Showing papers in "International Journal of Fuzzy Systems in 2020"

Extended Pythagorean Fuzzy TOPSIS Method Based on Similarity Measure for Sustainable Recycling Partner Selection

Abstract: Recently, the organizations have concentrated on sustainability development and introduced several strategies for sustainability due to government policies, society concern, environmental impacts and needs of economy. Uncertainty commonly occurred in the sustainability development. Pythagorean fuzzy sets (PFSs), an extension of IFSs, have been demonstrated as an extremely valuable tool to tackle the uncertainty and ambiguity arisen in many practical situations. Thus, the proposed study focuses under Pythagorean fuzzy environment. In the present study, an approach is developed on the basis of Pythagorean fuzzy sets and Technique for Order Preference by means of Similarity to Ideal Solution method for the purpose of solving sustainable recycling partner selection problems with completely unknown decision experts and criteria weights. To calculate criteria weights, new similarity measure based on trigonometric function for PFSs is developed. Aiming at showing the way our approach can be effectively used to evaluate the realistic multi-criteria decision making problems, we carry out a case study of sustainable recycling partner selection problem. In addition, the results obtained from the proposed method are compared to those of some presently existing methods to validate the proposed method. The analytical results confirm the proficiency and reasonableness of the proposed method.

TOPSIS Method for Developing Supplier Selection with Probabilistic Linguistic Information

Abstract: In this paper, we investigate the probabilistic linguistic multiple attribute group decision-making (MAGDM) with incomplete weight information. In this method, the linguistic term sets (LTSs) is converted into probabilistic linguistic term sets (PLTSs). For deriving the weight information of the attribute, an optimization model is built on the basis of the fundamental idea of conventional TOPSIS method, by which the attribute weights can be decided. In addition, the optimal alternative(s) is decided by computing the shortest distance from the probabilistic linguistic positive ideal solution (PLPIS) and on the other side the farthest distance of the probabilistic linguistic negative ideal solution (PLNIS). The method has precise trait in probabilistic linguistic information processing. The information distortion and losing was avoided which happen formerly in the probabilistic linguistic information processing. In the end, a case study for green supplier selection is given to demonstrate the merits of the developed method. The results display that the approach is uncomplicated, valid and simple to compute.

Evaluation of the Performance of Search and Rescue Robots Using T-spherical Fuzzy Hamacher Aggregation Operators

Abstract: Multi-attribute decision-making approach is a widely used algorithm that needs some aggregation tools and several such aggregation operators have been developed in past decades to serve the purpose. Hamacher aggregation operator is one such operator which is based on Hamacher t-norm and t-conorm. It is observed that the Hamacher aggregation operators of intuitionistic fuzzy set, Pythagorean fuzzy set and that of picture fuzzy set has some limitations in their applicability. To serve the purpose, in this paper, some Hamacher aggregation operators based on T-spherical fuzzy numbers are introduced. The concepts of T-spherical fuzzy Hamacher-weighted averaging and T-spherical fuzzy Hamacher-weighted geometric aggregation operators are proposed which described four aspects of human opinion including yes, no, abstinence and refusal with no limitations. Such type of aggregation operators efficiently describes the cases that left unsolved by the existing aggregation operators. The validity of the proposed aggregation operators is examined, and some basic properties are discussed. The proposed new Hamacher aggregation operators are used to analyze the performance of search and rescue robots using a multi-attribute decision-making approach as their performance in an emergency is eminent. The proposed Hamacher aggregation operators have two variable parameters, namely q and $$\gamma $$ which affects the decision-making process and their sensitivity towards decision-making results is analyzed. A comparative analysis of the results obtained using proposed Hamacher aggregation operators in view of the variable parameters q and $$\gamma $$ is established to discuss any advantages or disadvantages.

m-Polar Neutrosophic Topology with Applications to Multi-criteria Decision-Making in Medical Diagnosis and Clustering Analysis

Abstract: In this paper, we first introduce novel concepts of m-polar neutrosophic set (MPNS) and topological structure on m-polar neutrosophic set by combining the m-polar fuzzy set (MPFS) and neutrosophic set. Then, we investigate several characterizations of m-polar neutrosophic set and establish its various operations with the help of examples. We propose score functions for the comparison of m-polar neutrosophic numbers (MPNNs). We establish m-polar neutrosophic topology and define interior, closure, exterior, and frontier for m-polar neutrosophic sets (MPNSs) with illustrative examples. We discuss some results with counter examples, which hold for classical set theory, but do not hold for m-polar neutrosophic set theory. We introduce a cosine similarity measure and a set theoretic similarity measure for m-polar neutrosophic sets (MPNSs). Furthermore, we present three algorithms for multi-criteria decision-making (MCDM) in medical diagnosis and clustering analysis under uncertainty by using m-polar neutrosophic sets (MPNSs) and m-polar neutrosophic topology. Lastly, we present advantages, validity, flexibility, and comparison of our proposed algorithms with the existing techniques.

