Showing papers on "Membership function published in 2011"
TL;DR: The relationship between intutionistic fuzzy set and hesitant fuzzy set is discussed, based on which some operations and aggregation operators for hesitant fuzzy elements are developed and their application in solving decision making problems is given.
1,352 citations
01 Mar 2011
TL;DR: Experimental results show the effectiveness of the proposed method in contrast to conventional fuzzy C means algorithms and also type II fuzzy algorithm.
Abstract: This paper presents a novel intuitionistic fuzzy C means clustering method using intuitionistic fuzzy set theory. The intuitionistic fuzzy set theory considers another uncertainty parameter which is the hesitation degree that arises while defining the membership function and thus the cluster centers may converge to a desirable location than the cluster centers obtained using fuzzy C means algorithm. Also a new objective function which is the intuitionistic fuzzy entropy is incorporated in the conventional fuzzy C means clustering algorithm. This is done to maximize the good points in the class. This clustering method is used in clustering different regions of the CT scan brain images and these may be used to identify the abnormalities in the brain. Experimental results show the effectiveness of the proposed method in contrast to conventional fuzzy C means algorithms and also type II fuzzy algorithm.
334 citations
TL;DR: An entropy measure for interval-valued intuitionistic fuzzy sets is proposed, which generalizes three entropy measures defined independently by Szmidt, Wang and Huang, for intuitionism fuzzy sets and is applied to solve problems on pattern recognitions, multi-criteria fuzzy decision making and medical diagnosis.
294 citations
TL;DR: A new construction method based on the Lukasiewicz triangular norm is proposed, which is consistent with operations on ordinary fuzzy sets, and therefore is a true generalization of such operations.
275 citations
TL;DR: An extension of TOPSIS, a multi-criteria interval-valued intuitionistic fuzzy geometric aggregation operator, to a group decision environment is investigated, where inter-dependent or interactive characteristics among criteria and preference of decision makers are taken into account.
Abstract: An extension of TOPSIS, a multi-criteria interval-valued intuitionistic fuzzy decision making technique, to a group decision environment is investigated, where inter-dependent or interactive characteristics among criteria and preference of decision makers are taken into account. To get a broad view of the techniques used, first, some operational laws on interval-valued intuitionistic fuzzy values are introduced. Based on these operational laws, a generalized interval-valued intuitionistic fuzzy geometric aggregation operator is proposed which is used to aggregate decision makers' opinions in group decision making process. In addition, some of its properties are discussed. Then Choquet integral-based Hamming distance between interval-valued intuitionistic fuzzy values is defined. Combining the interval-valued intuitionistic fuzzy geometric aggregation operator with Choquet integral-based Hamming distance, an extension of TOPSIS method is developed to deal with a multi-criteria interval-valued intuitionistic fuzzy group decision making problems. Finally, an illustrative example is used to illustrate the developed procedures.
264 citations
TL;DR: A tentative assessment of the role of fuzzy sets in decision analysis is provided and a critical standpoint on the state-of-the-art is taken, in order to highlight the actual achievements and question what is often considered debatable by decision scientists observing the fuzzy decision analysis literature.
262 citations
TL;DR: A new method for handling multi-criteria fuzzy decision-making problems based on interval-valued intuitionistic fuzzy sets is presented, which can provide a useful way to efficiently help the decision-maker to make his decision.
Abstract: Out of several generalizations of fuzzy set theory for various objectives, the notions introduced by Atanassov (1983) and Atanassov and Gargov (1989) in defining intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are interesting and very useful in modeling real life problems. Ranking of interval-valued intuitionistic fuzzy sets plays a vital role in decision-making, data analysis, artificial intelligence and socioeconomic system and it was studied in Xu (2007c), Xu and Chen (2007a) and Ye (2009). In this paper a new method for ranking interval-valued intuitionistic fuzzy sets has been introduced and studied. The method is illustrated by numerical examples and compared with other methods. And then a new method for handling multi-criteria fuzzy decision-making problems based on interval-valued intuitionistic fuzzy sets is presented in which criterion values for alternatives are interval-valued intuitionistic fuzzy sets. The method proposed here can provide a useful way to efficiently help the decision-maker to make his decision. An illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
241 citations
TL;DR: The near optimum design for membership functions and control rules were found simultaneously by genetic algorithms (GAs) which are search algorithms based on the mechanism of natural selection and genetics which are easy to implement and efficient for multivariable optimization problems such as in fuzzy controller design.
