Showing papers on "Membership function published in 2022"

A q-rung orthopair basic probability assignment and its application in medical diagnosis

Abstract: Dempster-Shafer theory is widely used in decision-making and considered as one of the potential mathematical tools in order to fuse the evidence. However, existing studies in this theory show disadvantage due to conflicting nature of standard evidence set and the combination rule of evidence. In this paper, we have constructed the framework of q-rung evidence set to address the issue of conflicts based on the q-rung fuzzy number due to its more comprehensive range of advantage compared to the other fuzzy or discrete numbers. The proposed q-rung evidence set has the flexibility in assessing a parameter through the q-rung orthopair basic probability assignment consisting of membership and non-membership belief degree. Moreover, as the proposed q-rung orthopair basic probability assignment consists of pair of belief degrees, the possibility of conflicts cannot be ignored entirely. In this regard, a new association coefficient measure is introduced where each component of the belief degrees is modified through the weighted average mass technique. This paper uses various concept such as fuzzy soft sets, Deng entropy, association coefficient measure and score function for decision-making problem. Firstly, to obtain the initial q-rung belief function, we have implemented the Intuitionistic fuzzy soft set to assess the parameter of the alternatives and Deng entropy to find the uncertainty of the parameters. Secondly, the association coefficient measure is used to avoid the conflict through the modified form of evidence. Finally, we combined the evidence and found the score value of the Intuitionistic fuzzy numbers for the ranking of the alternatives based on the score values of alternatives. This study is validated with the case study in the medical diagnosis problem from the existing paper and compared the ranking of alternatives based on the score function of belief measures of the alternatives.

Feature Selection With Fuzzy-Rough Minimum Classification Error Criterion

Abstract: Classical fuzzy rough set often uses fuzzy rough dependency as an evaluation function of feature selection. However, this function only retains the maximum membership degree of a sample to one decision class, it cannot describe the classification error. Therefore, in this article, a novel criterion function for feature selection is proposed to overcome this weakness. To characterize the classification error rate, we first introduce a class of irreflexive and symmetric fuzzy binary relations to redefine the concepts of fuzzy rough approximations. Then, we propose a novel concept of dependency: inner product dependency to describe the classification error and construct a criterion function to evaluate the importance of candidate features. The proposed criterion function not only can maintain a maximum dependency function, but also guarantees the minimum classification error. The experimental analysis shows that the proposed criterion function is effective for datasets with a large overlap between different categories.

Fuzzy Set-Membership Filtering for Discrete-Time Nonlinear Systems

Abstract: In this article, the problem of state estimation is addressed for discrete-time nonlinear systems subject to additive unknown-but-bounded noises by using fuzzy set-membership filtering. First, an improved T-S fuzzy model is introduced to achieve highly accurate approximation via an affine model under each fuzzy rule. Then, compared to traditional prediction-based ones, two types of fuzzy set-membership filters are proposed to effectively improve filtering performance, where the structure of both filters consists of two parts: prediction and filtering. Under the locally Lipschitz continuous condition of membership functions, unknown membership values in the estimation error system can be treated as multiplicative noises with respect to the estimation error. Real-time recursive algorithms are given to find the minimal ellipsoid containing the true state. Finally, the proposed optimization approaches are validated via numerical simulations of a one-dimensional and a three-dimensional discrete-time nonlinear systems.

Ranking of Z-Numbers Based on the Developed Golden Rule Representative Value

Abstract: Real-world decision-making is based on human cognitive information, which is characterized by fuzziness and partial reliability. In order to better describe such information, Zadeh proposed the concept of Z-number. Ranking the Z-number is an indispensable step in solving the decision-making problem under the Z-number-based information. Golden rule representative value is a new concept introduced by Yager to rank interval values. This article expands it and proposes a new golden rule representative value for fuzzy numbers, and then, apply it to the ranking of the Z-number. Some new rules involving the centroid and fuzziness of fuzzy numbers are constructed to capture the preference of decision-makers. The Takagi–Sugeno–Kang fuzzy model is used to implement these rules. The obtained Rep function is used to construct a new golden rule representative value fuzzy subset of the Z-number and associate this new fuzzy subset with a scalar value. This fuzzy subset not only implies the fuzzy aspect of the Z-number but also contains the information in the hidden probability distribution. The scalar value is regarded as the golden rule representative value of the Z-number to participate in the ranking. The proposed method greatly retains the original information of the Z-number and can overcome the shortcomings of the existing methods. Some numerical examples are used to describe the specific process of the proposed method. The comparative analysis and discussion with existing methods clarify the advantages of the proposed method.

