Showing papers on "Membership function published in 2018"

Some q‐Rung Orthopair Fuzzy Aggregation Operators and their Applications to Multiple‐Attribute Decision Making

Abstract: The q-rung orthopair fuzzy sets (q-ROFs) are an important way to express uncertain information, and they are superior to the intuitionistic fuzzy sets and the Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the membership degree and the qth power of the degrees of non-membership is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we propose the q-rung orthopair fuzzy weighted averaging operator and the q-rung orthopair fuzzy weighted geometric operator to deal with the decision information, and their some properties are well proved. Further, based on these operators, we presented two new methods to deal with the multi-attribute decision making problems under the fuzzy environment. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.

Network-Based T–S Fuzzy Dynamic Positioning Controller Design for Unmanned Marine Vehicles

Abstract: This paper is concerned with a Takagi–Sugeno (T–S) fuzzy dynamic positioning controller design for an unmanned marine vehicle (UMV) in network environments. Network-based T–S fuzzy dynamic positioning system (DPS) models for the UMV are first established. Then, stability and stabilization criteria are derived by taking into consideration an asynchronous difference between the normalized membership function of the T–S fuzzy DPS and that of the controller. The proposed stabilization criteria can stabilize states of the UMV. The dynamic positioning performance analysis verifies the effectiveness of the networked modeling and the controller design.

Sustainable supply chain management using approximate fuzzy DEMATEL method

Abstract: This study develops the approximate fuzzy Decision Making Trial and Evaluation Laboratory (AFDEMATEL) to analyze uncertain influential factors. The approximate fuzzy arithmetic operations under the weakest t-norm (Tω) arithmetic operations to evaluate sustainable supply chain management based on AFDEMATEL. The fuzzy DEMATEL is one of important decision-making method under uncertain environment. The fuzzy DEMATEL had to be developed for clearly display expert’s options with linguistic variables. The fuzzy operations usually adopt α-cut arithmetic in fuzzy DEMATEL. In this research, the fuzzy DEMATEL technology is substituted with the AFDEMATEL technology. In the sustainable supply chain management example, the AFDEMATEL is employed to find fuzzy cause and effect relationships among criteria. Particular note should be made of the following: [1] the fuzzy DEMATEL with α-cut arithmetic model cannot exactly handle fuzzy cause and effect relationships under uncertain environment, and the fuzziness accumulation phenomenon of the α-cut arithmetic may influence final fuzzy cause and effect relationships; and [2] the approximate fuzzy arithmetic operations gives a justifiable fuzziness spread to analyze fuzzy cause and effect relationships. In the case of selection of cans suppliers, the AFDEMATEL examines the influential factors. Proposed method provides justifiable fuzzy cause and effect relationships with approximate fuzzy arithmetic and can analyze across quadrants phenomenon under uncertain environment, since decision-makers usually want to accurately estimate uncertain influential factors.

A Nonlinear Fuzzy Neural Network Modeling Approach Using an Improved Genetic Algorithm

Abstract: Fuzzy neural networks (FNNs) are quite useful for nonlinear system identification when only the input/output information is available. A new FNN framework is first proposed by combining an AutoRegressive with exogenous input (ARX) with the nonlinear Tanh function in the Takagi–Sugeno (T-S) type fuzzy consequent part. An improved genetic algorithm is then designed to optimize the structure and parameters of the FNN simultaneously under unknown plant dynamics. The hybrid encoding/decoding, neighborhood search operator, and maintain operator are presented to optimize the input structure of the ARX plus the nonlinear function submodel, the number of the fuzzy rules, and the parameters of the membership function. Three benchmarks and a liquid level modeling problem in an industrial coke furnace are utilized to compare the performance of several typical methods. Simulation results show that the proposed method is superior in structure simplification, modeling precision, and generalization capability.

