Fuzzification Process Research Articles

Recursive and noise-exclusive fuzzy switching median filter for impulse noise reduction

A new model for impulse noise reduction with a recursive and noise-exclusive fuzzy switching median filter is proposed. The filter uses a S-type membership function for fuzzifying the noisy input variable and then estimates a correction label for it that aims at canceling the noisy effect. The fuzzification process provides better smoothing and generalization that improve the performance of the filter. The recursive and noise-exclusive operations further enhance the noise reduction capability of the filter. The recursive operation replaces the current pixel with the filtered pixel(s) and the noise-exclusive filtering uses only noise-free pixel(s) of the working window. The net effect of the filtering process thus preserves the sharp edges and fine details of the image in a more effective manner. The superiority of the proposed model to others in removing high density noise is established both quantitatively and qualitatively with various benchmarks and real-time test data sets. With the incorporation of the functionalities like fuzzy reasoning and noise-exclusive operations in the filtering process, the model becomes more efficient and fast. The applicability of the model thus opens ample scopes for hardware implementation in many electronics products that deal with images and videos.

Synthesis of Multicriteria Controller by Means of Fuzzy Logic Approach

A two-mass fuzzy control system is considered. For fuzzification process, classical both linear and nonlinear membership functions are used. To find optimal values of membership function’s parameters, genetic algorithm is used. To take into account values of both output and intermediate parameters of the system, a penalty function is considered. Research is conducted for the case of speed control system and displacement control system. Obtained results are compared with the case of the system with classical, crisp controller.

The Shapley value of cooperative games under fuzzy settings: a survey

We survey the recent developments in the studies of cooperative games under fuzzy environment. The basic problems of a cooperative game in both crisp and fuzzy contexts are to find how the coalitions form vis-á-vis how the coalitions distribute the worth. One of the fuzzification processes assumes that the coalitions thus formed are fuzzy in nature having only partial participations of the players. A second group of researchers fuzzify the worths of the coalitions while a few others assume that both the coalitions and the worths are fuzzy quantities. Among the various solution concepts of a cooperative game, the Shapley value is the most popular one-point solution concept which is characterized by a set of rational axioms. We confine our study to the developments of the Shapley value in fuzzy setting and try to highlight the respective characterizations.

Hybridization of multi-objective evolutionary algorithms and fuzzy control for automated construction, tuning, and analysis of neuronal models

As of late, automated methods for generation and tuning of neuronal models have been gaining popularity (e.g. [1]). Several such techniques, including brute-force parameter search space exploration (e.g.[2]) or particle swarm optimization (e.g.[3]), have been successfully applied in this area; however, evolutionary/genetic algorithms seem to be the tool of choice for an increasing number of computational neuroscientists (e.g.[4,5]). Multi-objective evolutionary algorithms (MOEA) lend themselves especially well to this application, as they are capable of generating or tuning neuronal models by optimizing multiple, often conflicting, objectives at the same time (e.g.[6,7]). The one weakness of MOEA-based construction of neuronal models, however, is the fact that it solely relies on the convergence efficiency of the chosen algorithm, and it largely ignores the plethora of available biological knowledge (other than what is utilized in the initial stages of model building in terms of the overall design of the model structure and the definition of fitness functions) that could be used to make the process itself more efficient. In this work, we propose to remedy this situation by hybridizing multi-objective evolutionary algorithms with a fuzzy logic-based controller in order to supply the MOEA with expert knowledge that can improve the algorithm's effectiveness. Fuzzy logic (FL) is a form of multiple-valued logic, which can emulate and incorporate human-like intelligence into a system controlling a process within a closed loop [8]. Fuzzy IF-THEN rules can be used to determine the best possible adjustment to the process based on its current output. Here, the process is the evolutionary algorithm, and the models generated by it are subjected to a set of fuzzy rules to determine the best adjustments, if any, to increase the likelihood of generating models that meet the predefined criteria. The application of fuzzy logic allows for utilization of linguistic rules that are easy to articulate and understand by humans (e.g. IF spiking frequency is too low, THEN increase axon sodium conductance), but at the same time can be directly applied to the neuronal models generated by the MOEA via the process of fuzzification (i.e. translation of crisp numerical values into linguistic concepts) and defuzzification, after the pertinent rules have been triggered. Importantly, as the loop continues to execute, more rules can be extracted from the evolutionary algorithm itself by simply identifying the changes across the generations that produced improvement, and mapping that information onto the fuzzy logic domain.