Coronary Heart Disease Diagnosis Through Self-Organizing Map and Fuzzy Support Vector Machine with Incremental Updates

Abstract: The trade-off between computation time and predictive accuracy is important in the design and implementation of clinical decision support systems. Machine learning techniques with incremental updates have proven its usefulness in analyzing large collection of medical datasets for diseases diagnosis. This research aims to develop a predictive method for heart disease diagnosis using machine learning techniques. To this end, the proposed method is developed by unsupervised and supervised learning techniques. In particular, this research relies on Principal Component Analysis (PCA), Self-Organizing Map, Fuzzy Support Vector Machine (Fuzzy SVM), and two imputation techniques for missing value imputation. Furthermore, we apply the incremental PCA and FSVM for incremental learning of the data to reduce the computation time of disease prediction. Our data analysis on two real-world datasets, Cleveland and Statlog, showed that the use of incremental Fuzzy SVM can significantly improve the accuracy of heart disease classification. The experimental results further revealed that the method is effective in reducing the computation time of disease diagnosis in relation to the non-incremental learning technique.

Utilizing Linguistic Picture Fuzzy Aggregation Operators for Multiple-Attribute Decision-Making Problems

Abstract: The linguistic picture fuzzy set (LPFS) is an extension of the linguistic intuitionistic fuzzy set (LIFS), and can contain more information than the LIFS. In this paper, the degrees of positive, neutral and non-membership of PFSs are expressed in linguistic terms, which can more easily describe the uncertain and vague information existing in the real world. By combining the PFS and the linguistic term, we define the LPFS and propose operational rules for linguistic picture fuzzy numbers (LPFNs). We further propose weighted averaging and weighted geometric operators and discuss their properties. Additionally, we propose an approach to deal with a multiple-attribute group decision-making (MAGDM) problem based on the developed aggregation operators. Finally, we present an illustrative example to demonstrate the effectiveness and advantages of the developed method by comparing it with existing methods. In addition, our method can be utilized not only to solve problems with linguistic intuitionistic fuzzy numbers (LIFNs), but also to deal with problems with LPFNs, and is a generalization of a number of existing methods.

Sustainable Public Transportation System Evaluation: A Novel Two-Stage Hybrid Method Based on IVIF-AHP and CODAS

Abstract: As a multi-disciplinary process, planning of public transportation systems needs special attention from several groups of stakeholders such as passengers, transportation planners, system providers, and so on. Since each stakeholder has dissimilar viewpoints on the evaluation of the public transportation systems, they have contradictory goal and objectives. In this sense, multi-criteria decision-making (MCDM) provides an important procedural outline for the evaluation of public transportation alternatives. This paper presents an application of MCDM method to assess the public transportation alternatives designed for a public university in a large-sized metropolitan area. Two alternatives of MCDM methods, named Interval-Valued Intuitionistic Fuzzy Analytical Hierarchy Process & COmbinative Distance-based Assessment (IVIF-AHP & CODAS), are integrated in the evaluation process. The proposed method ensures consistent and reasonable results and provides suggestions for the forthcoming progresses of public transportation service quality. In order to validate robustness of the proposed method, sensitivity analyses are implemented. Also, at the end of the study, to prove the superiority of the proposed approach, a comparative analysis is employed.

Comparison of Evidential Reasoning Algorithm with Linear Combination in Decision Making

Abstract: Evidential reasoning (ER) approach is a representative method for analyzing uncertain multi-criteria decision-making (MCDM) and multi-criteria group decision-making (MCGDM) problems. Its core is ER algorithm used to combine belief distributions on criteria, which is developed based on Dempster’s rule of combination and probability theory. The ER algorithm is nonlinear and more computationally complex than linear combination of belief distributions. To address the necessity of the ER algorithm in MCDM and MCGDM, it is compared with linear combination from three perspectives by simulation. The first is to examine differences between the aggregated assessments derived from the ER algorithm and linear combination. The second is to examine error rates of best alternatives derived from two combination ways. The third is to examine alternative ranking differences derived from two combination ways. To facilitate the comparison, difference between aggregated assessments is designed and score function of alternative is developed from the expected utilities of alternative. Simulation experiments show that differences between the aggregated assessments are influenced by the number of assessment grades, and error rates of best alternatives and alternative ranking differences are influenced by the numbers of criteria and alternatives.