An Approach Towards the Design of Interval Type-3 T–S Fuzzy System

Abstract: This article providesa systematic approach for the design of an interval type-3 (IT3) Takagi–Sugeno (T–S) fuzzy logic system (FLS) using $\alpha $ - plane representation. An IT3 FLS is designed with the baseline of the general type-2 (GT2) FLS in a similar manner as an IT2 FLS was designed from the baseline of type-1 FLS. Hence, IT3 FLS evolved as a successor of GT2 FLS, where secondary membership function is an interval type-2 fuzzy set (FS), and values of tertiary membership are unity over the footprint of uncertainty of secondary membership. This extra degree of freedom in IT3 FLS provides better modeling capability as compared to GT2 FLS in the presence of a high degree of uncertainty and vagueness. The proposed system will be more appealing while dealing with uncertain information or data, which is supposed to be generated from uncertain sources; i.e., there exist uncertainties even in the presence of uncertainty. The computations needed for the design of IT3 FLS are derived using IT2 FS and GT2 FS mathematics. The design algorithms adopted for the baseline IT2 T–S fuzzy system are as per the modified interval type-2 fuzzy c-regression model clustering algorithm and hyper-plane-shaped membership function. The proposed methodology is applied to several benchmark examples and obtained results are compared with recently developed fuzzy modeling methods having a comparable number of rule bases. The proposed IT3 T–S FLS shows good performance in terms of accuracy when data is corrupted by noise and uncertainties related to missing or unvarying data exist. The computational cost is linear with design parameters and by optimum choice of $\alpha $ -planes, it is still bearable considering advantages and nature of applications.

Comparison Uncertainty of Different Types of Membership Functions in T2FLS: Case of International Financial Market

Abstract: This article deals with the determination and comparison of different types of functions of the type-2 interval of fuzzy logic, using a case study on the international financial market. The model is demonstrated on the time series of the leading stock index DJIA of the US market. Type-2 Fuzzy Logic membership features are able to include additional uncertainty resulting from unclear, uncertain or inaccurate financial data that are selected as inputs to the model. Data on the financial situation of companies are prone to inaccuracies or incomplete information, which is why the type-2 fuzzy logic application is most suitable for this type of financial analysis. This paper is primarily focused on comparing and evaluating the performance of different types of type-2 fuzzy membership functions with integrated additional uncertainty. For this purpose, several model situations differing in shape and level or degree of uncertainty of membership functions are constructed. The results of this research show that type-2 fuzzy sets with dual membership functions is a suitable expert system for highly chaotic and unstable international stock markets and achieves higher accuracy with the integration of a certain level of uncertainty compared to type-1 fuzzy logic.

Application of Soft Sets to Assessment Processes

Abstract: From the time that Zadeh introduced the concept of fuzzy set in 1965 a lot of research has been carried out for generalizing and extending the corresponding theory on the purpose of tackling more effectively the existing in real life uncertainty. One such generalization is the concept of soft set aiming, among others, to overcome the existing difficulty of defining properly the membership function of a fuzzy set. A new model using soft sets is presented in this paper for assessing human-machine performance in a parametric manner and examples are given to illustrate its applicability in practice. Such kind of models are very useful when the assessment has qualitative rather than quantitative characteristics.

Membership-Function-Dependent Control Design and Stability Analysis of Interval Type-2 Sampled-Data Fuzzy-Model-Based Control System

Abstract: This article investigates the design and stability analysis of the interval type-2 (IT2) sampled-data (SD) fuzzy-model-based (FMB) control system with the optimal guaranteed cost performance. An IT2 Takagi–Sugeno (T-S) fuzzy model is applied to describe the dynamics of the nonlinear systems where the parameter uncertainties are captured by the lower and upper membership functions. To conduct the stability analysis for the SD FMB control system, a looped-functional approach taking the advantage of the information about the sampling periods is employed. Because of the SD control strategy, the state will be sampled at each sampling instant and the control signal generated by the IT2SD fuzzy controller will be kept by the zero-order holder during the sampling period, which will result in mismatched membership grades between IT2 T-S fuzzy model and IT2SD fuzzy controller that leads to the complexity in carrying out stability analysis. Thanks to the imperfect premise matching concept, which allows the difference on the number of rules and the premise membership functions between model and controller, the design of the IT2SD fuzzy controller can be more flexible. To further relax the stability conditions and minimize the upper bound of the guaranteed cost index, the membership-function-dependent stability analysis approach which can make use of the features of the IT2 membership functions is adopted. The performance of the control system can also be adjusted through the choice of the weighting matrices in the cost function. The stability conditions building on the Lyapunov stability theory and the performance conditions building on the concept of the guaranteed cost control in the shape of linear matrix inequalities are established to assure the system stability and acquire the optimal guaranteed cost performance. The proposed IT2SDFMB control design is tested on the inverted pendulum system and the simulation results verify the effectiveness of the proposed approach.

