Type-2 Fuzzy Membership Functions Research Articles

An Experimental Private Small Hydropower Plant Investments Selection Classification System

Investment selection problems and models are crucial for humans, communities, and states. Private small hydroelectric power/ hydropower plant investments (PSHPPIs) selection problem is a unique one in those problems and models. Many available scientific methods can be implemented on this research topic. One methods group is type-2 Mamdani’s type fuzzy inference systems (FISs). This study presents an experimental one-node general type-2 4-zslices Mamdani’s type FIS model for PSHPPIs selection. There are 3 input variables (total estimated electricity generation: M1, total estimated cost: M2, change in the average runoff: M3), 1 output variable (O1: selected/unselected, selection classification of PSHPPIs), and 49 rules. M1 is designed in 5 triangular and trapezoidal general type-2 4-zslices fuzzy membership functions (MFs), M2 in 5 triangular and trapezoidal general type-2 4-zslices fuzzy MFs, M3 in 5 Gaussian type-2 4-zslices fuzzy MFs, and O1 in 2 Gaussian type-2 4-zslices fuzzy MFs. All modeling details are finalized by a human-expert decision process. JuzzyOnline V2.0, a browser-based platform of Juzzy (a Java-based library: Juzzy toolkit), is used for all FIS modeling and calculation activities. Five PSHPPI options assumed to be in their very early investment stages in Turkiye are evaluated in an experimental application. It is clear that an improved, tuned, and fine-tuned version of this model will help private investors to take more convenient/satisfying actions/decisions in a very short evaluation period in their PSHPPIs decision processes. An automatic investment selection classification system can be built in an appropriate development period after experiencing many methods and models. This study is one of the open-science humanoid robot, robot and platform development activities entitled Global Power Robots and Platforms: GPRP/GPRAP (Global Power Plants Developers: GP2D/G2PD/GPPD, Global Power Plants Engineers: GP2E/G2PE/ GPPE, Global Power Plants Owners: GP2O/G2PO/GPOO, Global Power Prediction Systems: GP2S/G2PS/GPPS), Global Profile Analyses Systems, and Global Social Network Analyses Systems.

Toward Effective Uncertainty Management in Decision-Making Models Based on Type-2 Fuzzy TOPSIS

Over the past century, there has been a dramatic increasing interest in the multi-criteria group decision-making (MCGDM) technique, with a considerable amount of studies published regarding it. One of the well-known approaches in the MCGDM paradigm is Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The integration of the TOPSIS method with fuzzy set theory has proven to be successful in various applications. Recently, a wide array of publications has proposed implementing a type-2 fuzzy set with TOPSIS. However, the additional degree of uncertainty represented by type 2 has largely been ignored, especially in a few specific mathematical operations in the model. We propose constructing interval type-2 fuzzy membership functions (IT2 MFs) using interval-based data gathered from a survey, where this is used to generate a new scale to represent ratings for each alternative. This procedure utilized all information gathered from decision makers. In addition, we present a complete algorithm for TOPSIS based on IT2 fuzzy sets (IT2 FSs) which preserve the interval-based form output. The output in the form of intervals offers decision makers (DMs) with more detailed information, enabling them to make more nuanced decisions. This can include cautious decisions when intervals are wider and overlapping. Although understanding the exact meaning of these intervals and their widths in a decision-making context is challenging, this paper introduces a systematic method for connecting input uncertainty to output uncertainty in the TOPSIS technique. This approach establishes a solid foundation for future research. Thus far, no other researchers have suggested a data-driven method that combines TOPSIS with fuzzification and provides intervals as the final output.

Improved interval type-2 fuzzy K-means clustering based on adaptive iterative center with new defuzzification method

Interval Type-2 Fuzzy K-means (IT2FKM) is an efficient clustering algorithm, which mainly focuses on further describes the uncertainty of the data sets by introducing interval type-2 fuzzy membership function. Since the estimation center obtained by two membership functions is an interval type-1 fuzzy set, it is necessary to use the defuzzification method to obtain a crisp cluster center. The existing IT2FKM algorithms adopt the generalized centroid method (GC) in the process of type-reduction and defuzzification for iterative clustering center. But unfortunately, this method simply uses a single numerical value 0.5 as the type-reduction coefficient to balance and synthesize for the left value and the right value of an interval cluster center, while ignoring the distribution of the clusters. This defect makes IT2FKM fail to update the optimal cluster center when facing with imbalanced clusters, which affect the accuracy in some cases. To address this failing, in this paper, some adverse effects caused by generalized centroid method when facing with imbalanced clusters are analyzed in detail. Thereafter, an improved type-reduction method of iterative cluster centers for IT2FKM clustering is proposed considering the imbalanced clustering distributions. On the basis of which, an enhanced IT2FKM algorithm is further developed. The enhanced IT2FKM algorithm has an average classification accuracy of 97.5% when faced with four datasets with different degrees imbalance, which is about 3.25% higher than other clustering algorithms. The effectiveness and superiority of the proposed algorithm are further demonstrated by some experimental analysis of UCI standard datasets.

