Showing papers on "Membership function published in 2017"

Generalized Orthopair Fuzzy Sets

Abstract: We note that orthopair fuzzy subsets are such that that their membership grades are pairs of values, from the unit interval, one indicating the degree of support for membership in the fuzzy set and the other support against membership. We discuss two examples, Atanassov's classic intuitionistic sets and a second kind of intuitionistic set called Pythagorean. We note that for classic intuitionistic sets the sum of the support for and against is bounded by one, while for the second kind, Pythagorean, the sum of the squares of the support for and against is bounded by one. Here we introduce a general class of these sets called q-rung orthopair fuzzy sets in which the sum of the ${\rm{q}}$ th power of the support for and the ${\rm{q}}$ th power of the support against is bonded by one. We note that as q increases the space of acceptable orthopairs increases and thus gives the user more freedom in expressing their belief about membership grade. We investigate various set operations as well as aggregation operations involving these types of sets.

Fuzzy best-worst multi-criteria decision-making method and its applications

Abstract: Fuzzy best-worst method is proposed to solve the issues under fuzzy environment.A consistency ratio for fuzzy best-worst method is proposed for verification.The results indicate the fuzzy best-worst method outperforms best-worst method.The fuzzy best-worst method has a higher comparison consistency. Considering the vagueness frequently representing in decision data due to the lack of complete information and the ambiguity arising from the qualitative judgment of decision-makers, the crisp values of criteria may be inadequate to model the real-life multi-criteria decision-making (MCDM) issues. In this paper, the latest MCDM method, namely best-worst method (BWM) was extended to the fuzzy environment. The reference comparisons for the best criterion and for the worst criterion were described by linguistic terms of decision-makers, which can be expressed in triangular fuzzy numbers. Then, the graded mean integration representation (GMIR) method was employed to calculate the weights of criteria and alternatives with respect to different criteria under fuzzy environment. According to the concept of BWM, the nonlinearly constrained optimization problem was built for determining the fuzzy weights of criteria and alternatives with respect to different criteria. The fuzzy ranking scores of alternatives can be derived from the fuzzy weights of alternatives with respect to different criteria multiplied by fuzzy weights of the corresponding criteria, and then the crisp ranking score of alternatives can be calculated by employing GMIR method for optimal alternative selection. Meanwhile, the consistency ratio was proposed for fuzzy BWM to check the reliability of fuzzy preference comparisons. Three case studies were performed to illustrate the effectiveness and feasibility of the proposed fuzzy BWM. The results indicate the proposed fuzzy BWM can not only obtain reasonable preference ranking for alternatives but also has higher comparison consistency than the BWM.

Adaptive Fuzzy Backstepping Tracking Control for Strict-Feedback Systems With Input Delay

Abstract: This paper investigates the problem of adaptive fuzzy tracking control for nonlinear strict-feedback systems with input delay and output constraint. Input delay is handled based on the information of Pade approximation and output constraint problem is solved by barrier Lypaunov function. Some adaptive parameters of the controller need to be updated online through considering the norm of membership function vector instead of all sub-vectors. A novel adaptive fuzzy tracking control scheme is developed to guarantee all variables of the closed-loop systems are semiglobally uniformly ultimately bounded, and the tracking error can be adjusted around the origin with a small neighborhood. The stability of the closed-loop systems is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach.

A Fitting Model for Feature Selection With Fuzzy Rough Sets

Abstract: A fuzzy rough set is an important rough set model used for feature selection. It uses the fuzzy rough dependency as a criterion for feature selection. However, this model can merely maintain a maximal dependency function. It does not fit a given dataset well and cannot ideally describe the differences in sample classification. Therefore, in this study, we introduce a new model for handling this problem. First, we define the fuzzy decision of a sample using the concept of fuzzy neighborhood. Then, a parameterized fuzzy relation is introduced to characterize the fuzzy information granules, using which the fuzzy lower and upper approximations of a decision are reconstructed and a new fuzzy rough set model is introduced. This can guarantee that the membership degree of a sample to its own category reaches the maximal value. Furthermore, this approach can fit a given dataset and effectively prevents samples from being misclassified. Finally, we define the significance measure of a candidate attribute and design a greedy forward algorithm for feature selection. Twelve datasets selected from public data sources are used to compare the proposed algorithm with certain existing algorithms, and the experimental results show that the proposed reduction algorithm is more effective than classical fuzzy rough sets, especially for those datasets for which different categories exhibit a large degree of overlap.