A New Fuzzy PID Control System Based on Fuzzy PID Controller and Fuzzy Control Process

Abstract: In this paper, we present a fuzzy PID control system as a combination of a fuzzy PID controller and a fuzzy control process, which is represented by a fuzzy control differential equation in linear form. We use the concepts of the generalized Hukuhara differentiability and the fuzzy integral of fuzzy-valued functions to study some qualitative properties for this system in the space of fuzzy numbers. We also study the existence and uniqueness result for solutions of fuzzy PID control differential equations under some suitable conditions. A number of examples are also provided to illustrate the results of the theory.

Grey Absolute Decision Analysis (GADA) Method for Multiple Criteria Group Decision-Making Under Uncertainty

Abstract: The study proposes a novel, convenient and dimensionless model of multi-criteria decision-making (MCDM), hereby referred to as Grey Absolute Decision Analysis (GADA) method. The foundation of the GADA method rests upon the Absolute Grey Relational Analysis (Absolute GRA) model and the system that the method follows to produce GADA Indexes and GADA Weights. The GADA Weights represent the relative weights of decision alternatives under given criteria. The method can handle both positive (“higher the better”) and negative (“lower the better”) criteria simultaneously in its algorithm. The method can deal with problems involving uncertainty and incomplete data. Two practical cases have been presented in the study to demonstrate the feasibility of the method. Furthermore, the GADA Weights obtained for the cases show that these values are comparable to the relative weights obtained through the traditional methods like AHP and SAW thus signifying the feasibility of the method. However, the conventional methods do not consider the mutual association between the judgments of the members of decision-making group (experts’ opinions), a weakness that the proposed method overwhelms. Therefore, the overall ranking obtained from the proposed method is acceptable, especially under the uncertain environment where the nature of mutual association between the judgments is not precise. The key benefit of the method lies in its adaptability to different scales of measurement. Also, it can provide relative weights and rankings of experts, criterion and alternatives. These benefits make the GADA method significant among the class of MCDM methods.

A New Uncertainty Measure of Discrete Z-numbers

Abstract: Today’s modern decision-making problem is designated by not being the most effective fuzziness; however, additionally partial reliability also plays a crucial role. The incomplete and unreliable information may also affect the selection maker to earn inaccurate decisions, ensuing in monetary losses and wastes of resources. Thus, it is vital to describe the reliability of the facts. To cope with it entirely, a notion of Z-number, i.e., a pair of fuzzy sets modeling a probability-qualified fuzzy statement, is the most suitable medium to access it. In this paper, we spout a new technique to measure the uncertainty of discrete Z-numbers based on Shannon entropy. In the given approach, by using characteristics of Z-number, all the potential probability distributions are estimated by the maximum entropy method. Then, a new fuzzy subset of the Z-number is formed based on the probability distributions and the membership functions of the fuzzy number. Finally, the centroid of the formulated set is determined to rank the degree of the uncertainty of Z-number. The applicability of the delivered approach is read with some numerical examples related to the decision-making process.

Simulation of a Bubble-Column Reactor by Three-Dimensional CFD: Multidimension- and Function-Adaptive Network-Based Fuzzy Inference System

Abstract: Recently, novel approaches have been developed for simulating bubbly flow as well as distributed and constant phase evolution by means of a two-phase reactor. Among these approaches, the Eulerian–Eulerian method and soft computing approaches can be mentioned. Since complex numerical methods (for example, multidimensional Eulerian–Eulerian method) require several runs for fluid conditions optimization, a method which can decrease these runs can be very useful and practical. This method is provided by joining computational fluid dynamic (CFD) to the adaptive neuro-fuzzy inference system (ANFIS). In this technique, valuable information is provided for a careful analysis of fluid conditions. Also, it can facilitate a vast amount of data categorization in synthetic neural network nodes, which eliminates the need for a complex nonstructured CFD mesh. Moreover, a neural geometry can be provided, in which no limitation of mesh numbers in the fluid domain would exist. The key CFD parameters in the scale-up of the reactorstaken into consideration in the current research are gas and liquid circulations. These factors are applied as output factors for prediction tool in various dimensions in the ANFIS method. The results obtained in this study show appropriate conformity concerning ANFIS and CFD results depending on multiple dimensions. In this study, the grouping of CFD and multifunction the ANFIS method delivers the nondiscrete domain in different dimensions and presents an intelligent instrument for the local prediction of multiphase flow. The result shows that three inputs, which represent the dimension of the reactor, and learning stage of the ANFIS method provide a better understanding of flow characteristics in the two-phase reactor, while the two-dimensional ANFIS method even with multistructured functions cannot predict well the multiphase flow in the reactor.

