the Greenfield–Chiclana Collapsing Defuzzifier, (4) the Karnik–Mendel Iterative Procedure (highest complexity possible), and (5) the Wu–Mendel Approximation.

Generation of diffuser dot patterns for light guides using fuzzy scheme strategy

We propose a fuzzy scheme strategy for the generation of the diffuser dot patterns in the light guide of an edge-lit backlight. The fuzzy scheme strategy is based on fuzzy logic and rules, which are closely related to the physical luminance properties of the light guide. During the process of generating diffuser dot patterns, two inputs are the dot radius and the distance from dots to a light source, and one output is the luminance of the light guide panel. This strategy converts the linguistic strategy based on expert knowledge the optimal dot-generation strategy. Furthermore, this study includes the discussion of fuzzification and defuzzification strategies, the derivation of fuzzy logic rules, and the analysis of fuzzy reasoning mechanisms. Experiment results reveal that the proposed strategy can achieve an even luminance condition by establishing dot patterns. Compared to conventional methods, the fuzzy scheme strategy has two advantages. It effectively integrates the dot generation scheme into the subsequent optical design phase to make dot patterns more efficient and easy to control. Moreover, optimized dot patterns realize sufficient luminance uniformity.

Fog forecasting using rule-based fuzzy inference system

Operational meteorology is perceived as a fuzzy environment in which information is vaguely defined. The mesoscale processes such as fog, stratus and convection are generally dependent on the topography of the place and has always been difficult to forecast for the meteorologists. The main objective of the present study is to introduce the concept of fuzzy inference system (FIS) in the prediction of fog. This approach uses the concept of a pure fuzzy logic system where the fuzzy rule base consists of a collection of fuzzy IF-THEN rules. The fuzzy inference engine uses these fuzzy IF-THEN rules to determine a mapping from fuzzy sets in the input universe of discourse to fuzzy sets in the output universe of discourse based on fuzzy logic principles. Basic weather elements, which affect weather characteristics of fog, are fuzzified. These are then used in fuzzy weather prediction models based on fuzzy inferences. These models are simulated and the crisp results obtained using developed defuzzification strategies are compared with the actual weather data. The basis of methodology is to construct the fuzzy rule base domain from the available daily current weather observations in winter season over New Delhi. The results reveal that dew point spread and rate of change of dew point spread are the most important parameters for the formation of fog. The results further indicate that fog formation over New Delhi are dominant when (i) dew point is greater then 7°C along with dew point spread between 1 and 3°C. (ii) rate of change of dew point spread must be negative and wind speed should be less than 4 knots. This study presents a technique for predicting the probability of fog over New Delhi for 5–6 hours in advance. The skill score indicates that the performance of FIS is appreciably good. The method is found to be promising for operational application.

An integrated intelligent system for injection molding process determination

AbstractBased on the characteristics of the injection molding process, an integrated intelligent model employing case‐based reasoning (CBR) and fuzzy inference has been constructed, considering the molding personnel's thought during the trial runs and the advantages of CBR and fuzzy inference. The ideology of CBR is adopted for the initial process parameters setting, which simulates the molding personnel's behavior that they often recall a previous case and set the initial process parameters of the current one by referring to that old case. The case design and matching have been described in detail, and four case adaptation strategies have been discussed. The ideology of fuzzy inference based on expert knowledge and practical experience reflects the test moldings for defects correction and process parameters optimization. Therefore, a fuzzy inference model was built for the correction and optimization process. Its key implementation techniques, such as fuzzification and defuzzification strategies, fuzzy rules definition, membership functions, etc, have been discussed. Finally, a corresponding intelligent system has been developed that is integrated with the injection machine by communicating with the controller. The system can be used to determine the initial process parameters and optimize them online. An experimental study has been carried out for verification. © 2008 Wiley Periodicals, Inc. Adv Polym Techn 26:191–205, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/adv.20097

A fuzzy set theoretic approach to validate simulation models

We develop a new approach to the validation of simulation models by exploiting elements from fuzzy set theory and machine learning. A fuzzy resemblance relation concept is used to set up a mathematical framework for measuring the degree of similarity between the input-output behavior of a simulation model and the corresponding behavior of the real system. A neuro-fuzzy inference algorithm is employed to automatically learn the required resemblance relation from real and simulated data. Ultimately, defuzzification strategies are applied to obtain a coefficient on the unit interval that characterizes the degree of model validity. An example in the airline industry illustrates the practical application of this methodology.