On a novel uncertain soft set model

Abstract: Graphical abstractDisplay Omitted HighlightsA novel Z-soft fuzzy rough set model is constructed.Novel idea and new results are different from Meng-SFR-model and Sun-SFR-model.A kind of decision making method based on the Z-SFR-sets is investigated.The comparisons of numerical experimentation are given.An overview of techniques based on some types of soft set models are discussed. In this paper, a kind of novel soft set model called a Z-soft fuzzy rough set is presented by means of three uncertain models: soft sets, rough sets and fuzzy sets, which is an important generalization of Z-soft rough fuzzy sets. As a novel Z-soft fuzzy rough set, its applications in the corresponding decision making problems are established. It is noteworthy that the underlying concepts keep the features of classical Pawlak rough sets. Moreover, this novel approach will involve fewer calculations when one applies this theory to algebraic structures. In particular, an approach for the method of decision making problem with respect to Z-soft fuzzy rough sets is proposed and the validity of the decision making methods is testified by a given example. At the same time, an overview of techniques based on some types of soft set models is investigated. Finally, the numerical experimentation algorithm is developed, in which the comparisons among three types of hybrid soft set models are analyzed.

Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process

Abstract: Pythagorean fuzzy set, an extension of the intuitionistic fuzzy set which relax the condition of sum of their membership function to square sum of its membership functions is less than one. Under these environment and by incorporating the idea of the confidence levels of each Pythagorean fuzzy number, the present study investigated a new averaging and geometric operators namely confidence Pythagorean fuzzy weighted and ordered weighted operators along with their some desired properties. Based on its, a multi criteria decision-making method has been proposed and illustrated with an example for showing the validity and effectiveness of it. A computed results are compared with the aid of existing results.

An Interval Type-2 Fuzzy Likelihood-Based MABAC Approach and Its Application in Selecting Hotels on a Tourism Website

Abstract: As an extension of type-1 fuzzy sets (T1FSs), interval type-2 fuzzy sets (IT2FSs) can be used to model both extrinsic and intrinsic uncertainties. Based on the likelihood of interval type-2 fuzzy numbers (IT2FNs), this paper proposes a new multi-attributive border approximation area comparison (MABAC) approach to solve multi-criteria decision-making (MCDM) problems. First, an algorithm to decompose IT2FNs into the embedded type-1 fuzzy numbers (T1FNs) is proposed. Second, based on the closeness degree of T1FNs, the likelihood of IT2FNs is defined using the decomposition algorithm, and related properties are discussed. Third, the total ranking of alternatives is obtained using the MABAC approach based on the likelihood of IT2FNs. Finally, a practical example of selecting hotels from a tourism website is presented to verify the validity and feasibility of the proposed approach. A comparative analysis with existing methods is also described.

Complex neutrosophic set

Abstract: Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature. To overcome this difficulty, we introduce complex neutrosophic set. A complex neutrosophic set is a neutrosophic set whose complex-valued truth membership function, complex-valued indeterminacy membership function, and complex-valued falsehood membership functions are the combination of real-valued truth amplitude term in association with phase term, real-valued indeterminate amplitude term with phase term, and real-valued false amplitude term with phase term, respectively. Complex neutrosophic set is an extension of the neutrosophic set. Further set theoretic operations such as complement, union, intersection, complex neutrosophic product, Cartesian product, distance measure, and ź-equalities of complex neutrosophic sets are studied here. A possible application of complex neutrosophic set is presented in this paper. Drawbacks and failure of the current methods are shown, and we also give a comparison of complex neutrosophic set to all such methods in this paper. We also showed in this paper the dominancy of complex neutrosophic set to all current methods through the graph.