240 citations
01 Jan 2011
TL;DR: In this article, a novel intuitionistic fuzzy C-means clustering method using fuzzy set theory is presented, which considers another uncertainty parameter which is the hesitation degree that arises while defining the membership function and thus cluster centers may converge to a desirable location than the cluster centers obtained using fuzzy C means algorithm.
Abstract: This paper presents a novel intuitionistic fuzzy C means clustering method using intuitionistic fuzzy set theory The intuitionistic fuzzy set theory considers another uncertainty parameter which is the hesitation degree that arises while defining the membership function and thus the cluster centers may converge to a desirable location than the cluster centers obtained using fuzzy C means algorithm Also vailable online 12 May 2010 eywords: ntuitionistic fuzzy set esitation degree uzzy clustering a new objective function which is the intuitionistic fuzzy entropy is incorporated in the conventional fuzzy Cmeans clustering algorithm This is done tomaximize the good points in the class This clustering method is used in clustering different regions of the CT scan brain images and these may be used to identify the abnormalities in the brain Experimental results show the effectiveness of the proposed method in contrast to conventional fuzzy C means algorithms and also type II fuzzy algorithm ntuitionistic fuzzy entropy ntuitionistic fuzzy generator
224 citations
01 Jan 2011
TL;DR: A novel fuzzy class-association-rule mining method based on genetic network programming (GNP) for detecting network intrusions and can be flexibly applied to both misuse and anomaly detection in network-intrusion-detection problems.
Abstract: As the Internet services spread all over the world, many kinds and a large number of security threats are increasing. Therefore, intrusion detection systems, which can effectively detect intrusion accesses, have attracted attention. This paper describes a novel fuzzy class-association-rule mining method based on genetic network programming (GNP) for detecting network intrusions. GNP is an evolutionary optimization technique, which uses directed graph structures instead of strings in genetic algorithm or trees in genetic programming, which leads to enhancing the representation ability with compact programs derived from the reusability of nodes in a graph structure. By combining fuzzy set theory with GNP, the proposed method can deal with the mixed database that contains both discrete and continuous attributes and also extract many important class-association rules that contribute to enhancing detection ability. Therefore, the proposed method can be flexibly applied to both misuse and anomaly detection in network-intrusion-detection problems. Experimental results with KDD99Cup and DARPA98 databases from MIT Lincoln Laboratory show that the proposed method provides competitively high detection rates compared with other machine-learning techniques and GNP with crisp data mining.
190 citations
Book•
14 Feb 2011
TL;DR: The purpose of this monograph is to explore the relationship between Fuzzy Data, Bayes' Theorem, and Problems, and the role that these models play in the development of knowledge and understanding of fuzzy data.
Abstract: Preface. Part I FUZZY INFORMATION. 1. Fuzzy Data. 1.1 One-dimensional Fuzzy Data. 1.2 Vector-valued Fuzzy Data. 1.3 Fuzziness and Variability. 1.4 Fuzziness and Errors. 1.5 Problems. 2. Fuzzy Numbers and Fuzzy Vectors. 2.1 Fuzzy Numbers and Characterizing Functions. 2.2 Vectors of Fuzzy Numbers and Fuzzy Vectors. 2.3 Triangular Norms. 2.4 Problems. 3. Mathematical Operations for Fuzzy Quantities. 3.1 Functions of Fuzzy Variables. 3.2 Addition of Fuzzy Numbers. 3.3 Multiplication of Fuzzy Numbers. 3.4 Mean Value of Fuzzy Numbers. 3.5 Differences and Quotients. 3.6 Fuzzy Valued Functions. 3.7 Problems. Part II DESCRIPTIVE STATISTICS FOR FUZZY DATA. 4. Fuzzy Samples. 4.1 Minimum of Fuzzy Data. 4.2 Maximum of Fuzzy Data. 4.3 Cumulative Sum for Fuzzy Data. 4.4 Problems. 5. Histograms for Fuzzy Data. 5.1 Fuzzy Frequency of a Fixed Class. 5.2 Fuzzy Frequency Distributions. 