Distance Measure of Pythagorean Fuzzy Sets

Abstract: The main feature of Pythagorean fuzzy sets is that it is characterized by four parameters, namely membership degree, nonmembership degree, strength of commitment about membership, and direction of commitment. In this paper, we propose a variety of distance measures for Pythagorean fuzzy sets and Pythagorean fuzzy numbers, which take into account the four parameters of Pythagorean fuzzy sets. Finally, a numerical example is provided to illustrate the validity and applicability of the presented distance measures.

Large-Scale Multimodality Attribute Reduction With Multi-Kernel Fuzzy Rough Sets

Abstract: In complex pattern recognition tasks, objects are typically characterized by means of multimodality attributes, including categorical, numerical, text, image, audio, and even videos. In these cases, data are usually high dimensional, structurally complex, and granular. Those attributes exhibit some redundancy and irrelevant information. The evaluation, selection, and combination of multimodality attributes pose great challenges to traditional classification algorithms. Multikernel learning handles multimodality attributes by using different kernels to extract information coming from different attributes. However, it cannot consider the aspects fuzziness in fuzzy classification. Fuzzy rough sets emerge as a powerful vehicle to handle fuzzy and uncertain attribute reduction. In this paper, we design a framework of multimodality attribute reduction based on multikernel fuzzy rough sets. First, a combination of kernels based on set theory is defined to extract fuzzy similarity for fuzzy classification with multimodality attributes. Then, a model of multikernel fuzzy rough sets is constructed. Finally, we design an efficient attribute reduction algorithm for large scale multimodality fuzzy classification based on the proposed model. Experimental results demonstrate the effectiveness of the proposed model and the corresponding algorithm.

Isomorphic Multiplicative Transitivity for Intuitionistic and Interval-Valued Fuzzy Preference Relations and Its Application in Deriving Their Priority Vectors

Abstract: Intuitionistic fuzzy preference relations (IFPRs) are used to deal with hesitation, while interval-valued fuzzy preference relations (IVFPRs) are for uncertainty in multicriteria decision making (MCDM) This paper aims to explore the isomorphic multiplicative transitivity for IFPRs and IVFPRs, which builds the substantial relationship between hesitation and uncertainty in MCDM To do that, the definition of the multiplicative transitivity property of IFPRs is established by combining the multiplication of intuitionistic fuzzy sets and Tanino's multiplicative transitivity property of fuzzy preference relations It is proved to be isomorphic to the multiplicative transitivity of IVFPRs derived via Zadeh's extension principle The use of the multiplicative transitivity isomorphism is twofold: 1) to discover the substantial relationship between IFPRs and IVFPRs, which will bridge the gap between hesitation and uncertainty in MCDM problems; and 2) to strengthen the soundness of the multiplicative transitivity property of IFPRs and IVFPRs by supporting each other with two different reliable sources, respectively Furthermore, based on the existing isomorphism, the concept of multiplicative consistency for IFPRs is defined through a strict mathematical process, and it is proved to satisfy the following several desirable properties: weak transitivity, max–max transitivity, and center-division transitivity A multiplicative consistency-based multiobjective programming (MOP) model is investigated to derive the priority vector from an IFPR This model has the advantage of not losing information, as the priority vector representation coincides with that of the input information, which was not the case with the existing methods, where crisp priority vectors were derived as a consequence of the modeling transitivity just for the intuitionistic membership function and not for the intuitionistic nonmembership function Finally, a numerical example concerning green supply selection is given to validate the efficiency and practicality of the proposed multiplicative consistency MOP model

Step-by-Step Fuzzy Diagnosis Method for Equipment Based on Symptom Extraction and Trivalent Logic Fuzzy Diagnosis Theory

Abstract: A step-by-step fuzzy diagnostic method based on frequency-domain symptom extraction and trivalent logic fuzzy diagnosis theory (TLFD), which is established by combining the trivalent logic inference theory with the possibility and fuzzy theories, is proposed herein. The features for diagnosing a number of abnormal states are extracted sequentially from the measured signals using statistical tests in the frequency domain. The symptom parameters (SPs) that can sensitively reflect symptoms of abnormal states are then selected to provide effective information for the discrimination of each state. The membership function of each state is then generated based on the possibility theory using the probability functions of the SPs. The step-by-step fuzzy diagnoses are performed based on the TLFD. This method can be used extensively to diagnose anomalies in various equipment. In this study, the diagnosis of structure faults of a rotating machine is cited as an example to demonstrate the effectiveness and universality of this method.