Entropy-based fuzzy support vector machine for imbalanced datasets

Abstract: Imbalanced problem occurs when the size of the positive class is much smaller than that of the negative one. Positive class usually refers to the main interest of the classification task. Although conventional Support Vector Machine (SVM) results in relatively robust classification performance on imbalanced datasets, it treats all samples with the same importance leading to the decision surface biasing toward the negative class. To overcome this inherent drawback, Fuzzy SVM (FSVM) is proposed by applying fuzzy membership to training samples such that different samples provide different contributions to the classifier. However, how to evaluate an appropriate fuzzy membership is the main issue to FSVM. In this paper, we propose a novel fuzzy membership evaluation which determines the fuzzy membership based on the class certainty of samples. That is, the samples with higher class certainty are assigned to larger fuzzy memberships. As the entropy is utilized to measure the class certainty, the fuzzy membership evaluation is named as entropy-based fuzzy membership evaluation. Therefore, the Entropy-based FSVM (EFSVM) is proposed by using the entropy-based fuzzy membership. EFSVM can pay more attention to the samples with higher class certainty, i.e. enhancing the importance of samples with high class certainty. Meanwhile, EFSVM guarantees the importance of the positive class by assigning positive samples to relatively large fuzzy memberships. The contributions of this work are: (1) proposing a novel entropy-based fuzzy membership evaluation method which enhances the importance of certainty samples, (2) guaranteeing the importance of the positive samples to result in a more flexible decision surface. Experiments on imbalanced datasets validate that EFSV outperforms the compared algorithms.

A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making

Abstract: This paper introduces the notion of Z-soft rough fuzzy sets of hemirings, which is an extended notion of soft rough sets and rough fuzzy sets. It is pointed out that this novel concept removes the limiting condition that full soft sets require in Feng-soft rough fuzzy sets and Meng-soft rough fuzzy sets. We study roughness in hemirings with respect to a ZS-approximation space. Some new soft rough fuzzy operations over hemirings are explored. In particular, Z-lower and Z-upper soft rough fuzzy ideals (k-ideals, h-ideals, strong h-ideals) are investigated. Finally, we put forth an approach for decision making problem based on Z-soft rough fuzzy sets and give an example. Corresponding decision making methods based on Z-soft rough fuzzy sets are analysed.

Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making

Abstract: As a combination of the hesitant fuzzy set (HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truth-hesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS. Correlation and correlation coefficient have been applied widely in many research domains and practical fields. This paper, motivated by the idea of correlation coefficients derived for HFSs, IFSs, DHFSs and SVNSs, focuses on the correlation and correlation coefficient of SVNHFSs and investigates their some basic properties in detail. By using the weighted correlation coefficient information between each alternative and the optimal alternative, a decision-making method is established to handling the single-valued neutrosophic hesitant fuzzy information. Finally, an effective example is used to demonstrate the validity and applicability of the proposed approach in decision making, and the relationship between the each existing method and the developed method is given as a comparison study.

Distance measures between type-2 intuitionistic fuzzy sets and their application to multicriteria decision-making process

Abstract: Type-2 fuzzy set (T2FS) is a generalization of the ordinary fuzzy set in which the membership value for each member of the set is itself a fuzzy set. However, it is difficult, in some situations, for the decision-makers to give their preferences towards the object in terms of single or exact number. For handling this, a concept of type-2 intuitionistic fuzzy set (T2IFS) has been proposed and hence under this environment, a family of distance measures based on Hamming, Euclidean and Hausdorff metrics are presented. Some of its desirable properties have also been investigated in details. Finally, based on these measures, a group decision making method has been presented for ranking the alternatives. The proposed measures has been illustrated with a numerical example.

An improved Dempster–Shafer approach to construction safety risk perception

Abstract: This paper proposes a novel hybrid approach that merges fuzzy matter element (FME), Monte Carlo (MC) simulation technique, and Dempster–Shafer (D–S) evidence theory to perceive the risk magnitude of tunnel-induced building damage at an early construction stage. The membership measurement in FME is used to construct basic probability assignments (BPAs) of influential factors within different risk states. An improved evidence fusion rule that integrates the Dempster’ rule and the weighted average rule is developed to synthesize multi-source conflicting evidence. A new defuzzification method, Centre of Distribution (COD), is proposed to achieve a crisp value that represents the final safety risk perception result. A confidence indicator, δ , is put forward to measure the reliability of the safety risk perception result. A comprehensive information fusion framework that incorporates 14 influential factors is proposed to perceive the risk magnitude of tunnel-induced building damage. Six existing buildings adjacent to the excavation of Wuhan Yangtze Metro Tunnel (WYMT), China, are utilized as a case study to verify the effectiveness and applicability of the proposed approach. Results indicate that the proposed approach is capable of (i) achieving a more accurate result for safety risk perception, and (ii) identifying global sensitivities of input factors throughout a series of MC simulation enabled iterations. A discussion on how to define a reasonable membership function for configuration of BPAs is further presented. The authors recommend that the constant coefficient λ that affects the shape of the defined correlation function in BPA (Basic Probability Assignment) constructs should have a value of three, and the risk perception result can thus reach up to the highest reliability level. This approach can enable a comprehensive preliminary safety risk perception during tunnel design phases, which can further substantially reduce the risk of building damage induced by tunneling excavation.

