Showing papers on "Membership function published in 2013"

Pythagorean fuzzy subsets

Abstract: We introduce a new class of non-standard fuzzy subsets called Pythagorean fuzzy subsets and the related idea of Pythagorean membership grades. We focus on the negation operation and its relationship to the Pythagorean theorem. We compare Pythagorean fuzzy subsets with intuitionistic fuzzy subsets. We look at the basic set operations for the Pythagorean fuzzy subsets.

Picture fuzzy sets - A new concept for computational intelligence problems

Abstract: Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory, other try to handle imprecision and uncertainty in different way. In this paper, we introduce a new notion of picture fuzzy sets (PFS), which are directly extensions of fuzzy sets and of intuitonistic fuzzy sets (Atanassov). Then some operations on picture fuzzy sets are defined and some properties of these operations are considered. Here the basic preliminaries of PFS theory are presented.

Generalized hesitant fuzzy sets and their application in decision support system

Abstract: Hesitant fuzzy sets are very useful to deal with group decision making problems when experts have a hesitation among several possible memberships for an element to a set. During the evaluating process in practice, however, these possible memberships may be not only crisp values in [0,1], but also interval values. In this study, we extend hesitant fuzzy sets by intuitionistic fuzzy sets and refer to them as generalized hesitant fuzzy sets. Zadeh's fuzzy sets, intuitionistic fuzzy sets and hesitant fuzzy sets are special cases of the new fuzzy sets. We redefine some basic operations of generalized hesitant fuzzy sets, which are consistent with those of hesitant fuzzy sets. Some arithmetic operations and relationships among them are discussed as well. We further introduce the comparison law to distinguish two generalized hesitant fuzzy sets according to score function and consistency function. Besides, the proposed extension principle enables decision makers to employ aggregation operators of intuitionistic fuzzy sets to aggregate a set of generalized hesitant fuzzy sets for decision making. The rationality of applying the proposed techniques is clarified by a practical example. At last, the proposed techniques are devoted to a decision support system.

Adaptive neuro-fuzzy approach for wind turbine power coefficient estimation

Abstract: Wind energy has become a large contender of traditional fossil fuel energy, particularly with the successful operation of multi-megawatt sized wind turbines. However, reasonable wind speed is not adequately sustainable everywhere to build an economical wind farm. In wind energy conversion systems, one of the operational problems is the changeability and fluctuation of wind. In most cases, wind speed can vacillate rapidly. Hence, quality of produced energy becomes an important problem in wind energy conversion plants. Several control techniques have been applied to improve the quality of power generated from wind turbines. In this study, the adaptive neuro-fuzzy inference system (ANFIS) is designed and adapted to estimate optimal power coefficient value of the wind turbines. Neural network in ANFIS adjusts parameters of membership function in the fuzzy logic of the fuzzy inference system (FIS). The back propagation learning algorithm is used for training this network. This intelligent controller is implemented using Matlab/Simulink and the performances are investigated. The simulation results presented in this paper show the effectiveness of the developed method.

Decision and Game Theory in Management With Intuitionistic Fuzzy Sets

Abstract: This book is an academic monograph based on the SCI and EI citing more than 50 papers published in international journals by the author in recent years. The focus of this book is on both decision and games with intuitionistic fuzzy sets. This book is divided into 11 chapters in which the main contents are as follows: intuitionistic fuzzy set theories, intuitionistic fuzzy aggregation operators and multiattribute decision-making methods with intuitionistic fuzzy sets, multiattribute decision-making methods with intuitionistic fuzzy sets, multiattribute decision-making methods with interval-valued intuitionistic fuzzy sets, multiattribute decision-making methods with intuitionistic fuzzy numbers, multiattribute group decision-making methods with intuitionistic fuzzy sets, matrix games with payoffs of intuitionistic fuzzy sets and linear and nonlinear programming methods, matrix games with payoffs of interval-valued intuitionistic fuzzy sets and linear and nonlinear programming methods, matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers and solution methods, matrix games with goals of intuitionistic fuzzy sets and linear programming method, bi-matrix games with payoffs of intuitionistic fuzzy sets and bilinear programming method. The aim of this book is to develop and establish a new research field of decision and games with intuitionistic fuzzy sets. This book is addressed to people in theoretical researches and practical applications from different fields: decision theory, game theory, management science, fuzzy system theory, applied mathematics, economics, control theory, artificial intelligence, expert system, etc. Moreover, it is also addressed to teachers, postgraduates and doctors in colleges and universities in different disciplines or majors: decision analysis, management, business, operational research, fuzzy mathematics, systems engineering, project management, industrial engineering, applied mathematics, optimizing design of engineering and industrial system, hydrology and water resources and so on.