Multiplicative Consistency Adjustment Model and Data Envelopment Analysis-Driven Decision-Making Process with Probabilistic Hesitant Fuzzy Preference Relations

Abstract: Unlike other fuzzy modellings, probabilistic fuzzy sets can reflect clearly the importance of different numerical values. In group decision-making (GDM) problems, it is quite common for decision-makers (DMs) to elicit their knowledge with probabilistic hesitant fuzzy preference relations (PHFPRs), in which consistency adjustment and alternatives’ weight vector determination play a key role in the decision-making process. This study aims at constructing a decision-making model with PHFPRs. First, several new concepts are introduced, including the multiplicative consistency and consistency index of PHFPRs. Then, we present a construction approach for the multiplicative consistent PHFPRs, and a convergent local consistency improvement process for PHFPRs is designed to detect and improve their consistency when the PHFPRs do not meet the consistency level. The local adjustment strategy is utilized to retain the preference evaluation of DMs as much as possible. Afterwards, based on the obtained efficiency score values, we propose a new data envelopment analysis model to derive the weight values of alternatives. Furthermore, we explore a decision-making method with PHFPRs to obtain the optimal selection from the alternatives. Finally, an applied case about logistics company assessment is presented, and the effectiveness and rationality of the explored method are verified by the comparison with the various approaches.

Fuzzy Logic in Dynamic Parameter Adaptation of Harmony Search Optimization for Benchmark Functions and Fuzzy Controllers

Abstract: Nowadays the use of fuzzy logic has been increasing in popularity, and this is mainly due to the inference mechanism that allows simulating human reasoning in knowledge-based systems. The main contribution of this work is using the concepts of fuzzy logic in a method for dynamically adapting the main parameters of the harmony search algorithm during execution. Dynamical adaptation of parameters in metaheuristics has been shown to improve performance and accuracy in a wide range of applications. For this reason, we propose and approach for fuzzy adaptation of parameters in harmony search. Two case studies are considered for testing the proposed approach, the optimization of mathematical functions, which are unimodal, multimodal, hybrid, and composite functions and a control problem without noise and when noise is considered. A statistical comparison between the harmony search algorithm and the fuzzy harmony search algorithm is presented to verify the advantages of the proposed approach.

General Type-2 Fuzzy Gain Scheduling PID Controller with Application to Power-Line Inspection Robots

Abstract: In this paper, a general type-2 fuzzy gain scheduling PID (GT2FGS-PID) controller is presented to achieve self-balance adjustment of the power-line inspection (PLI) robot system. As the PLI robot system is an under-actuated nonlinear system, obtaining the full information of the four-state variables is necessary to balance the PLI robot. However, as the number of input variables increases, the number of control rules increases exponentially, making the design of the fuzzy controller extremely complex. Therefore, the proposed controller prevents the problem of rule explosion using information fusion and then simplifies the control design. Moreover, the particle swarm optimization algorithm is used to select improved controller parameters and make the controller achievable. In this paper, the control performance and anti-interference ability of the traditional PID control, type-1 fuzzy control, interval type-2 fuzzy control, and general type-2 fuzzy control methods are compared. By means of numerical simulation, we can conclude that the GT2FGS-PID controller exhibits superior stability and robustness over other controllers for the PLI robot system.

A Convolutional Fuzzy Neural Network Architecture for Object Classification with Small Training Database

Abstract: In this paper, we propose a novel architecture that combines the convolutional neural network (CNN) with a fuzzy neural network (FNN). We utilize the fuzzy neural network with semi-connected layers to sum up feature information. During the training process, to map membership values, the CNN generates feature maps as outputs and feeds into fuzzifier layers, alternatively called fuzzy maps. The proposed method increases classification accuracy, because fuzzy neural networks can generate not only crisp values but also fuzzy values; this means that there is potentially more information contained in the fuzzy set. Our model is evaluated by cross-validation tests. While big data is necessary for training in general, we train our model with small data and test with big data to demonstrate its ability of object classification in cases where sufficient data are not available.