5.3 Axonometric Diagram of the Fuzzy Histogram. 5.4 Problems. 6. Empirical Distribution Functions. 6.1 Fuzzy Valued Empirical Distribution Function. 6.2 Fuzzy Empirical Fractiles. 6.3 Smoothed Empirical Distribution Function. 6.4 Problems. 7. Empirical Correlation for Fuzzy Data. 7.1 Fuzzy Empirical Correlation Coefficient. 7.2 Problems. Part III FOUNDATIONS OF STATISTICAL INFERENCE WITH FUZZY DATA. 8. Fuzzy Probability Distributions. 8.1 Fuzzy Probability Densities. 8.2 Probabilities based on Fuzzy Probability Densities. 8.3 General Fuzzy Probability Distributions. 8.4 Problems. 9. A Law of Large Numbers. 9.1 Fuzzy Random Variables. 9.2 Fuzzy Probability Distributions induced by Fuzzy Random Variables. 9.3 Sequences of Fuzzy Random Variables. 9.4 Law of Large Numbers for Fuzzy Random Variables. 9.5 Problems. 10. Combined Fuzzy Samples. 10.1 Observation Space and Sample Space. 10.2 Combination of Fuzzy Samples. 10.3 Statistics of Fuzzy Data. 10.4 Problems. Part IV CLASSICAL STATISTICAL INFERENCE FOR FUZZY DATA. 11. Generalized Point Estimations. 11.1 Estimations based on Fuzzy Samples. 11.2 Sample Moments. 11.3 Problems. 12. Generalized Confidence Regions. 12.1 Confidence Functions. 12.2 Fuzzy Confidence Regions. 12.3 Problems. 13. Statistical Tests for Fuzzy Data. 13.1 Test Statistics and Fuzzy Data. 13.2 Fuzzy p-Values. 13.3 Problems. Part V BAYESIAN INFERENCE AND FUZZY INFORMATION. 14. Bayes' Theorem and Fuzzy Information. 14.1 Fuzzy a-priori Distributions. 14.2 Updating Fuzzy a-priori Distributions. 14.3 Problems. 15. Generalized Bayes' Theorem. 15.1 Likelihood Function for Fuzzy Data. 15.2 Bayes' Theorem for Fuzzy a-priori Distribution and Fuzzy Data. 15.3 Problems. 16. Bayesian Confidence Regions. 16.1 Confidence Regions based on Fuzzy Data. 16.2 Fuzzy HPD-Regions. 16.3 Problems. 17. Fuzzy Predictive Distributions. 17.1 Discrete Case. 17.2 Discrete Models with Continuous Parameter Space. 17.3 Continuous Case. 17.4 Problems. 18. Bayesian Decisions and Fuzzy Information. 18.1 Bayesian Decisions. 18.2 Fuzzy Utility. 18.3 Discrete State Space. 18.4 Continuous State Space. 18.5 Problems. References. Part VI REGRESSION ANALYSIS AND FUZZYINFORMATION. 19 Classical regression analysis. 19.1 Regression models. 19.2 Linear regression models with Gaussian dependent variables. 19.3 General linear models. 19.4 Nonidentical variances. 19.5 Problems. 20 Regression models and fuzzy data. 20.1 Generalized estimators for linear regression models based on the extension principle. 20.2 Generalized confidence regions for parameters. 20.3 Prediction in fuzzy regression models. 20.4 Problems. 21 Bayesian regression analysis. 21.1 Calculation of a posteriori distributions. 21.2 Bayesian confidence regions. 21.3 Probabilities of hypotheses. 21.4 Predictive distributions. 21.5 A posteriori Bayes estimators for regression parameters. 21.6 Bayesian regression with Gaussian distributions. 21.7 Problems. 22 Bayesian regression analysis and fuzzy information. 22.1 Fuzzy estimators of regression parameters. 22.2 Generalized Bayesian confidence regions. 22.3 Fuzzy predictive distributions. 22.4 Problems. Part VII FUZZY TIME SERIES. 23 Mathematical concepts. 23.1 Support functions of fuzzy quantities. 23.2 Distances of fuzzy quantities. 23.3 Generalized Hukuhara difference. 24 Descriptive methods for fuzzy time series. 24.1 Moving averages. 24.2 Filtering. 24.2.1 Linear filtering. 24.2.2 Nonlinear filters. 24.3 Exponential smoothing. 24.4 Components model. 24.4.1 Model without seasonal component. 24.4.2 Model with seasonal component. 24.5 Difference filters. 24.6 Generalized Holt-Winter method. 24.7 Presentation in the frequency domain. 25 More on fuzzy random variables and fuzzy random vectors. 25.1 Basics. 25.2 Expectation and variance of fuzzy random variables. 25.3 Covariance and correlation. 25.4 Further results. 26 Stochastic methods in fuzzy time series analysis. 26.1 Linear approximation and prediction. 26.2 Remarks concerning Kalman filtering. Part VIII APPENDICES. A1 List of symbols and abbreviations. A2 Solutions to the problems. A3 Glossary. A4 Related literature. References. Index.