γ-Open sets and γ-continuous mappings in fuzzy bitopological spaces

Abstract: In this paper we introduce the notion of γ-open sets and γ-continuous functions in fuzzy bitopological spaces. We examine some basic properties and prove some characterization theorems for the said functions. It is observed that every pairwise fuzzy γ-continuous functions is pairwise fuzzy precontinuous but the converse not true.

IVTURS: A Linguistic Fuzzy Rule-Based Classification System Based On a New Interval-Valued Fuzzy Reasoning Method With Tuning and Rule Selection

Abstract: Interval-valued fuzzy sets have been shown to be a useful tool to deal with the ignorance related to the definition of the linguistic labels. Specifically, they have been successfully applied to solve classification problems, performing simple modifications on the fuzzy reasoning method to work with this representation and making the classification based on a single number. In this paper, we present IVTURS, which is a new linguistic fuzzy rule-based classification method based on a new completely interval-valued fuzzy reasoning method. This inference process uses interval-valued restricted equivalence functions to increase the relevance of the rules in which the equivalence of the interval membership degrees of the patterns and the ideal membership degrees is greater, which is a desirable behavior. Furthermore, their parametrized construction allows the computation of the optimal function for each variable to be performed, which could involve a potential improvement in the system's behavior. Additionally, we combine this tuning of the equivalence with rule selection in order to decrease the complexity of the system. In this paper, we name our method IVTURS-FARC, since we use the FARC-HD method to accomplish the fuzzy rule learning process. The experimental study is developed in three steps in order to ascertain the quality of our new proposal. First, we determine both the essential role that interval-valued fuzzy sets play in the method and the need for the rule selection process. Next, we show the improvements achieved by IVTURS-FARC with respect to the tuning of the degree of ignorance when it is applied in both an isolated way and when combined with the tuning of the equivalence. Finally, the significance of IVTURS-FARC is further depicted by means of a comparison by which it is proved to outperform the results of FARC-HD and FURIA, which are two high performing fuzzy classification algorithms.

Fault-Tolerant Control for Six-Phase PMSM Drive System via Intelligent Complementary Sliding-Mode Control Using TSKFNN-AMF

Abstract: An intelligent complementary sliding-mode control (CSMC) (ICSMC) is proposed in this paper for the fault-tolerant control of a six-phase permanent-magnet synchronous motor (PMSM) drive system with open phases. First, the dynamics of the six-phase PMSM drive system with a lumped uncertainty is described in detail. Then, the fault detection and operating decision method is briefly introduced. Moreover, a CSMC is designed to stabilize the fault-tolerant control of the six-phase PMSM drive system. Furthermore, to improve the required control performance and to maintain the stability of the six-phase PMSM drive system under faulty condition, the ICSMC is developed. In this approach, a Takagi-Sugeno-Kang-type fuzzy neural network with asymmetric membership function (TSKFNN-AMF) estimator with accurate approximation capability is employed to estimate the lumped uncertainty. In addition, the adaptive learning algorithms for the online training of the TSKFNN-AMF are derived using the Lyapunov theorem to guarantee the closed-loop stability. Additionally, to enhance the control performance of the proposed intelligent fault-tolerant control, a 32-b floating-point digital signal processor, TMS320F28335, is adopted for the implementation of the proposed fault-tolerant control system. Finally, some experimental results are illustrated to demonstrate the validity of the proposed fault-tolerant control for the six-phase PMSM drive system via ICSMC.

Intuitionistic fuzzy soft set theory and its decision making

Abstract: In this work, we first defined the intuitionistic fuzzy soft sets IFS-sets and their operations By using them, we then give some results and construct a decision making method Finally, we give an application which shows that this approach is useful to handle several realistic uncertain problems

Fuzzy Rules Interpolation for Sparse Fuzzy Rule-Based Systems Based on Interval Type-2 Gaussian Fuzzy Sets and Genetic Algorithms

Abstract: In this paper, we present a new method for fuzzy rules interpolation for sparse fuzzy rule-based systems based on interval type-2 Gaussian fuzzy sets and genetic algorithms. First, we present a method to deal with the interpolation of fuzzy rules based on interval type-2 Gaussian fuzzy sets. We also prove that the proposed method guarantees to produce normal interval type-2 Gaussian fuzzy sets. Then, we present a method to learn optimal interval type-2 Gaussian fuzzy sets for sparse fuzzy rule-based systems based on genetic algorithms. We also apply the proposed fuzzy rules interpolation method and the proposed learning method to deal with multivariate regression problems and time series prediction problems. The experimental results show that the proposed fuzzy rules interpolation method using the optimally learned interval type-2 Gaussian fuzzy sets gets higher average accuracy rates than the existing methods.