Adaptive Type-2 Fuzzy Approach for Filtering Salt and Pepper Noise in Grayscale Images

Abstract: This paper proposes a novel adaptive Type-2 fuzzy filter for removing salt and pepper noise from the images. The filter removes noise in two steps. In the first step, the pixels are categorized as good or bad based on their primary membership function (MF) values in the respective filter window. In this paper, two approaches have been proposed for finding threshold between good or bad pixels by designing primary MFs. a) MFs with distinct Means and same Variance and b) MFs with distinct Means and distinct Variances. The primary MFs of the Type-2 fuzzy set is chosen as Gaussian membership functions. Whereas, in the second step, the pixels categorized as bad are denoised. For denoising, a novel Type-1 fuzzy approach based on a weighted mean of good pixels is presented in the paper. The proposed filter is validated for several standard images with the noise level as low as 20% to as high as 99%. The results show that the proposed filter performs better in terms of peak signal-noise-ratio values compared to other state-of-the-art algorithms.

Typhoon disaster assessment based on Dombi hesitant fuzzy information aggregation operators

Abstract: Hesitant fuzzy set is an extension of the traditional fuzzy set, and it has the membership function which was expressed by several possible numbers. Since it was introduced, it has been received wide attention from scholars due to its powerful ability in describing the uncertainty. In this paper, we first introduce some new operations on hesitant fuzzy elements (HFEs) based on Dombi t-conorm and t-norm and then proposed some new aggregation operators for HFEs, such as hesitant fuzzy Dombi weighted averaging, hesitant fuzzy Dombi ordered weighted averaging, hesitant fuzzy Dombi weighted geometric, hesitant fuzzy Dombi ordered weighted geometric, hesitant fuzzy Dombi hybrid averaging and hesitant fuzzy Dombi hybrid geometric operator. Finally, a multiple attribute group decision-making approach under hesitant fuzzy environment is presented based on these proposed operators. A real example about typhoon disaster assessment is presented to show the advantages of the proposed method.

A Novel Decision-Making Method Based on Rough Fuzzy Information

Abstract: Fuzzy sets and rough sets are two different mathematical models to cope with vagueness, but they are correlated. Dubois and Prade combined these two sets to make new hybrid models including fuzzy rough sets and rough fuzzy sets. In this research study, we introduce several basic notions, concerning rough fuzzy digraph, and investigate some related properties. We present applications of rough fuzzy digraphs in decision-making problems. In particular, we develop efficient algorithms to solve decision-making problems.

Local Stabilization for Continuous-time Takagi–Sugeno Fuzzy Systems With Time Delay

Abstract: This brief paper investigates the local stabilization for continues-time Takagi–Sugeno fuzzy systems with constant time delay. In order to deal with the time delay, we design a Lyapunov–Krasovskii functional that is dependent on the membership function. Based on the Lyapunov–Krasovskii functional and the analysis of the time derivative of the membership function, less conservative results can be obtained; however, the Lyapunov–Krasovskii functional is designed so complicated that the Lyapunov level set is hard to be measured directly. Alternatively, two sets are obtained to estimate the local stabilization. One set is for the time-varying initial conditions and the other is for the time-invariant initial conditions. The relationship between the two sets are also discussed. In the end, two examples are given to illustrate the effectiveness of the proposed approach.