Multiobjective Evolutionary Optimization of Type-2 Fuzzy Rule-Based Systems for Financial Data Classification

Abstract: Classification techniques are becoming essential in the financial world for reducing risks and possible disasters. Managers are interested in not only high accuracy, but in interpretability and transparency as well. It is widely accepted now that the comprehension of how inputs and outputs are related to each other is crucial for taking operative and strategic decisions. Furthermore, inputs are often affected by contextual factors and characterized by a high level of uncertainty. In addition, financial data are usually highly skewed toward the majority class. With the aim of achieving high accuracies, preserving the interpretability, and managing uncertain and unbalanced data, this paper presents a novel method to deal with financial data classification by adopting type-2 fuzzy rule-based classifiers (FRBCs) generated from data by a multiobjective evolutionary algorithm (MOEA). The classifiers employ an approach, denoted as scaled dominance, for defining rule weights in such a way to help minority classes to be correctly classified. In particular, we have extended PAES-RCS, an MOEA-based approach to learn concurrently the rule and data bases of FRBCs, for managing both interval type-2 fuzzy sets and unbalanced datasets. To the best of our knowledge, this is the first work that generates type-2 FRBCs by concurrently maximizing accuracy and minimizing the number of rules and the rule length with the objective of producing interpretable models of real-world skewed and incomplete financial datasets. The rule bases are generated by exploiting a rule and condition selection (RCS) approach, which selects a reduced number of rules from a heuristically generated rule base and a reduced number of conditions for each selected rule during the evolutionary process. The weight associated with each rule is scaled by the scaled dominance approach on the fuzzy frequency of the output class, in order to give a higher weight to the minority class. As regards the data base learning, the membership function parameters of the interval type-2 fuzzy sets used in the rules are learned concurrently to the application of RCS. Unbalanced datasets are managed by using, in addition to complexity, selectivity and specificity as objectives of the MOEA rather than only the classification rate. We tested our approach, named IT2-PAES-RCS, on 11 financial datasets and compared our results with the ones obtained by the original PAES-RCS with three objectives and with and without scaled dominance, the FRBCs, fuzzy association rule-based classification model for high-dimensional dataset (FARC-HD) and fuzzy unordered rules induction algorithm (FURIA), the classical C4.5 decision tree algorithm, and its cost-sensitive version. Using nonparametric statistical tests, we will show that IT2-PAES-RCS generates FRBCs with, on average, accuracy statistically comparable with and complexity lower than the ones generated by the two versions of the original PAES-RCS. Further, the FRBCs generated by FARC-HD and FURIA and the decision trees computed by C4.5 and its cost-sensitive version, despite the highest complexity, result to be less accurate than the FRBCs generated by IT2-PAES-RCS. Finally, we will highlight how these FRBCs are easily interpretable by showing and discussing one of them.

An overview of interval-valued intuitionistic fuzzy information aggregations and applications

Abstract: Interval-valued intuitionistic fuzzy set, generalized by Atanassov and Gargov, can be used to characterize the uncertain information more sufficiently and accurately when we face the fact that the values of the membership function and the non-membership function in an intuitionistic fuzzy set are difficult to be expressed as exact real numbers in many real-world decision-making problems. In this paper, we provide an overview of interval-valued intuitionistic fuzzy information aggregation techniques, and their applications in various fields such as decision-making, entropy measure, supplier selection and some practical decision-making problems. Meanwhile, we also review some important methods for decision-making with interval-valued intuitionistic fuzzy information, including the QUALIFLEX-based method, the TOPSIS method, the extended VIKOR method, the module partition schemes evaluation (MPSE) approach, the outranking choice method, the inclusion-based LINMAP method and the risk attitudinal ranking method, the evidential reasoning methodology, etc. Finally, we point out some possible directions for future research.