General and Interval Type-2 Fuzzy Face-Space Approach to Emotion Recognition

Abstract: Facial expressions of a person representing similar emotion are not always unique. Naturally, the facial features of a subject taken from different instances of the same emotion have wide variations. In the presence of two or more facial features, the variation of the attributes together makes the emotion recognition problem more complicated. This variation is the main source of uncertainty in the emotion recognition problem, which has been addressed here in two steps using type-2 fuzzy sets. First a type-2 fuzzy face space is constructed with the background knowledge of facial features of different subjects for different emotions. Second, the emotion of an unknown facial expression is determined based on the consensus of the measured facial features with the fuzzy face space. Both interval and general type-2 fuzzy sets (GT2FS) have been used separately to model the fuzzy face space. The interval type-2 fuzzy set (IT2FS) involves primary membership functions for m facial features obtained from n-subjects, each having l-instances of facial expressions for a given emotion. The GT2FS in addition to employing the primary membership functions mentioned above also involves the secondary memberships for individual primary membership curve, which has been obtained here by formulating and solving an optimization problem. The optimization problem here attempts to minimize the difference between two decoded signals: the first one being the type-1 defuzzification of the average primary membership functions obtained from the n-subjects, while the second one refers to the type-2 defuzzified signal for a given primary membership function with secondary memberships as unknown. The uncertainty management policy adopted using GT2FS has resulted in a classification accuracy of 98.333% in comparison to 91.667% obtained by its interval type-2 counterpart. A small improvement (approximately 2.5%) in classification accuracy by IT2FS has been attained by pre-processing measurements using the well-known interval approach.

A generalization of the Wilcoxon signed-rank test and its applications

Abstract: This paper extends the Wilcoxon signed-rank test to the case where the available observations are imprecise quantities, rather than crisp. To do this, the associated test statistic is extended, using the α-cuts approach. In addition, the concept of critical value is generalized to the case when the significance level is given by a fuzzy number. Finally, to accept or reject the null hypothesis of interest, a preference degree between two fuzzy sets is employed for comparing the observed fuzzy test statistic and fuzzy critical value.

Calibrated fuzzy AHP for current bank account selection

Abstract: Fuzzy AHP is a hybrid method that combines Fuzzy Set Theory and AHP. It has been developed to take into account uncertainty and imprecision in the evaluations. Fuzzy Set Theory requires the definition of a membership function. At present, there are no indications of how these membership functions can be constructed. In this paper, a way to calibrate the membership functions with comparisons given by the decision-maker on alternatives with known measures is proposed. This new technique is illustrated in a study measuring the most important factors in selecting a student current account.

A web based decision support system driven by fuzzy logic for the diagnosis of typhoid fever

Abstract: Research has identified Typhoid Fever (TF) as the major cause of morbidity and mortality in most developing countries. The diagnosis of TF involves several variables which usually makes it difficult to arrive at accurate and timely diagnosis. This research proposes a Web-Based Decision Support System (WBDSS) driven by Fuzzy Logic (FL) for the diagnosis of TF. The system comprises of a Knowledge Base (KB) and a Fuzzy Inference System (FIS).The FIS is composed of a Fuzzifier, Fuzzy Inference Engine (FIE), and a Defuzzifier. The FIE is the core of the FIS and it adopts the Root Sum Square (RSS) technique in drawing valid conclusion. The Fuzzifier uses a triangular membership function to determine the degree of contribution of each decision variable while the Defuzzifier adopts the Centroid of Area (CoA) defuzzification technique to generate a crisp output for a given diagnosis. An experimental study of the proposed system was conducted using medical records of TF patients obtained from the Federal Medical Center, Owo, Ondo State-Nigeria over a period of six months and the results of the study were found to be within the range of predefined limit as examined by medical experts. Standard statistical metrics were used to measure the efficiency of the proposed system and the results obtained show that the proposed system is 94% efficient in providing accurate diagnosis.