TL;DR: A fuzzy similarity-based self-constructing algorithm for feature clustering that can run faster and obtain better extracted features than other methods, and the user need not specify the number of extracted features in advance.
Abstract: Feature clustering is a powerful method to reduce the dimensionality of feature vectors for text classification. In this paper, we propose a fuzzy similarity-based self-constructing algorithm for feature clustering. The words in the feature vector of a document set are grouped into clusters, based on similarity test. Words that are similar to each other are grouped into the same cluster. Each cluster is characterized by a membership function with statistical mean and deviation. When all the words have been fed in, a desired number of clusters are formed automatically. We then have one extracted feature for each cluster. The extracted feature, corresponding to a cluster, is a weighted combination of the words contained in the cluster. By this algorithm, the derived membership functions match closely with and describe properly the real distribution of the training data. Besides, the user need not specify the number of extracted features in advance, and trial-and-error for determining the appropriate number of extracted features can then be avoided. Experimental results show that our method can run faster and obtain better extracted features than other methods.
TL;DR: This study integrates kernel functions with fuzzy rough set models and proposes two types of kernelized fuzzy rough sets, and extends the measures existing in classical rough sets to evaluate the approximation quality and approximation abilities of the attributes.
Abstract: Kernel machines and rough sets are two classes of commonly exploited learning techniques. Kernel machines enhance traditional learning algorithms by bringing opportunities to deal with nonlinear classification problems, rough sets introduce a human-focused way to deal with uncertainty in learning problems. Granulation and approximation play a pivotal role in rough sets-based learning and reasoning. However, a way how to effectively generate fuzzy granules from data has not been fully studied so far. In this study, we integrate kernel functions with fuzzy rough set models and propose two types of kernelized fuzzy rough sets. Kernel functions are employed to compute the fuzzy T-equivalence relations between samples, thus generating fuzzy information granules in the approximation space. Subsequently fuzzy granules are used to approximate the classification based on the concepts of fuzzy lower and upper approximations. Based on the models of kernelized fuzzy rough sets, we extend the measures existing in classical rough sets to evaluate the approximation quality and approximation abilities of the attributes. We discuss the relationship between these measures and feature evaluation function ReliefF, and augment the ReliefF algorithm to enhance the robustness of these proposed measures. Finally, we apply these measures to evaluate and select features for classification problems. The experimental results help quantify the performance of the KFRS.
TL;DR: Type-2 fuzzy logic systems developed with the aid of evolutionary optimization forms a useful modeling tool subsequently resulting in a collection of efficient ''If-Then'' rules, which efficiently capture the factor of uncertainty.
TL;DR: The results show empirically that the use of the methodology outperforms the initial Fuzzy Rule-Based Classification System and also improves the behavior of the genetic tuning based on the 3-tuples fuzzy linguistic representation.
TL;DR: This work presents the adaptive neurocomplex-fuzzy-inferential system (ANCFIS), which is the first neurofuzzed system architecture to implement complex fuzzy rules (and, in particular, the signature property of rule interference).
Abstract: Complex fuzzy sets (CFSs) are an extension of type-1 fuzzy sets in which the membership of an object to the set is a value from the unit disc of the complex plane. Although there has been considerable progress made in determining the properties of CFSs and complex fuzzy logic, there has yet to be any practical application of this concept. We present the adaptive neurocomplex-fuzzy-inferential system (ANCFIS), which is the first neurofuzzy system architecture to implement complex fuzzy rules (and, in particular, the signature property of rule interference). We have applied this neurofuzzy system to the domain of time-series forecasting, which is an important machine-learning problem. We find that ANCFIS performs well in one synthetic and five real-world forecasting problems and is also very parsimonious. Experimental comparisons show that ANCFIS is comparable with existing approaches on our five datasets. This work demonstrates the utility of complex fuzzy logic on real-world problems.