Short-Term Load Forecasting by Separating Daily Profiles and Using a Single Fuzzy Model Across the Entire Domain

Abstract: The problem of energy load forecasting has emerged as an essential area of research for electrical distributors seeking to minimize costs. This problem has a high degree of complexity; therefore, this paper solves the problem of short-term load forecasting for a day ahead using an adaptive fuzzy model, defined across the entire input space in order to share information between different areas. The proposed solution first separates the forecasting of daily load profiles into smaller, simpler subproblems, which are solved separably using a Takagi–Sugeno fuzzy model. This is done in order to solve smaller subproblems better, which brings improved forecasting accuracy after combining the subproblem results. The identification of the model is based on a recursive Gustafson–Kessel clustering and recursive weighted least mean squares, to which a combined membership function is proposed in order to improve domain partitioning. The model was tested on the real data obtained from a large Slovenian energy distribution company, at which the developed model forecast outperformed other methods, especially in the start of the week and the winter.

A T–S Fuzzy Model Identification Approach Based on a Modified Inter Type-2 FRCM Algorithm

Abstract: Hyper-plane-shaped clustering (HPSC) has been demonstrated to be more effective in Takagi–Sugeno (T–S) fuzzy model identification compared to hyper-sphere-shaped clustering. Although some HPSC algorithms, based on type-2 fuzzy theory, have already been developed and have been demonstrated to have outstanding performance in T–S fuzzy modeling, mismatching of the traditional hyper-sphere-shaped membership function and HPSC results will inevitably restrict the modeling performance. In this paper, a modified inter type-2 fuzzy c-regression model (IT2-FCRM) clustering and new hyper-plane-shaped Gaussian membership function were proposed for T–S fuzzy modeling. In the proposed approach, the coefficients of the upper and lower hyperplanes were deduced based on an IT2-FCRM algorithm. Then, a hyper-plane-shaped membership function was directly defined using the hyperplanes to identify the antecedent parameters of the T–S fuzzy model. The experimental results of several benchmark problems show that identification of T–S model accuracy was greatly promoted.

On Nie-Tan Operator and Type-Reduction of Interval Type-2 Fuzzy Sets

Abstract: Type-reduction of type-2 fuzzy sets is considered to be a defuzzification bottleneck because of the computational complexity involved in the process of type-reduction. In this paper, we prove that the closed-form Nie-Tan operator, which outputs the average of the upper and lower bounds of the footprint of uncertainty, is actually an accurate method for defuzzifying interval type-2 fuzzy sets.

SQI Quality Evaluation Mechanism of Single-Lead ECG Signal Based on Simple Heuristic Fusion and Fuzzy Comprehensive Evaluation.

Abstract: For both the acquisition of mobile electrocardiogram (ECG) devices and early warning and diagnosis of clinical work, high-quality ECG signals is particularly important. We describe an effective system which could be deployed as a stand-alone signal quality assessment algorithm for vetting the quality of ECG signals. The proposed ECG quality assessment method is based on the simple heuristic fusion and fuzzy comprehensive evaluation of the SQIs. This method includes two modules, i.e., the quantification and extraction of Signal Quality Indexes (SQIs) for different features, intelligent assessment and classification. First, simple heuristic fusion is executed to extract SQIs and determine the following SQIs: R peak detection match qSQI, QRS wave power spectrum distribution pSQI, kurtosis kSQI, and baseline relative power basSQI. Then, combined with Cauchy distribution, rectangular distribution and trapezoidal distribution, the membership function of SQIs was quantified, and the fuzzy vector was established. The bounded operator was selected for fuzzy synthesis, and the weighted membership function was used to perform the assessment and classification. The performance of the proposed method was tested on the database from Physionet ECG database, with an accuracy (Acc) of 97.67%, sensitivity (Se) of 96.33% and specificity (Sp) of 98.33% on the training set. Testing against the test datasets resulted in scores of 94.67, 90.33, and 93.00%, respectively. There's no gold standard exists for determining the quality of ECGs. However, the proposed algorithm discriminates between high- and poor-quality ECGs, which could aid in ECG acquisition for mobile ECG devices, early clinical diagnosis and early warning.