Interval Type-2 Fuzzy Sets Constructed From Several Membership Functions: Application to the Fuzzy Thresholding Algorithm

Abstract: An important problem in working with fuzzy sets is the correct construction of the membership functions that represent the objects of the system. Different experts construct different membership functions to represent the same object. In this paper, we construct an interval type-2 fuzzy set (IT2FS) with different fuzzy sets such that the length of the (membership) interval represents the uncertainty of the expert with respect to the choice of the membership function. We analyze this problem in the context of image segmentation. We propose a new version of the classical fuzzy thresholding algorithm, in which an expert can select multiple membership functions, to avoid the problem of selecting only one to represent the image. From these membership functions, we construct an IT2FS, and by minimizing its entropy, we find a threshold with which to binarize the image. We present experimental results that show that it is advisable to use this methodology when it is not known which membership function is the most suitable.

Fault-Tolerant Control of a Six-Phase Motor Drive System Using a Takagi–Sugeno–Kang Type Fuzzy Neural Network With Asymmetric Membership Function

Abstract: A Takagi-Sugeno-Kang type fuzzy neural network with asymmetric membership function (TSKFNN-AMF) is proposed in this study for the fault-tolerant control of a six-phase permanent-magnet synchronous motor (PMSM) drive system First, the dynamics of the six-phase PMSM drive system is described in detail Then, the fault detection and operating decision method is briefly introduced Moreover, to achieve the required control performance and to maintain the stability of a six-phase PMSM drive system under faulty condition, the TSKFNN-AMF control, which combines the advantages of a Takagi-Sugeno-Kang type fuzzy logic system and an asymmetric membership function, is developed The network structure, online learning algorithm using a delta adaptation law, and convergence analysis of the TSKFNN-AMF are described in detail Furthermore, to enhance the control performance of the proposed intelligent fault-tolerant control, a 32-bit floating-point digital signal processor TMS320F28335 is adopted for the implementation of the proposed fault-tolerant control system Finally, some experimental results are illustrated to show the validity of the proposed TSKFNN-AMF fault-tolerant control for the six-phase PMSM drive system

Extraction of fuzzy rules from fuzzy decision trees: An axiomatic fuzzy sets (AFS) approach

Abstract: In this study, we introduce a new type of coherence membership function to describe fuzzy concepts, which builds upon the theoretical findings of the Axiomatic Fuzzy Set (AFS) theory. This type of membership function embraces both the factor of fuzziness (by capturing subjective imprecision) and randomness (by referring to the objective uncertainty) and treats both of them in a consistent manner. Furthermore we propose a method to construct a fuzzy rule-based classifier using coherence membership functions. Given the theoretical developments presented there, the resulting classification systems are referred to as AFS classifiers. The proposed algorithm consists of three major steps: (a) generating fuzzy decision trees by assuming some level of specificity (detailed view) quantified in terms of threshold; (b) pruning the obtained rule-base; and (c) determining the optimal threshold resulting in a final tree. Compared with other fuzzy classifiers, the AFS classifier exhibits several essential advantages being of practical relevance. In particular, the relevance of classification results is quantified by associated confidence levels. Furthermore the proposed algorithm can be applied to data sets with mixed data type attributes. We have experimented with various data commonly present in the literature and compared the results with that of SVM, KNN, C4.5, Fuzzy Decision Trees (FDTs), Fuzzy SLIQ Decision Tree (FS-DT), FARC-HD and FURIA. It has been shown that the accuracy is higher than that being obtained by other methods. The results of statistical tests supporting comparative analysis show that the proposed algorithm performs significantly better than FDTs, FS-DT, KNN and C4.5.

Triangular Hesitant Fuzzy Set and Its Application to Teaching Quality Evaluation

Abstract: As a generalization of fuzzy set, hesitant fuzzy set is a very useful technique to express people’s hesitancy in daily life. But there are weak points in traditional hesitant fuzzy set, which expressed the membership degrees of an element to a given set only by several crisp numbers. In this paper, we extend the traditional hesitant fuzzy set to Triangular Fuzzy Hesitant Fuzzy Set (TFHFS), in which the membership degree of an element to a given set is expressed by several possible triangular fuzzy numbers. Then a series of aggregation operators for TFHFEs are proposed. Furthermore, we apply them to multiple attribute decision making with triangular fuzzy hesitant fuzzy information.

Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions

Abstract: In this article, the fuzzy Lyapunov function approach is considered for stabilising continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality LMI stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing slack LMI variables into the problem formulation. The relaxation conditions given can also be used with a class of fuzzy Lyapunov functions which also depends on the membership function first-order time-derivative. The stability results are thus extended to systems with large number of rules under membership function order relations and used to design parallel-distributed compensation PDC fuzzy controllers which are also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilising conditions presented.