A high speed railway control system based on the fuzzy control method

This paper proposed a high-speed railway control system based on the fuzzy control method. The fuzzy control system of the high-speed railway is designed in the Matlab software according to the expert experience and knowledge. At first the input and output variables have been fuzzified in the fuzzification process. Then the membership function is designed and the control rules are discussed in detail bring into correspondence with expert knowledge. The parameters discussion about the maximum speed and traction effort are studied in detail. Finally, the defuzzify process can output the results directly to control the high speed railway train. The results indicated that the fuzzy control system is effective and accurate in the high speed railway control process.

Classification of convective/stratiform echoes in radar reflectivity observations using a fuzzy logic algorithm

AbstractIn radar reflectivity observations, the convective and stratiform rain types always have poorly defined boundaries, which caused problem for rain classification. A fuzzy logic (FL) algorithm is developed to classify convective and stratiform rainfall based on the radar reflectivity observations in the next three steps: First, the algorithm is calibrated on Hefei Doppler radar site in China. Four features are selected based on a dataset for calibration, which spanned the period from 29 June to 23 July 2003; and the features basically represent a subjective choice of characteristics that are expected to distinguish different rain types. In the second step, membership functions are used to determine the degree to which each feature belongs to each rain type in the fuzzification process. Finally, the degree of fuzzification for each input feature is multiplied by predetermined weighting coefficients. The weighted degrees of the fuzzification are aggregated to produce a single value for each rain type. The aggregation can represent the possibility of classified rainfall type, and larger value reveals the higher potential for a particular class. The FL algorithm has been applied to four typical independent individual cases collected by Hefei Doppler radar, which have not been included in the database for calibration. Results show that the classification using the proposed FL algorithm is physically reasonable according to the analysis of three‐dimensional radar reflectivity patterns, implying that the proposed FL algorithm has a great potential for the precipitation classification.

Predicting mobile promotion response behaviour: a mathematical modelling approach

The paper attempts to build a mathematical model for predicting mobile promotion response behaviour of users towards promotional Short Messaging Services (SMS). The conceptual model has been assumed to predict the response behaviour towards useful to not useful information. The conceptual model has been converted into a mathematical model and empirically tested through fuzzification process. The results show that: 1) the users ignore the promotional SMS irrespective of useful to not useful information; 2) the model shows the cyclical response behaviour of users towards promotional SMS in the short to long run.

Normal type-2 fuzzy rational B-spline curve

In this paper, we proposed a new form of type-2 fuzzy data points(T2FDPs) that is normal type-2 data points(NT2FDPs). These brand-new forms of data were defined by using the definition of normal type-2 triangular fuzzy number(NT2TFN). Then, we applied fuzzification(alpha-cut) and type-reduction processes towards NT2FDPs after they had been redefined based on the situation of NT2FDPs. Furthermore, we redefine the defuzzification definition along with the new definitions of fuzzification process and type-reduction method to obtain crisp type-2 fuzzy solution data points. For all these processes from the defining the NT2FDPs to defuzzification of NT2FDPs, we demonstrate through curve representation by using the rational B-spline curve function as the example form modeling these NT2FDPs.

Forecasting of energy and diesel consumption and the cost of energy production in isolated electrical systems in the Amazon using a fuzzification process in time series models

Understanding the uncertainty inherent in the analysis of diesel fuel consumption and its impact on the generation of electricity is an important topic for planning the expansion of isolated thermoelectric systems in the state of Amazonas. In light of this, a decision support system has been developed to forecast the cost of electricity production using non-stationary data by integrating the methodology of time series models with fuzzy systems and optimization tools. The method presented herein combines the potential of the Autoregressive Integrated Moving Average (ARIMA) and the Seasonal ARIMA (SARIMA) models, such as the forecasting tool, with the advantages of fuzzy set theory to compensate for the uncertainties and errors encountered in the observed data, which would degrade the validity of forecasted values. The results show that incorporation of the α-cut concept facilitated the evaluation of risks while allowing simultaneous consideration of intervals for the unitary cost of energy production. This provides the analyst with the ability to make decisions using various predicted intervals with different membership values instead of the common practice of simply using the specific costs.

Fuzzy motion adaptive algorithm and its hardware implementation for video de-interlacing

Abstract Interlacing techniques were introduced in the early analog TV transmission systems as an efficient mechanism capable of halving the video bandwidth. Currently, interlacing is also used by some modern digital TV transmission systems, however, there is a problem at the receiver side since the majority of modern display devices require a progressive scanning. De-interlacing algorithms convert an interlaced video signal into a progressive one by performing interpolation. To achieve good de-interlacing results, dynamical and local image features should be considered. The gradual adaptation of the de-interlacing technique as a function of the level of motion detected in each pixel is a powerful method that can be carried out by means of fuzzy inference. The starting point of our study is an algorithm that uses a fuzzy inference system to evaluate motion locally (FMA algorithm). Our approach is based on convolution techniques to process a fuzzy rulebase for motion-adaptive de-interlacing. Different strategies based on bi-dimensional convolution techniques are proposed. In particular, the algorithm called ‘single convolution algorithm’ introduces significant advantages: a more accurate measurement of the level of motion using a matrix of weights, and a unique fuzzification process after the global estimation, which reduces the computational cost. Different architectures for the hardware implementation of this algorithm are described in VHDL language. The physical realization is carried out on a RC100 Celoxica FPGA development board.