Takagi–Sugeno Fuzzy Neural Network Hysteresis Modeling for Magnetic Shape Memory Alloy Actuator Based on Modified Bacteria Foraging Algorithm

Abstract: The magnetic shape memory alloy (MSMA)-based actuator, as a new type of actuator, has a great application prospect in the micro-precision positioning field. However, the input-to-output hysteresis nonlinearity largely hinders its wide application. In this paper, a Takagi–Sugeno fuzzy neural network (TSFNN) model based on the modified bacteria foraging algorithm (MBFA) is innovatively utilized to describe the complex hysteresis nonlinearity of the MSMA-based actuator, and the parameters of TSFNN are optimized by the MBFA. The TSFNN is a combination of the fuzzy-logic system and neural network; thus, it has the capability of approximating the nonlinear mapping function and self-adjustment and is suitable for hysteresis modeling. The MBFA, which can obtain better optimization values, is employed for the parameter identification procedure. To demonstrate the effectiveness of the proposed model, a TSFNN based on the gradient descent algorithm (GDA) is used for comparison. Experimental results clearly show that the proposed modeling method can accurately describe the hysteresis nonlinearity of the MSMA-based actuator and has significance for its future application.

Anti-windup TS Fuzzy PI-like Control for Discrete-Time Nonlinear Systems with Saturated Actuators

Abstract: This paper deals with piecewise constant set-points tracking control of nonlinear discrete-time systems represented by Takagi-Sugeno models under actuators’ saturation. To this end, a fuzzy Proportional Integral-like (PI-like) discrete-time control scheme is considered, which consists of a proportional state feedback, an integral action over the tracking error, and an anti-windup action. All the control gains are obtained through a convex optimization procedure formulated in term of Linear Matrix Inequalities (LMIs). The proposed method yields a Parameter Distributed Compensation (PDC) PI-like control and a non-PDC anti-windup action structure. Due to the actuators’ saturation, a local approach is considered with a fuzzy Lyapunov function to ensure the local closed-loop stability, to provide an estimate of the region of attraction, and to compute the amplitude bounds of set-points changes. This latter issue allows delivering operational security by providing a bounded range for the set-points variation. To validate and illustrate the performance of the proposed tracking control approach, real-time experiments has been performed on an industrial oriented process consisting on the nonlinear level control of two interactive tanks.

Performance Analysis of MPPT Techniques for Dynamic Irradiation Condition of Solar PV

Abstract: Solar Photovoltaic (PV) systems are playing a major role in the present electrical energy systems. The solar PV gives nonlinear I–V and P–V characteristics. As a result, it is difficult to extract the maximum power of the solar PV. Under Partial Shading Conditions (PSCs), the solar PV characteristics consist of multiple local Maximum Power Points (MPPs) and one global MPP. The classical Maximum Power Point Tracking (MPPT) techniques cannot track the global MPP under PSCs. Accordingly, this work aims to study the performance of five soft computing MPPT techniques. The studied five soft computing MPPT techniques are Modified Variable Step Size-Radial Basis Functional Network (MVSS-RBFN), Modified Hill-Climb with Fuzzy Logic Controller (MHC-FLC), Artificial Neuro-Fuzzy Inference System (ANFIS), Perturb and Observe with Practical Swarm Optimization (P&O-PSO), and Adaptive Cuckoo Search (ACS). The comparative performance analysis of five soft computing techniques has been carried out against the Variable Step Size-Incremental Resistance (VSS-INR), and Variable Step Size-Feedback Controller (VSS-FC)-based MPPT techniques. The performance analysis of seven MPPT techniques has been done by considering the parameters are steady-state settling time, MPP tracking speed, algorithm complexity, PV array dependency, handling of partial shading, and efficiency.