TL;DR: In this paper a new method for ranking interval-valued intuitionistic fuzzy sets has been introduced and compared with other methods by numerical examples.
TL;DR: A fuzzy min-max neural network based on data core (DCFMN) is proposed for pattern classification and has strong robustness and high accuracy in classification taking onto account the effect of data core and noise.
Abstract: A fuzzy min-max neural network based on data core (DCFMN) is proposed for pattern classification. A new membership function for classifying the neuron of DCFMN is defined in which the noise, the geometric center of the hyperbox, and the data core are considered. Instead of using the contraction process of the FMNN described by Simpson, a kind of overlapped neuron with new membership function based on the data core is proposed and added to neural network to represent the overlapping area of hyperboxes belonging to different classes. Furthermore, some algorithms of online learning and classification are presented according to the structure of DCFMN. DCFMN has strong robustness and high accuracy in classification taking onto account the effect of data core and noise. The performance of DCFMN is checked by some benchmark datasets and compared with some traditional fuzzy neural networks, such as the fuzzy min-max neural network (FMNN), the general FMNN, and the FMNN with compensatory neuron. Finally the pattern classification of a pipeline is evaluated using DCFMN and other classifiers. All the results indicate that the performance of DCFMN is excellent.
TL;DR: The experimental results show that the proposed weighted fuzzy interpolative reasoning method by the use of the optimally learned weights that were obtained by the proposed GA-based weight-learning algorithm has statistically significantly smaller error rates than the existing methods.
Abstract: In this paper, we propose a weighted fuzzy interpolative reasoning method for sparse fuzzy rule-based systems. It is based on a genetic algorithm (GA)-based weight-learning technique. The proposed method can deal with fuzzy rule interpolation with weighted antecedent variables. It also can deal with fuzzy rule interpolation based on polygonal membership functions and bell-shaped membership functions. We also propose a GA-based weight-learning algorithm to automatically learn the optimal weights of the antecedent variables of the fuzzy rules. Furthermore, we apply the proposed weighted fuzzy interpolative reasoning method and the proposed GA-based weight-learning algorithm to deal with the truck backer-upper control problem, the computer activity prediction problem, multivariate regression problems, and time series prediction problems. Based on statistical analysis techniques, the experimental results show that the proposed weighted fuzzy interpolative reasoning method by the use of the optimally learned weights that were obtained by the proposed GA-based weight-learning algorithm has statistically significantly smaller error rates than the existing methods.
TL;DR: The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method extended to intuitionistic fuzzy environments is proposed to select appropriate personnel among candidates to deal with vagueness in fuzzy environments.
Abstract: One of the most important activities carried out by human resource management is personnel selection, concerned with identifying an individual from a pool of candidates suitable for a vacant position. Traditionally, personnel selection is a group decision-making problem under multiple criteria containing subjectivity, imprecision, and vagueness, which are best represented with fuzzy data. In this article, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method extended to intuitionistic fuzzy environments is proposed to select appropriate personnel among candidates. An intuitionistic fuzzy set (IFS), which is characterized by membership function, nonmembership function, and hesitation margin, is a more suitable way to deal with vagueness when compared to a fuzzy set. To demonstrate the applicability and effectiveness of the intuitionistic fuzzy TOPSIS method, a numerical example of personnel selection in a manufacturing company for a sales manager position is given. © 2011 Wiley Periodicals, Inc. © 2011 Wiley Periodicals, Inc.
TL;DR: An improvement to Liu's centroid type-reduction strategy to carry out type reduction for type-2 fuzzy sets by employing the previously obtained result to construct the starting values in the current application of the Karnik-Mendel algorithm.
Abstract: Karnik and Mendel proposed an algorithm to compute the centroid of an interval type-2 fuzzy set efficiently. Based on this algorithm, Liu developed a centroid type-reduction strategy to carry out type reduction for type-2 fuzzy sets. A type-2 fuzzy set is decomposed into a collection of interval type-2 fuzzy sets by -cuts. Then, the Karnik-Mendel algorithm is called for each interval type-2 fuzzy set iteratively. However, the initialization of the switch point in each application of the Karnik-Mendel algorithm is not a good one. In this paper, we present an improvement to Liu's algorithm. We employ the previously obtained result to construct the starting values in the current application of the Karnik-Mendel algorithm. Convergence in each iteration, except the first one, can then speed up, and type reduction for type-2 fuzzy sets can be carried out faster. The efficiency of the improved algorithm is analyzed mathematically and demonstrated by experimental results.