Assessment of the environmental comfort of lactating sows via improved analytic hierarchy process and fuzzy comprehensive evaluation

Abstract: : Since there are many interacting influence factors of the comfortable degree of lactating sows, a method that combines improved analytic hierarchy process (IAHP) and fuzzy comprehensive evaluation (FCE) was introduced to conduct a quantitative evaluation of the comfortable degree. Besides, an evaluation index system was established, and the weights of different indicators were determined by using IAHP method, including temperature, relative humidity, concentrations of carbon dioxide (CO 2 ), ammonia (NH 3 ), hydrogen sulfide (H 2 S), and air speed. The construction method of fuzzy membership function and the calculation method of the parameters were proposed following the principle that the summation of membership degrees is equal to 1. Three basic types of membership functions (MFs), i.e., ridgemf, gaussmf, and trimf were used to build an evaluation model which fitted IAHP-FCE well. The proposed method was verified and applied based on the environmental data in different seasons obtained from a pig farm in Zhenjiang City, Jiangsu Province, China. It is demonstrated that the proposed IAHP-FCE model with various types of MFs has drawn a unique and consistent conclusion. Moreover, the IAHP-FCE model has a higher correlation coefficient of 0.874 compared with the single-factor evaluation (SFE) model. The IAHP-FCE model could be served as a beneficial strategy for the precise regulation and early warning of environmental conditions to improve sow welfare.

Breast cancer disease classification using fuzzy-ID3 algorithm based on association function

Abstract: Breast cancer is the second leading cause of mortality among female cancer patients worldwide. Early detection of breast cancer is considerd as one of the most effective ways to prevent the disease from spreading and enable human can make correct decision on the next process. Automatic diagnostic methods were frequently used to conduct breast cancer diagnoses in order to increase the accuracy and speed of detection. The fuzzy-ID3 algorithm with association function implementation (FID3-AF) is proposed as a classification technique for breast cancer detection. The FID3-AF algorithm is a hybridisation of the fuzzy system, the iterative dichotomizer 3 (ID3) algorithm, and the association function. The fuzzy-neural dynamicbottleneck-detection (FUZZYDBD) is considered as an automatic fuzzy database definition method, would aid in the development of the fuzzy database for the data fuzzification process in FID3-AF. The FID3-AF overcame ID3’s issue of being unable to handle continuous data. The association function is implemented to minimise overfitting and enhance generalisation ability. The results indicated that FID3-AF is robust in breast cancer classification. A thorough comparison of FID3-AF to numerous existing methods was conducted to validate the proposed method’s competency. This study established that the FID3-AF performed well and outperform other methods in breast cancer classification.

Approach to multi-attribute decision-making problems based on neutrality aggregation operators of T-spherical fuzzy information

Abstract: In the process of decision-making, uncertain information is always challenging to deal with. T-spherical fuzzy set (TSFS) operates vagueness of data by analysing three independent functions, namely membership, non-membership, and abstinence function. The TSFS provides us robust scheme with parameter $$q\ge 1$$ to handle the countless opportunities. Hence, this set proves its superiority over the existing picture fuzzy set (PFS) and spherical fuzzy set (SFS). Now a day, decision-makers usually assign impartial values throughout the assessment. This manuscript demonstrates some new operational laws by fusing the neutral characteristics of the degrees of membership and using the probability sum (PS) function. Meanwhile, we determine several aggregation operators (AOs) including weighted averaging neutral, ordered weighed neutral, and hybrid averaging neutral AOs to aggregate the data under T-spherical fuzzy (TSF) environment. As it came to the notice that weighted neutral averaging aggregation operators of the Pythagorean fuzzy set (PyFS), single-valued neutrosophic fuzzy set (SVNFS), and $$q$$ -rung orthopair fuzzy set ( $$q$$ -ROFS) have some restrictions during the decision-making problems. So, to overcome this, we introduce a new multi-attribute group decision-making method (MAGDM) based on proposed AOs. Lastly, we provide various numerical instances to explain the method and exhibit its supremacy. Furthermore, a comparative analysis is conducted to compare the potential of proposed AOs with some other existing methods.