An Efficient System for Heart Disease Prediction using Hybrid OFBAT with Rule-Based Fuzzy Logic Model

Abstract: The objective of the work is to predict heart disease using computing techniques like an oppositional firefly with BAT and rule-based fuzzy logic (RBFL) The system would help the doctors to automate heart disease diagnosis and to enhance the medical care In this paper, a hybrid OFBAT-RBFL heart disease diagnosis system is designed Here, at first, the relevant features are selected from the dataset using locality preserving projection (LPP) algorithm which helps the diagnosis system to develop a classification model using the fuzzy logic system After that, the rules for the fuzzy system are created from the sample data Among the entire rules, the important and relevant group of rules are selected using OFBAT algorithm Here, the opposition based learning (OBL) is hybrid to the firefly with BAT algorithm to improve the performance of the FAT algorithm while optimizing the rules of the fuzzy logic system Next, the fuzzy system is designed with the help of designed fuzzy rules and membership functions so that classification can be carried out within the fuzzy system designed At last, the experimentation is performed by means of publicly available UCI datasets, ie, Cleveland, Hungarian and Switzerland datasets The experimentation result proves that the RBFL prediction algorithm outperformed the existing approach by attaining the accuracy of 78%

A Multi-Valued Neutrosophic Qualitative flexible Approach Based on Likelihood for Multi-Criteria Decision-Making Problems

Abstract: In this paper, multi-criteria decision-making (MCDM) problems based on the qualitative flexible multiple criteria method (QUALIFLEX), in which the criteria values are expressed by multi-valued neutrosophic information, are investigated. First,multi-valued neutrosophic sets(MVNSs),which allow the truth-membership function,indeterminacy-membership function and falsity-membership function to have a set of crisp values between zeroand one, are introduced.

A new MPPT scheme based on a novel fuzzy approach

Abstract: In this paper, after defining Maximum Power Point Tracking (MPPT) control expectations, with the aim of finding the optimum routine in fulfilling these expectations, a review over the available MPPT control methods is presented. Throughout the review, by comparing conventional MPPT routines in terms of accomplishing defined control objectives, the necessity of designing a new MPPT control scheme based on adaptive fuzzy logic is expressed. Based on the conducted review, a new routine to optimize the MPPT performance of a Photovoltaic (PV)-setup and to fulfill all the MPPT control requirements is proposed. The optimization is performed in tracking the Maximum Power Point (MPP) of the PV-module by a Boost-converter using an “antecedent-consequent adaptive” indirect fuzzy-based MPPT scheme. The fuzzy-based scheme is tuned online using a novel computationally light membership function tuning routine, where the antecedent and consequent membership functions are tuned synchronously. As a result, a fast, smooth and computationally light MPPT controller is proposed. In this regard, the presented MPPT scheme tuned using the proposed novel tuning routine is compared with conventional direct and indirect fuzzy-based MPPT schemes, showing superiority of the proposed MPPT routine over conventional schemes.

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. Those concepts have been utilized successfully to model uncertainty in several areas of application such as control, reasoning, game theory, pattern recognition, and computer vision. Nonetheless, there are many problems in real-world applications containing indeterminate and inconsistent information that cannot be effectively handled by the neutrosophic set and soft set. In this paper, we propose the notation of bipolar neutrosophic soft sets that combines soft sets and bipolar neutrosophic sets. Some algebraic operations of the bipolar neutrosophic set such as the complement, union, intersection are examined. We then propose an aggregation bipolar neutrosophic soft operator of a bipolar neutrosophic soft set and develop a decision making algorithm based on bipolar neutrosophic soft sets. Numerical examples are given to show the feasibility and effectiveness of the developed approach.

A Membership-Function-Dependent Approach to Design Fuzzy Pointwise State Feedback Controller for Nonlinear Parabolic Distributed Parameter Systems With Spatially Discrete Actuators

Abstract: This paper gives a membership-function-dependent approach to solve the design problem of fuzzy pointwise state feedback controller for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs), where only a few actuators are discretely distributed in space. In the proposed design method, a Takagi–Sugeno (T–S) fuzzy PDE model obtained by using the sector nonlinearity method is first utilized to accurately describe the nonlinear spatiotemporal dynamics of the PDE system. As only the state information at some known specified points in the spatial domain (i.e., the pointwise state information) is available for the controller design, the favorable property offered by sharing all the same premises in the fuzzy PDE plant model and fuzzy controller cannot be employed to develop the fuzzy control design method. To overcome this drawback, a linear matrix inequality (LMI) relaxation technique is developed to enhance the stabilization ability of the fuzzy controller. Based on the T–S fuzzy PDE model, a membership-function-dependent fuzzy pointwise state feedback control design is then proposed by employing the Lyapunov technique, integration by parts, the vector-valued Wirtinger’s inequality and the LMI relaxation technique, and presented in term of standard LMIs. Finally, the satisfactory and better performance of the proposed design method are demonstrated by the extensive numerical simulation results of two numerical examples.