TL;DR: A new method is proposed for solving fuzzy transportation problems by assuming that a decision maker is uncertain about the precise values of the transportation cost, availability and demand of the product.
TL;DR: A new method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), the enrollments of the University of Alabama and the inventory demand based on high-order fuzzy logical relationships is presented.
Abstract: People usually use many methods to predict the weather, the temperature, the stock index, the enrollments, the earthquake, the economy, etc. Based on these forecasting results, people can prevent damages to occur or get benefits from the forecasting activities. In this paper, we present a new method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), the enrollments of the University of Alabama and the inventory demand based on high-order fuzzy logical relationships. First, the proposed method fuzzifies the historical data into fuzzy sets to form high-order fuzzy logical relationships. Then, it calculates the value of the variable between the subscripts of adjacent fuzzy sets appearing in the antecedents of high-order fuzzy logical relationships. Then, it lets the high-order fuzzy logical relationships with the same variable value form a high-order fuzzy logical relationship group. Finally, it chooses a high-order fuzzy logical relationship group to forecast the TAIEX. The proposed method gets a higher average forecasting accuracy rate to forecast the TAIEX, the enrollments of the University of Alabama and the inventory demand than the existing methods.
TL;DR: The design methodology of an optimized fuzzy controller with the aid of particle swarm optimization (PSO) for ball and beam system is introduced and type-2 fuzzy cascade controllers based on PSO based on type-1/type-2 FLC are applied.
Abstract: In this study, we introduce the design methodology of an optimized fuzzy controller with the aid of particle swarm optimization (PSO) for ball and beam system. The ball and beam system is a well-known control engineering experimental setup which consists of servo motor, beam and ball. This system exhibits a number of interesting and challenging properties when being considered from the control perspective. The ball and beam system determines the position of ball through the control of a servo motor. The displacement change of the position of ball leads to the change of the angle of the beam which determines the position angle of a servo motor. The fixed membership function design of type-1 based fuzzy logic controller (FLC) leads to the difficulty of rule-based control design when representing linguistic nature of knowledge. In type-2 FLC as the expanded type of type-1 FL, we can effectively improve the control characteristic by using the footprint of uncertainty (FOU) of the membership functions. Type-2 FLC exhibits some robustness when compared with type-1 FLC. Through computer simulation as well as real-world experiment, we apply optimized type-2 fuzzy cascade controllers based on PSO to ball and beam system. To evaluate performance of each controller, we consider controller characteristic parameters such as maximum overshoot, delay time, rise time, settling time, and a steady-state error. In the sequel, the optimized fuzzy cascade controller is realized and also experimented with through running two detailed comparative studies including type-1/type-2 fuzzy controller and genetic algorithms/particle swarm optimization.
01 Dec 2011
TL;DR: In this paper, a new design methodology of type-2 fuzzy models whose intent is to effectively exploit the uncertainty of non-numeric membership functions is offered and a new performance index is used to navigate the construction of the fuzzy model.
Abstract: In this paper, we offer a new design methodology of type-2 fuzzy models whose intent is to effectively exploit the uncertainty of non-numeric membership functions. A new performance index, which guides the development of the fuzzy model, is used to navigate the construction of the fuzzy model. The underlying idea is that an optimal granularity allocation throughout the membership functions used in the fuzzy model leads to the best design. In contrast to the commonly utilized criterion where one strives for the highest accuracy of the model, the proposed index is formed in such a way so that the type-2 fuzzy model produced intervals, which ''cover'' the experimental data and at the same time are made as narrow (viz. specific) as possible. Genetic algorithm is proposed to automate the design process and further improve the results by carefully exploiting the search space. Experimental results show the efficiency of the proposed design methodology.
TL;DR: A novel method, based on the areas on the left and the right sides of fuzzy numbers is proposed for ranking fuzzy numbers, which has very easy and simple calculations compared to other methods.
Abstract: In this paper, a novel method, based on the areas on the left and the right sides of fuzzy numbers is proposed for ranking fuzzy numbers. The merits of the results given here is to overcome certain shortcomings in the recent literature that mostly does not end in the right ordering of fuzzy numbers. The method also has very easy and simple calculations compared to other methods. Moreover, numerical examples are given to compare the proposed method with other existing ones.