K-Means Clustering Based High Order Weighted Probabilistic Fuzzy Time Series Forecasting Method

Abstract: Abstract In the present study, we propose a novel high-order weighted fuzzy time series (FTS) forecasting method using k-mean clustering, weighted fuzzy logical relations and probabilistic fuzzy set (PFS). Objective of proposed forecasting method is to handle occurrence of recurrence of fuzzy logical relations and both non-probabilistic and probabilistic uncertainties in assigning membership grades to time series datum. The proposed PFS-based forecasting method uses Gaussian probability distribution function to assign probabilities to membership grades. Proposed FTS forecasting method uses high-order weighted fuzzy logical relation in which each fuzzy logical relation uses the weight in ascending order. Superiority of proposed method is shown by implementing it on SBI share price at BSE, India and University of Alabama enrollments. Error measures and statistical parameters, for example, coefficient of correlation, coefficient of determination, performance parameter, evaluation parameter and tracking signal are also used to confirm the outperformance and validity of the proposed PFS-based forecasting method.

Monotonic Takagi–Sugeno models with cubic spline membership functions

Abstract: In the paper we present sufficient monotonicity conditions for zero order Takagi–Sugeno fuzzy systems with cubic spline membership functions. Those fuzzy models have some advantages comparing with commonly used membership functions. In contrast to triangular membership functions the corresponding mapping is smooth. Comparing to Gaussian membership functions the monotonicity conditions are less conservative, more intuitive and admit membership functions with different width. Finally, the derived monotonicity conditions are formulated as linear constraints on the parameters of fuzzy system that can be easily incorporated into related optimization problems solvable by efficient algorithms. Performance of the proposed fuzzy system is tested on two benchmark datasets and output prediction of a nonlinear dynamical system.

Fuzzy Controller for Optimization of Operation Time in Washing Machine

Abstract: The washing machine is one of the important home appliance. Most of today's common washing machines do not yet have smart features. Smart white goods have some decision-making functions instead of users. Smart washing machines can collect some data through their different sensors and use this data in appropriate actions. In this paper, it is aimed to suggest the most suitable program duration to the user and save energy, water and time by using a fuzzy controller system with three inputs and one output. Three different inputs are used; the dirt level of the laundry, the amount of oil and the amount of load. These input values can be obtained through related sensors. Washing time will be obtained as a single output. It is aimed to obtain optimum washing time by trying different methods in fuzzy controller. Two different types of fuzzification methods, triangular and trapezoidal, are applied as membership functions. As the fuzzy inference engine methods, product and minimum inference engine are used comparatively. This study also analyze the effects of the application of different defuzzification methods. We deployed five defuzzification methods: center of gravity, bisector, largest of maximum, smallest of maximum, and mean of maximum. The codes are written using Python programming language. For the evaluation, the results obtained from different methods were compared with each other. According to results, most suitable washing time can be obtained by using the methods of trapezoidal membership function for fuzzification, minimum inference engine and center of gravity for defuzzification.

Application of Adaptive Neuro–Fuzzy Inference System for Forecasting Pavement Roughness in Laos

Abstract: Laos Pavement Management System (PMS) manages 7700 km of National Roads (NRs) and estimates their Maintenance and Rehabilitation (MR) needs based on assessing pavement roughness conditions. This research aims to develop two International Roughness Index (IRI) models for Double Bituminous Surface Treatment (DBST) and Asphalt Concrete (AC) pavement sections using Adaptive Neuro-Fuzzy Inference System (ANFIS). A historical database of 14 years was employed for predicting the IRI as a function of pavement age and Cumulative Equivalent Single-Axle Load (CESAL). The optimum ANFIS structure comprises a hybrid learning algorithm with six fuzzy rules of generalized bell curve membership functions (Gbellmf) for the DBST model and nine fuzzy rules of two-sided Gaussian membership functions (Gauss2mf) for the AC model. Both models used the constant membership function for the output variable (IRI). The statistical evaluation results revealed that both ANFIS models (DBST and AC) have a good prediction capacity with high values of coefficient of determination (R2 0.93 and 0.88) and low values of Mean Absolute Error (MAE 0.28 and 0.27) and Root Mean Squared Percentage Error (RMSPE 7.03 and 9.98). In addition, results revealed that ANFIS models yielded higher prediction accuracy than Multiple Linear Regression (MLR) models previously developed under the same conditions.