A survey of defuzzification strategies

Defuzzification is an important operation in the theory of fuzzy sets. It transforms a fuzzy set information into a numeric data information. This operation along with the operation of fuzzification is critical to the design of fuzzy systems as both of these operations provide nexus between the fuzzy set domain and the real-valued scalar domain. We need the synergy of both of these domains to solve many of our ill-posed problems effectively. In this paper, we address the problem of defuzzification, we present merits and demerits of various defuzzification strategies that are used in the theory and practice, and in design and implementation of applications involving fuzzy theory, fuzzy control, and fuzzy rule base, and fuzzy inference-based systems. We also present in this paper a simple and yet a novel defuzzification mechanism. © 2001 John Wiley & Sons, Inc.

A trainable transparent universal approximator for defuzzification in Mamdani-type neuro-fuzzy controllers

A novel technique of designing application specific defuzzification strategies with neural learning is presented. The proposed neural architecture considered as a universal defuzzification approximator is validated by showing the convergence when approximating several existing defuzzification strategies. The method is successfully tested with fuzzy controlled reverse driving of a model truck. The transparent structure of the universal defuzzification approximator allows us to analyze the generated customized defuzzification method using the existing theories of defuzzification. The integration of universal defuzzification approximator instead of traditional methods in Mamdani-type fuzzy controllers can also be considered as an addition of trainable nonlinear noise to the output of the fuzzy rule inference before calculating the defuzzified crisp output. Therefore, nonlinear noise trained specifically for a given application shows a grade of confidence on the rule base, providing an additional opportunity to measure the quality of the fuzzy rule base. The possibility of modeling a Mamdani-type fuzzy controller as a feedforward neural network with the ability of gradient descent training of the universal defuzzification approximator and antecedent membership functions fulfil the requirement known from multilayer preceptrons in finding solutions to nonlinear separable problems.

Multimode-oriented polynomial transformation-based defuzzification strategy and parameter learning procedure

In an earlier paper (1996), we proposed a set of generalized defuzzification strategies which can be characterized as single-mode-oriented strategies. A single-mode-oriented defuzzification strategy, although useful in many research projects and real world applications, cannot be applied to a multimode situation where two or more distinct possibility peaks exist in its membership function distribution. In this paper, for multimode-oriented generalized defuzzification applications, a multimode-oriented polynomial transformation based defuzzification strategy (M-PTD) is introduced. The new M-PTD strategy, which uses the Kalman filter in parameter learning procedure, offers a constraint-free and self-renewal defuzzification solution.

Generalized defuzzification strategies and their parameter learning procedures

Defuzzification is a procedure of crucial importance for fuzzy systems because a final crisp output (control) action is required in many theoretical and practical applications. The choice of defuzzification strategy, therefore, can directly affect the success of such applications. Among the existing strategies, neither the center of area (COA) nor the mean of maximum (MOM) emerges as the better defuzzification strategy. A compromise strategy that combines the two methods may offer a synergetic solution. In this paper, the authors introduce two new objective defuzzification strategies, Gaussian distribution transformation-based defuzzification (GTD) and polynomial transformation-based defuzzification (PTD), which are based on a discrete universe of discourse. Both strategies can perform better than the existing strategies and the PTD strategy offers a generalized defuzzification tool for a wide class of practical problems. Both strategies include the COA and MOM strategies as special cases, and both are based on parameter learning processes using the extended Kalman filter as their iterative improvement algorithms on sample database containing fuzzy sets and the associate defuzzified values. The proposed parameter learning procedures are capable of either off-line or on-line processing.

Fuzzy control on the basis of equality relations with an example from idle speed control

The way engineers use fuzzy control in real world applications is often not coherent with an understanding of the control rules as logical statements or implications. In most cases fuzzy control can be seen as an interpolation of a partially specified control function in a vague environment, which reflects the indistinguishability of measurements or control values. In this paper the authors show that equality relations turn out to be the natural way to represent such vague environments and they develop suitable interpolation methods to obtain a control function. As a special case of our approach the authors obtain Mamdani's model and can justify the inference mechanism in this model and the use of triangular membership functions not only for the reason of simplified computations, and they can explain why typical fuzzy partitions are preferred. The authors also obtain a criterion for reasonable defuzzification strategies. The fuzzy control methodology introduced in this paper has been applied successfully in a case study of engine idle speed control for the Volkswagen Golf GTI.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Equality relations as a basis for fuzzy control

Abstract The aim of this paper is to introduce a fuzzy control model with well-founded semantics in order to explain the concepts applied in fuzzy control. Assuming that the domains of the input and output variables for the process are endowed with equality relations, that reflect the indistinguishability of values lying closely together, the use of triangular and trapezoidal membership functions can be justified and max-⨅ inference where ⨅ is a t-norm turns out to be a consequence of our model. Distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like MOM or COA are appropriate or lead to undesired results.