A Hybrid Short-Term Building Electrical Load Forecasting Model Combining the Periodic Pattern, Fuzzy System, and Wavelet Transform

Abstract: Accurate forecasting and scientific analysis of building electrical load can improve the level of building energy management to meet the requirements of energy saving. To further strengthen the forecasting accuracy, this study presents a hybrid model for building electrical load forecasting. The proposed method combines the fuzzy inference system and the periodicity knowledge together to generate accurate forecasting results. In this method, in order to better reflect the actual characteristic of the electrical load, the wavelet transform method is firstly utilized to filter the original building electrical load data. Then, the daily periodic pattern is extracted from such filtered electrical load data, and the residual data are obtained through removing the daily periodic pattern. Further, the residual data-driven forecasting model is constructed by the functionally weighted single-input-rule-modules connected fuzzy inference system (FWSIRM-FIS). This FWSIRM-FIS model is used to provide the compensation to the periodic component. In other words, the daily periodic component and the residual forecasting are combined to achieve the final forecasting result. Specifically, in order to assure the forecasting performance of the FWSIRM-FIS model, the subtraction clustering method is employed to construct the SIRMs while the least square estimation is utilized to optimize the parameters in the functional weights of the FWSIRM-FIS. Finally, in this paper, two real-world experiments are made and detailed comparisons with four traditional models are given. Experimental and comparison results demonstrate that the proposed hybrid model has the smallest forecasting errors and can achieve the best performance.

Comprehensive Evaluation of Non-waste Cities Based on Two-Tuple Mixed Correlation Degree

Abstract: Under the background of vigorously promoting the construction of ecological civilization, the importance of constructing the “non-waste cities” becomes increasingly prominent. Taking 39 cities in the Yangtze River Economic Zone as the research objects, this paper establishes a new evaluation index system for “non-waste cities,” and proposes a multi-source, heterogeneous and multi-attribute decision-making method for the comprehensive evaluation of “non-waste cities.” Specifically, the evaluation index system of “non-waste cities” is constructed from four aspects: economic level, environmental pollution, resource consumption, and waste utilization. Considering that there is the characteristic of multi-source heterogeneity for the attribute values (that is, real numbers, interval numbers, and fuzzy linguistic variables coexist), the multi-source heterogeneous data are uniformly converted into two-tuples, and then a new two-tuple entropy weight method is proposed to determine the weights of evaluation attributes. Moreover, combining the traditional grey relational analysis method with TOPSIS, a multi-source, heterogeneous and multi-attribute decision-making method based on two-tuple mixed correlation degree (TTMCD-MSHMADM) is proposed to evaluate the “non-waste cities,” and an empirical analysis is made for the 39 cities in the Yangtze River Economic Zone. The result gives a theoretical basis for the formulation of sustainable economic development policies in the Yangtze River Economic Zone, and provides a decision reference for selecting the demonstration cities of “non-waste cities.”

Multiple Attribute Group Decision Making Method Based on Intuitionistic Fuzzy Einstein Interactive Operations

Abstract: The intuitionistic fuzzy numbers (IFNs) have been extensively studied in recent years. However, the traditional operational rules (ORs) of the IFNs still have some drawbacks in solving the practical decision-making problems. Einstein t-conorm and t-norm (TAT) are an important and typical class of the TAT, but the ORs for the IFNs based on the Einstein TAT (ETAT) cannot consider the interaction between the membership degree (MD) and the non-membership degree (N-MD), they may get the unreasonable evaluation results in some realistic decision-making situations. So this paper proposes some new Einstein interactive ORs for the IFNs, then, it further presents the intuitionistic fuzzy Einstein interactive weighted averaging (IFEIWA) operator to overcome above existing drawbacks, and some properties of this operator are proved. Simultaneously, in order to eliminate the effects of the existing biases of some decision experts in the process of evaluating attributes, this paper proposes the intuitionistic fuzzy Einstein interactive power averaging (IFEIPA) operator and the intuitionistic fuzzy Einstein interactive weighted power averaging (IFEIWPA) operator based on the revised power weighted averaging operator, and then gives their some desirable properties. Further, by using the IFEIPA operator and the IFEIWPA operator, this paper presents a novel method for the multi-attribute group decision making (MAGDM) problems to solve practical decision-making problems. Lastly, this paper uses some actual application examples to verify the applicability and validity of the proposed MAGDM method, and then demonstrates the superiority of novel method by detailed comparison analysis with other typical methods.