01 Mar 2011
TL;DR: The interval-valued fuzzy ELECTRE method is presented aiming at solving MCDM problems in which the weights of criteria are unequal, using interval- valued fuzzy set concepts.
Abstract: Decision-making is the process of finding the best option among the feasible alternatives. In classical multiple criteria decision-making (MCDM) methods, the ratings and the weights of the criteria are known precisely. However, if decision makers cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy set theory can provide a more accurate modeling. In this paper, the interval-valued fuzzy ELECTRE method is presented aiming at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy set concepts. For the purpose of proving the validity of the proposed model, we present a numerical example and build a practical maintenance strategy selection problem.
01 Jan 2011
TL;DR: The concepts of membership function, variance, entropy and distance of uncertain sets, based on uncertain set theory, are proposed and fuzzy logic will be discussed at the end of this paper.
Abstract: This paper discusses uncertain set theory and proposes the concepts of membership function, variance, entropy and distance of uncertain sets. In order to determine membership functions, uncertain statistics is also suggested. Based on uncertain set theory, uncertain logic is presented for dealing with human language by using uncertain quantier, uncertain subject and uncertain predicate. As an application, uncertain logic provides a means for extracting linguistic summary from a collection of raw data. Finally, fuzzy logic will be discussed at the end of this paper. c
TL;DR: The fuzzy set theory is used to add more information and flexibility to process capability analyses (PCA) by converting linguistic definition of the quality characteristic measurements to fuzzy numbers and fuzzy PCIs are produced based on these measurements and fuzzy specification limits (SLs).
Abstract: Process performance can be analyzed by using process capability indices (PCIs), which are summary statistics to depict the process location and dispersion successfully. Although they are very usable statistics, they have some limitations which prevent a deep and flexible analysis because of the crisp measurements and specification limits (SLs). If the specification limits or measurements are expressed by linguistic variables, traditional PCIs cause some misleading results. In this paper, the fuzzy set theory is used to add more information and flexibility to process capability analyses (PCA). For this aim, linguistic definition of the quality characteristic measurements are converted to fuzzy numbers and fuzzy PCIs are produced based on these measurements and fuzzy specification limits (SLs). Also fuzzy control charts are derived for fuzzy measurements of the related quality characteristic. They are used to increase the accuracy of PCA by determining whether or not the process is in statistical control. The fuzzy formulation of the indices C"p and C"p"k, which are the most used two traditional PCIs, are produced when SLs and measurements are both triangular (TFN) and trapezoidal fuzzy numbers (TrFN). The proposed methodologies are applied in a piston manufacturer in Konya's Industrial Area, Turkey.
01 Jan 2011
TL;DR: An innovative fuzzy approach for ranking alternatives in multiple attribute decision making problems based on TOPSIS is presented in-depth and studied through simulation comparison with the original method.
Abstract: In this paper, an innovative fuzzy approach for ranking alternatives in multiple attribute decision making problems based on TOPSIS is presented in-depth and studied through simulation comparison with the original method. The TOPSIS method provides the principle of compromise that the chosen alternative should have the shortest distance from the ideal solution and, simultaneously, the farthest distance from the negative ideal solution. However, the TOPSIS method does not always produce results in harmony with this principle due to an oversimplified definition of its aggregation function which does not grasp the contradictory nature of the principle's formulation. Our approach addresses this issue through the introduction of a fuzzy set representation of the closeness to the ideal and to the negative ideal solution for the definition of the aggregation function which is modeled as the membership function of the intersection of two fuzzy sets. This model enables a parameterization of the method according to the risk attitude of the decision maker. Thus, a class of methods is formulated whose different instances correspond to different risk attitudes of the decision makers. In order to define some clear advises for decision makers facilitating a proper parameterization of the method, a comparative analysis of the proposed class of methods with the original TOPSIS method is performed according to well defined simulation techniques. The results of the simulation experiment show on the one hand that there is no direct correspondence between the proposed class of methods and TOPSIS, and on the other hand that it is adequate to distinguish three instances that correspond respectively to risk-averse, risk-neutral and risk-seeking decision makers. Finally, a numerical example pertaining to the problem of service provider selection is presented to illustrate the application of the proposed class of methods and its functioning.