Interval-Valued Fuzzy Sets Applied to Stereo Matching of Color Images

Stereo matching problem attempts to find corresponding locations between pairs of displaced images of the same scene. Correspondence estimation between pixels suffers from occlusions, noise, and bias. This paper introduces a novel approach to represent images by means of interval-valued fuzzy sets. These sets allow one to overcome the uncertainty due to the aforementioned problems. The aim is to take advantage of the new representation to develop a stereo matching algorithm. The interval-valued fuzzification process for images that is proposed here is based on image segmentation. Interval-valued fuzzy similarities are introduced to compare windows whose pixels are represented by intervals. To make use of color information, the similarities of the RGB channels were aggregated using the luminance formula. The experimental analysis makes a comparison with other methods. The new representation that is proposed together with the new similarity measure show a better overall behavior, providing more accurate correspondences, mainly near depth discontinuities and for images with a large amount of color.

Consideration of Fuzzy Components for Prediction of Machining Performance: A Review

This paper presents the application of artificial intelligence techniques especially fuzzy logic (FL) in predicting machining performance. FL is chosen because it is widely used to predict the machining performances such as surface roughness, cutting force and material removal rate. Previous works on FL focusing on fuzzy components has been presented. The FL components are fuzzification, fuzzy rule, inference engine and defuzzification. The review shows that the FL components for fuzzification, which is logical operator, membership function (MF) and IF-THEN rule, is the necessary facts that must be considered before applying FL in prediction. Fuzzy rule that is derived from fuzzification process is important in the development of inference engine. Therefore, the defuzzification of the inference engine will give desired fuzzy system. The review also revealed that there are several types of defuzzification which include centroid, bisector, smallest of maximum, mean of maximum and largest of maximum. There are important facts that must be considered in FL development. To conclude, this paper revealed that MF and defuzzification is important in predicting machining performance. It shows that for MF and defuzzification, triangular and centroid are respectively mostly used in the prediction process.

A fuzzy logic optimization methodology for the estimation of the critical flashover voltage on insulators

The objective of this paper is to present a new methodology for predicting the critical flashover voltage of polluted insulators based on fuzzy logic. The prediction contains not only the estimated value, but also the respective confidence interval based on the re-sampling method. Various parameters, such as the number and the base width of the triangular membership functions used for the fuzzification process, etc., are assigned different values in order to optimize the estimation of the critical flashover voltage. Additionally, different methods for training the fuzzy system are applied and compared for their appropriateness in accurately predicting the critical flashover voltage.

Three-way analysis of imprecise data

Data are often affected by uncertainty. Uncertainty is usually referred to as randomness. Nonetheless, other sources of uncertainty may occur. In particular, the empirical information may also be affected by imprecision. Also in these cases it can be fruitful to analyze the underlying structure of the data. In this paper we address the problem of summarizing a sample of three-way imprecise data. In order to manage the different sources of uncertainty a twofold strategy is adopted. On the one hand, imprecise data are transformed into fuzzy sets by means of the so-called fuzzification process. The so-obtained fuzzy data are then analyzed by suitable generalizations of the Tucker3 and CANDECOMP/PARAFAC models, which are the two most popular three-way extensions of Principal Component Analysis. On the other hand, the statistical validity of the obtained underlying structure is evaluated by (nonparametric) bootstrapping. A simulation experiment is performed for assessing whether the use of fuzzy data is helpful in order to summarize three-way uncertain data. Finally, to show how our models work in practice, an application to real data is discussed.