Bipolar Neutrosophic Soft Sets and Applications in Decision Making

Abstract: Neutrosophic set, proposed by Smarandache considers a truth membership function, an indeterminacy membership function and a falsity membership function. Soft set, proposed by Molodtsov is a mathematical framework which has the ability of independency of parameterizations inadequacy, syndrome of fuzzy set, rough set, probability.

Local Community Detection With the Dynamic Membership Function

Abstract: Most of the community detection methods require the global information of the original network to be available, however, it is often expensive (even no way) to obtain the global information of the network in many real-world networks. So, the local community detection, only based on the local information, becomes especially important. The local community is the community in the network to which a given starting node belongs. Some local community detection methods have been proposed. However, these methods did not consider the characteristics of the local community during the local community formation. In this paper, we analyze the formation of the local community and propose two local community detection algorithms based on the dynamic membership function. Each of the algorithms is divided into three stages: 1) the initial stage, 2) the middle stage, and 3) the closing stage. At the initial stage, we design a dynamical membership function to detect local community and nodes with the greatest neighborhood intersect rate could be added to the local community. At the middle stage, we design another dynamical membership function, and the goal of this stage is to make the connection of the node in the local community closest. At the closing stage, the third dynamical membership function is provided, and the local community is further improved by collecting some nodes that should not be omitted. We test our algorithms on several synthetic datasets and real datasets; the results show that the local communities detected by our method are closer to the real local communities.

Intuitionistic fuzzy multi-objective linear programming problem with various membership functions

Abstract: This study addresses intuitionistic fuzzy multi-objective linear programming problems using triangular intuitionistic fuzzy numbers with mixed constraints. We convert the problem into single objective fuzzy programming problem. Then using different types of membership functions (linear and nonlinear), we transform the problem into crisp linear/non-linear programming problem, which is solved by suitable crisp programming approaches. The methodology is demonstrated with the help of a numerical example and the usefulness of various membership functions is discussed.

A Novel Approach for Real-Time Recognition of Epileptic Seizures Using Minimum Variance Modified Fuzzy Entropy

Abstract: Objective: Validation of epileptic seizures annotations from long-term electroencephalogram (EEG) recordings is a tough and tedious task for the neurological community. It is a well-known fact that computerized qualitative methods thoroughly assess the complex brain dynamics toward seizure detection and proven as one of the acceptable clinical indicators. Methods: This research study suggests a novel approach for real-time recognition of epileptic seizure from EEG recordings by a technique referred as minimum variance modified fuzzy entropy (MVMFzEn). Multichannel EEG recordings of 4.36 h of epileptic seizures and 25.74 h of normal EEG were considered. Signal processing techniques such as filters and independent component analysis were appropriated to reduce noise and artifacts. Unlike, the predefined fuzzy membership function, the modified fuzzy entropy utilizes relative energy as a membership function followed by scaling operation to obtain the feature. Results: Results revealed that MVMFzEn drops abruptly during an epileptic activity and this fact was used to set a threshold. An automated threshold derived from MVMFzEn assesses the classification efficiency of the given data during validation. It was observed from the results that the proposed method yields a classification accuracy of 100% without the use of any classifier. Conclusion: The graphical user interface was designed in MATLAB to automatically label the normal and epileptic segments in the long-term EEG recordings. Significance: The ground truth clinical validation using validation specificity and validation sensitivity confirms the suitability of the proposed technique for automated annotation of epileptic seizures in real time.