An Overview of the Fuzzy Data Envelopment Analysis Research and Its Successful Applications

Abstract: Data envelopment analysis (DEA) is a prominent technique to make decisions and improve alternatives based on non-parameter modeling and ratio calculation. However, an obvious difficulty to use this method is how to obtain accurate input and output data in the real application. To address this issue, the fuzzy DEAs (FDEAs) are proposed which have been successfully applied in many real fields. The FDEAs hold two aforementioned advantages; meanwhile, it can conveniently present uncertain evaluation information. Therefore, the FDEAs have received much attention from researchers. To summarize the current status, development trends, and further studies of the FDEA research, this paper investigates the related publications from two perspectives of description analysis and literature review, which includes the following details: (1) the literature retrospective analysis of the FDEA with bibliometric technique. Based on it, the publication overview, the cluster network, the emerging trend, and the burst detection are demonstrated in detail. (2) The method review of the basic FDEAs and two kinds of extended FDEAs. These FDEAs are proposed by introducing different fuzzy inputs and outputs, developing different theoretical DEAs, and integrating different mathematical models, respectively. (3) The application review of the FDEAs in some real-life situations. The obtained results provide some clues for researchers who are interested in the FDEA research to do further investigations on theory development and practical applications.

Wavelet Interval Type-2 Fuzzy Quad-Function-Link Brain Emotional Control Algorithm for the Synchronization of 3D Nonlinear Chaotic Systems

Abstract: This study provides a novel quad-function-link network to adjust the lower and upper weights of a wavelet interval type-2 fuzzy brain emotional structure to increase the response and performance for the synchronization of 3D nonlinear chaotic systems. The proposed control system is a hybrid method that comprises a new wavelet interval type-2 fuzzy quad-function-link brain emotional controller and a robust controller. It contains a fuzzy inference system and three substructures with five layers. The substructures are an amygdala, a prefrontal cortex, and a novel quad-function-link network that can adjust the weights efficiently for the amygdala and prefrontal cortex networks to achieve the synchronization of the master–slave systems well with reduced tracking errors. Then, a Lyapunov stability function is employed to provide the adaptive laws, and they are effectively used online to adjust the system parameters. Finally, simulation studies of two 3D nonlinear chaotic systems are used to verify the superiority and advantage of the proposed algorithm.

The Medical Treatment Service Matching Based on the Probabilistic Linguistic Term Sets with Unknown Attribute Weights

Abstract: In multi-attribute two-sided matching (MATSM) problems, the attribute weights play an important role. The existing methods usually neglect the interaction and the effect among multiple attributes, resulting in irrational matching results. This paper takes this interaction into consideration. With the complexity of the matching environment, the uncertainties of agents should be considered. The probabilistic linguistic term set (PLTS) is a useful tool to describe the uncertainty and the limited cognition of agents. Thus, this paper aims to provide a novel MATSM method under the probabilistic linguistic environment with unknown attribute weights. Firstly, the attribute weights are determined by providing the probabilistic linguistic decision-making trial and evaluation laboratory (PL-DEMATEL) method. Besides, this paper constructs the gain and loss (GL) matrices and calculates the agents’ perceived values (PVs) by introducing prospect theory (PT). Then, the PVs are aggregated into the comprehensive PVs (CPVs) based on the obtained attribute weights. Next, this paper also proposes a ranking method, called probabilistic linguistic multi-attribute border approximation area comparison (PL-MABAC) method, to rank the multiple agents, which lay a solid foundation for stable matching constraint of the programming model. The matching results are obtained by solving the programming model. Finally, a case study of matching medical treatment service providers and demanders is presented to validate the proposed method. The comparative analyses and discussions are also provided to demonstrate its effectiveness.

A Study of a Backorder EOQ Model for Cloud-Type Intuitionistic Dense Fuzzy Demand Rate

Abstract: This paper deals with a backorder inventory problem under intuitionistic dense fuzzy environment. In fuzzy set theory, the concept of dense fuzzy set is quite new that depends upon the number of negotiations/turnovers made by the decision makers (DMs) of any kind of industrial setup. Moreover, we have discussed the preliminary concept on intuitionistic dense fuzzy set (IDFS) with their corresponding (non)membership functions and defuzzification methods. The graphical overview resembles the graphs obtained from a cloud aggregation model developed by Mao et al. in 2018. The basic difference is that they considered interval-valued hesitant fuzzy model with unsharp boundary but the content of present study is solely associated with nonrandom uncertainty having proper boundary. Finally, numerical examples, comparative study, sensitivity analysis, graphical illustration, and conclusion are made for justification of the new approach.