Three-dimensional segmentation of tumors from CT image data using an adaptive fuzzy system

A new segmentation method using a fuzzy rule based system to segment tumors in a three-dimensional CT data was developed. To initialize the segmentation process, the user selects a region of interest (ROI) within the tumor in the first image of the CT study set. Using the ROI's spatial and intensity properties, fuzzy inputs are generated for use in the fuzzy rules inference system. With a set of predefined fuzzy rules, the system generates a defuzzified output for every pixel in terms of similarity to the object. Pixels with the highest similarity values are selected as tumor. This process is automatically repeated for every subsequent slice in the CT set without further user input, as the segmented region from the previous slice is used as the ROI for the current slice. This creates a propagation of information from the previous slices, used to segment the current slice. The membership functions used during the fuzzification and defuzzification processes are adaptive to the changes in the size and pixel intensities of the current ROI. The method is highly customizable to suit different needs of a user, requiring information from only a single two-dimensional image. Test cases success in segmenting the tumor from seven of the 10 CT datasets with <10% false positive errors and five test cases with <10% false negative errors. The consistency of the segmentation results statistics also showed a high repeatability factor, with low values of inter- and intra-user variability for both methods.

A novel approach to neuro-fuzzy classification

A new model for neuro-fuzzy (NF) classification systems is proposed. The motivation is to utilize the feature-wise degree of belonging of patterns to all classes that are obtained through a fuzzification process. A fuzzification process generates a membership matrix having total number of elements equal to the product of the number of features and classes present in the data set. These matrix elements are the input to neural networks. The effectiveness of the proposed model is established with four benchmark data sets (completely labeled) and two remote sensing images (partially labeled). Different performance measures such as misclassification, classification accuracy and kappa index of agreement for completely labeled data sets, and beta index of homogeneity and Davies-Bouldin (DB) index of compactness for remotely sensed images are used for quantitative analysis of results. All these measures supported the superiority of the proposed NF classification model. The proposed model learns well even with a lower percentage of training data that makes the system fast.

Mutual information-based feature selection and partition design in fuzzy rule-based classifiers from vague data

Algorithms for preprocessing databases with incomplete and imprecise data are seldom studied. For the most part, we lack numerical tools to quantify the mutual information between fuzzy random variables. Therefore, these algorithms (discretization, instance selection, feature selection, etc.) have to use crisp estimations of the interdependency between continuous variables, whose application to vague datasets is arguable. In particular, when we select features for being used in fuzzy rule-based classifiers, we often use a mutual information-based ranking of the relevance of inputs. But, either with crisp or fuzzy data, fuzzy rule-based systems route the input through a fuzzification interface. The fuzzification process may alter this ranking, as the partition of the input data does not need to be optimal. In our opinion, to discover the most important variables for a fuzzy rule-based system, we want to compute the mutual information between the fuzzified variables, and we should not assume that the ranking between the crisp variables is the best one. In this paper we address these problems, and propose an extended definition of the mutual information between two fuzzified continuous variables. We also introduce a numerical algorithm for estimating the mutual information from a sample of vague data. We will show that this estimation can be included in a feature selection algorithm, and also that, in combination with a genetic optimization, the same definition can be used to obtain the most informative fuzzy partition for the data. Both applications will be exemplified with the help of some benchmark problems.

On the transitivity of a parametric family of cardinality-based similarity measures

We introduce a parametric family of cardinality-based similarity measures for ordinary sets (on a finite universe) harbouring numerous well-known similarity measures. We characterize the Łukasiewicz-transitive and product-transitive members of this family. Their importance derives from their one-to-one correspondence with pseudo-metrics. Fuzzification schemes based on a commutative quasi-copula are then used to transform these similarity measures for ordinary sets into similarity measures for fuzzy sets, rendering them applicable on graded feature set representations of objects. The main result of this paper is that transitivity, and hence also the corresponding dual metric interpretation, is preserved along this fuzzification process.

A novel fuzzy classifier based on product aggregation operator

The present article proposes a fuzzy set-based classifier with a better learning and generalization capability. The proposed classifier exploits the feature-wise degree of belonging of a pattern to all classes, generalization in the fuzzification process and the combined class-wise contribution of features effectively. The classifier uses a π -type membership function and product aggregation reasoning rule (operator). Its effectiveness is verified with two conventional (completely labeled) data sets and two remote sensing images (partially labeled data sets). The proposed classifier is compared with similar fuzzy methods. Different performance measures are used for quantitative evaluation of the proposed classifier.

Fuzzifying P Systems

Uncertainty is an inherent property of all living systems. Curiously enough, computational models inspired by biological systems do not take, in general, under consideration this essential aspect of living systems. In this paper, after introducing the notion of a multi-fuzzy set (i.e. an orthogonal approach to the fuzzification of multisets), we introduce two variants of P systems with fuzzy components: P systems with fuzzy data and P systems with fuzzy multiset rewriting rules. By silently assuming that fuzzy data are not the result of some fuzzification process, P systems with fuzzy data are shown to be a promising step towards real hypercomputation. On the other hand, P systems with fuzzy multiset rewriting rules are shown to be equivalent to fuzzy Turing machines. The paper concludes with remarks concerning the present work and future research.