IC-FNN: A Novel Fuzzy Neural Network With Interpretable, Intuitive, and Correlated-Contours Fuzzy Rules for Function Approximation

Abstract: In this paper, a novel fuzzy neural network with intuitive, interpretable, and correlated-contours fuzzy rules (IC-FNN), for function approximation, is presented. The surfaces of these fuzzy rules are similar to the surfaces of the hills in the function landscape. Contours of the hills could be correlated and nonseparable with different shapes and directions. Thus, to obtain nonseparable and correlated fuzzy rules, a proper optimization problem is introduced and solved. To form contours with different shapes, a novel shapeable membership function with an adaptive shape is introduced to define the fuzzy sets. Next, based on a hierarchical Levenberg–Marquardt learning method, the parameters of the extracted fuzzy rules are fine tuned. The performance of the proposed method is evaluated in real-world regression and time-series prediction problems, and compared with other existing methods. According to these experiments, the proposed method could construct more parsimonious structures with higher accuracy, in comparison to the existing methods. Although the performance of the proposed method for complex and correlated functions is premier, for simple and uncorrelated cases, it is appropriate but with a more complex structure.

Optimal Type-2 Fuzzy System For Arterial Traffic Signal Control

Abstract: Arterial traffic is the artery of urban transport and loads huge traffic pressure. In order to alleviate its traffic pressure effectively, a coordinated arterial traffic type-2 fuzzy logic control (FLC) method is proposed. First, arterial traffic flow model and evaluation index model are set up, in which the turning vehicles and lane length are given full consideration. The traditional queue spillover phenomenon in the traffic models can be prevented here. Second, aiming at the coordination and dynamic uncertainty problem in arterial traffic, a coordinated arterial traffic type-2 fuzzy coordination control method is put forward. It consists of two-layer type-2 fuzzy controller, the basic control layer and the coordination layer. The former allocates green time according to the traffic situation of each intersection, while the latter adjusts each intersection’s green time on basis of the vehicles between the intersection and the downstream intersections for the purpose of enlarging green wave band. Finally, in order to configure the high-dimensional complex parameters of the coordinated two-layer type-2 FLC effectively, the parameters of membership function and the rules of the two controllers are optimized alternately by gravitational search algorithm. The simulation results verify the effectiveness of the proposed method from several aspects.

δ -equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis

Abstract: Intuitionistic fuzzy set is capable of handling uncertainty with counterpart falsities which exist in nature. Proximity measure is a convenient way to demonstrate impractical significance of values of memberships in the intuitionistic fuzzy set. However, the related works of Pappis (Fuzzy Sets Syst 39(1):111–115, 1991), Hong and Hwang (Fuzzy Sets Syst 66(3):383–386, 1994), Virant (2000) and Cai (IEEE Trans Fuzzy Syst 9(5):738–750, 2001) did not model the measure in the context of the intuitionistic fuzzy set but in the Zadeh’s fuzzy set instead. In this paper, we examine this problem and propose new notions of δ-equalities for the intuitionistic fuzzy set and δ-equalities for intuitionistic fuzzy relations. Two fuzzy sets are said to be δ-equal if they are equal to an extent of δ. The applications of δ-equalities are important to fuzzy statistics and fuzzy reasoning. Several characteristics of δ-equalities that were not discussed in the previous works are also investigated. We apply the δ-equalities to the application of medical diagnosis to investigate a patient’s diseases from symptoms. The idea is using δ-equalities for intuitionistic fuzzy relations to find groups of intuitionistic fuzzified set with certain equality or similar degrees then combining them. Numerical examples are given to illustrate validity of the proposed algorithm. Further, we conduct experiments on real medical datasets to check the efficiency and applicability on real-world problems. The results obtained are also better in comparison with 10 existing diagnosis methods namely De et al. (Fuzzy Sets Syst 117:209–213, 2001), Samuel and Balamurugan (Appl Math Sci 6(35):1741–1746, 2012), Szmidt and Kacprzyk (2004), Zhang et al. (Procedia Eng 29:4336–4342, 2012), Hung and Yang (Pattern Recogn Lett 25:1603–1611, 2004), Wang and Xin (Pattern Recogn Lett 26:2063–2069, 2005), Vlachos and Sergiadis (Pattern Recogn Lett 28(2):197–206, 2007), Zhang and Jiang (Inf Sci 178(6):4184–4191, 2008), Maheshwari and Srivastava (J Appl Anal Comput 6(3):772–789, 2016) and Support Vector Machine (SVM).