Intuitionistic Fuzzy Sliding Controller for Uncertain Hyperchaotic Synchronization

Abstract: In this study, the design of an intuitionistic fuzzy controller for synchronization of two non-identical hyperchaotic systems is proposed. Since hyperchaotic systems has high sensitivity to the initial condition, disturbance and parameter variability. Synchronization of hyperchaotic systems is used to test the controller performance. On the other hand, using of fuzzy logic-based controller has an increasing tendency. As known, fuzzy logic control (FLC), only membership functions are used to obtain a realistic model of the systems. But the intuitionistic fuzzy logic control (IFLC) allows us to obtain a more realistic model than FLC because it also takes into account the degree of non-membership and the degree of uncertainty beside of degree of membership to model examined system. Fuzzy logic-based controllers are hybridized with robust control methods such as sliding mode controller to improve the performance of controller. To take advantages of SMC with fuzzy logic-based IFLC, the IFSMC controller obtained by hybridizing these two methods was designed for hyperchaotic systems. To demonstrate the performance of IFSMC, the results obtained from the synchronization of hyperchaotic systems with FSMC (fuzzy sliding mode controller) and IFSMC were compared. The stability of IFSMC is proved by Lyapunov stability condition. The numerical results and analysis show the efficiency of the IFSMC with regards to synchronization control of uncertain chaotic systems having challenging external disturbances in terms of robustness, minimum tracking error.

Multicriteria Group Decision-Making for Supplier Selection Based on Intuitionistic Cubic Fuzzy Aggregation Operators

Abstract: This article is an advanced approach to intuitionistic fuzzy set through application of cubic set theory. For instance, we establish the idea of the intuitionistic cubic fuzzy set (ICFS) theory and define several operations for ICFS ; also establish a series of weighted aggregation operators under intuitionistic cubic fuzzy information, so-called intuitionistic cubic fuzzy weighted averaging (ICFWA) operator, intuitionistic cubic fuzzy order weighted averaging (ICFOWA) operator, intuitionistic cubic fuzzy weighted geometric (ICFWG) operator, intuitionistic cubic fuzzy order weighted geometric (ICFOWG) operator, intuitionistic cubic fuzzy hybrid averaging (ICFHA) operator, and intuitionistic cubic fuzzy hybrid geometric (ICFHG) operator; and further study their fundamental properties and showed the relationship among these aggregation operators. In order to demonstrate the feasibility and practicality of the mentioned new technique, we develop multicriteria group decision-making algorithm under intuitionistic cubic fuzzy environment. Further, the proposed method applied to supply chain management and for implementation, consider numerical application of supply chain management. Also the selected supplier by ICFD aggregation operators is verified by VIKOR method. Comparing the proposed techniques with other pre-existing aggregation operators, we concluded that the proposed technique is better, reliable, and effective.

A Novel Three-Way Investment Decisions Based on Decision-Theoretic Rough Sets with Hesitant Fuzzy Information

Abstract: As a classic model of three-way decisions, the decision-theoretic rough sets (DTRSs) have been adopted to help make profit-based investment decisions. However, there is epistemic uncertainty in the assessment of investment projects, hence the hesitant fuzzy sets (HFSs) are appropriate tool for characterizing the revenue functions and cost functions. To get a more reasonable result in the three-way investment decisions, we introduce HFSs to DTRSs and explore a new three-way investment decision model. Firstly, we take into account the revenue and cost of DTRSs with hesitant fuzzy elements and propose a hesitant fuzzy decision-theoretic rough sets (HFDTRSs) model. Then, we calculate the revenue functions and cost functions by aggregating hesitant fuzzy elements with the Bayesian decision procedure. Considering the differences in the personalities and attitudes of decision-makers, we propose optimistic strategy and pessimistic strategy to aggregate revenue functions and cost functions. Finally, based on the score of profit maximization, we make three-way investment decisions. A case study of coal investment was used to demonstrate the proposed methods.

Pythagorean Fuzzy Entropy and Its Application in Multiple-Criteria Decision-Making

Abstract: In this paper, a Pythagorean fuzzy decision-making method based on overall entropy is presented. First, a new definition is proposed for fuzzy entropy for any given Pythagorean fuzzy set (PFS). The proposed definition is based on the relationship between the fuzziness contained in the given PFS and the distance from a point to a line on a projection plane. Some related properties are introduced. Second, the overall entropy of the PFS is determined based on fuzzy entropy and the degree of hesitancy; proofs are presented to formalize some related properties. Third, an entropy weight formula is provided that is based on overall entropy, and a Pythagorean fuzzy decision-making method is developed on this basis. Finally, the effectiveness and practicability of the proposed methods are illustrated by an example and three comparative analyses.