Maximal Product and Symmetric Difference of Complex Fuzzy Graph with Application

Abstract: A complex fuzzy set (CFS) is described by a complex-valued truth membership function, which is a combination of a standard true membership function plus a phase term. In this paper, we extend the idea of a fuzzy graph (FG) to a complex fuzzy graph (CFG). The CFS complexity arises from the variety of values that its membership function can attain. In contrast to a standard fuzzy membership function, its range is expanded to the complex plane’s unit circle rather than [0,1]. As a result, the CFS provides a mathematical structure for representing membership in a set in terms of complex numbers. In recent times, a mathematical technique has been a popular way to combine several features. Using the preceding mathematical technique, we introduce strong approaches that are properties of CFG. We define the order and size of CFG. We discuss the degree of vertex and the total degree of vertex of CFG. We describe basic operations, including union, join, and the complement of CFG. We show new maximal product and symmetric difference operations on CFG, along with examples and theorems that go along with them. Lastly, at the base of a complex fuzzy graph, we show the application that would be important for measuring the symmetry or asymmetry of acquaintanceship levels of social disease: COVID-19.

Design of single and double acceptance sampling plans based on interval type-2 fuzzy sets

Abstract: Defectiveness of items is generally considered as a certain value in acceptance sampling plans (ASPs). It is clear that, it may not be certainly known in some real-case problems. Uncertainties of the inspection process such as measurement errors, inspectors’ hesitancies or vagueness of the process etc. should be taken into account to obtain more reliable results. The fuzzy set theory (FST) is one of the best methods to overcome these problems. There are some studies in the literature formulating the ASPs with the help of FST. Deciding the right membership functions of the fuzzy sets (FSs) has a vital importance on the quality of the uncertainty modeling. Additionally, the fuzzy set extensions have been offered to model more complicated uncertainties to achieve better modeling. As one of these extensions, type-2 fuzzy sets (T2FSs) gives an ability to model uncertainty in situations where it is not possible to determine exact membership function parameters. In this study, single and double ASPs based on interval T2FSs (IT2FSs) have been designed for binomial and Poisson distributions. Thus, it becomes possible to make more flexible, sensitive and descriptive sensitivity analyzes. The main characteristic functions of ASPs have been derived and the suggested formulations have been illustrated on a comparative application from manufacturing process. Results allowing for more comprehensive analysis as against to the traditional and T1FSs based plans have been obtained.

Fuzzy-Swarm Intelligence-Based Short-Term Load Forecasting Model as a Solution to Power Quality Issues Existing in Microgrid System

Abstract: Load demand is highly stochastic and uncertain. This is because it was highly influenced by a number of variables like load type, weather conditions, time of day, the seasonality factor, economic constraints, and other randomness effects. The loads are categorized as holiday loads (national and religious), weekdays, and weekend days. The nonlinearity and uncertain characteristics of electrical load in a microgrid are one of the major sources of power quality problems in a microgrid system, and they can be handled using an accurate load forecast model. The fuzzy load prediction model can effectively handle these nonlinearity and uncertainty characteristics to have an accurate load forecast, but the main challenge with this model is its inability to accommodate a large volume of historical load and weather information when the membership function of the input and output fuzzy variables and the number of the fuzzy rules are tremendous. The swarm intelligence load forecast model based on particle swarm optimization algorithms can improve the limitations of the fuzzy system and increase its forecasting performance. The parameters of time, temperature, historical load, and error correction factors are considered as the Fuzzy and Fuzzy-PSO model input variables, while the forecasted industrial load is the only output variable. The Gaussian membership function is considered for both the input and output fuzzy variables. A 3-year historical hourly load data of an Ethiopian industrial system is used to train and validate both prediction models. The mean absolute percentage error (MAPE) is used to evaluate the performance of these prediction models. The Fuzzy-PSO load prediction model shows results that have superior performance to the fuzzy-alone load prediction results.