A Spatial Fuzzy Co-Location Pattern Mining Method Based on Interval Type-2 Fuzzy Sets

The goal of spatial co-location pattern mining is to find subsets of spatial features whose instances are often neighbors in a geographical space. In many practical cases, instances of spatial features contain not only spatial location information but also attribute information. Although there have been several studies that use type-1 fuzzy membership functions to mine spatial fuzzy co-location patterns, there is great uncertainty associated with such membership functions. To address this problem, we propose a spatial fuzzy co-location pattern mining method based on interval type-2 fuzzy sets. First, we collect the interval evaluation values of the interval data of attribute information from experts to form granular data. Next, the original type-1 fuzzy membership function is extended to a granular type-2 fuzzy membership function based on elliptic curves. We use a gradual method to adjust the parameters of the fuzzy membership function so that its footprint of uncertainty satisfies both the connectivity and the given confidence. Based on this granular type-2 fuzzy membership function, we fuzzify the attribute information of instances and define the concepts of fuzzy features and fuzzy co-location patterns. A fuzzy co-location pattern mining algorithm based on spatial cliques is then proposed, termed the FCPM-Clique algorithm. In order to improve the efficiency of the algorithm, we propose two pruning strategies. In addition, we extend two classical spatial pattern mining algorithms, the Join-based algorithm and the Joinless algorithm, to mine fuzzy co-location patterns based on interval type-2 fuzzy sets. Many experiments on synthetic and real-world datasets are conducted, the performance of the three algorithms is compared, and the effectiveness and efficiency of our proposed FCPM-Clique algorithm is demonstrated.

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

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.

A Novel Approach to Generate Type-1 Fuzzy Triangular and Trapezoidal Membership Functions to Improve the Classification Accuracy

Fuzzy logic is an approach that reflects human thinking and decision making by handling uncertainty and vagueness using fuzzy membership functions. When a human is engaged in the design of a fuzzy system, symmetric properties are naturally preferred. Fuzzy c-means clustering is a clustering algorithm that can cluster datasets to produce membership matrix and cluster centers, which results in generating type-1 fuzzy membership functions. However, fuzzy c-means algorithm has a limitation of producing only a single membership function type, Gaussian MF. Generation of multiple fuzzy membership functions is of immense importance as it provides more efficient and optimal solutions to a problem. Therefore, an approach to generate multiple type-1 fuzzy membership functions through fuzzy c-means is required for the optimal and improved results of classification datasets. Hence, to overcome the limitation of the fuzzy c-means algorithm, an approach for the generation of type-1 fuzzy triangular and trapezoidal membership function through fuzzy c-means is considered in this study. The approach is used to calculate and enhance the accuracy of classification datasets called iris, banknote authentication, blood transfusion, and Haberman’s survival. The proposed approach of generating MFs using FCM produce asymmetric MFs, whose results are compared with the MFs produced from grid partitioning (GP), which are symmetric MFs. The results show that the proposed approach of generating type-1 fuzzy membership function through fuzzy c-means is effective and can be adopted.

Memristor Crossbar-Based Hardware Implementation of Type-2 Fuzzy Membership Function and On-Chip Learning

Utilizing fuzzy techniques, especially fuzzy type-2, is one of the most widely used methods in machine learning to model uncertainty. In addition to algorithm provision, the hardware implementation capability, and proper performance in real-time applications are other challenges. The use of hardware platforms that have biological similarities and are comparable to human neural systems in terms of implementation volume has always been considered. Memristor is one of the emerging elements for the implementation of fuzzy logic based algorithms. In this element, by providing current and selecting the appropriate direction for the applied current, the resistance of the memristor (memristance) will increase or decrease. Various implementations of type-1 fuzzy systems exist, but no implementation of type-2 fuzzy systems has been done based on memristors. In this paper, memristor-crossbar structures are used to implement type-2 fuzzy membership functions. In the proposed hardware, the membership functions can have any shape and resolution. Our proposed implementation of type-2 fuzzy membership function has the potential to learn (On-Chip learning capability regardless of host system). Besides, the proposed hardware is analog and can be used as a basis in the construction of evolutionary systems. Furthermore, the proposed approach is applied to memristor emulator to demonstrate its correct operation.

Small Lung Nodules Detection Based on Fuzzy-Logic and Probabilistic Neural Network With Bioinspired Reinforcement Learning

Internal organs, like lungs, are very often examined by the use of screening methods. For this purpose, we present an evaluation model based on a composition of fuzzy system combined with a neural network. The input image is evaluated by means of custom rules, which use type-1 fuzzy membership functions. The results are forwarded to a neural network for final evaluation. Our model was validated by using X-ray images with lung nodules. The results show the high performances of our approach with sensitivity and specificity reaching almost 95% and 90%, respectively, with an accuracy of 92.56%. The new methodology lowers the computational demands considerably and increases detection performances.

Modeling of Complex System Phenomena via Computing With Words in Fuzzy Cognitive Maps

Fuzzy cognitive maps (FCMs) play an important role in high-level reasoning but are limited in their ability to model complex systems with singularities. We are interested in systems that exhibit discontinuous behaviors as one or more of their internal node states approach a threshold. In a new approach to FCM dynamics, we define general classes of aggregation functions which “jump” to a boundary value when any input crosses a threshold, or when all inputs do. The threshold value is a context-dependent parameter which can be readily understood by subject matter experts. Aggregation functions are applied separately to positively and negatively causal antecedents to each node then combined to form the nodal state. This modeling is applied in Computing with Words (CWW) settings, in which link strengths and activation levels are elicited using vocabulary words represented by interval type-2 fuzzy membership functions. We illustrate the behaviors of these novel FCM systems in comparison with their nonsingularity versions.

Corrections to “An Automatic Approach for Learning and Tuning Gaussian Interval Type-2 Fuzzy Membership Functions Applied to Lung CAD Classification System” [Apr 12 224-234

The potential of type-2 fuzzy sets to manage high levels of uncertainty in the subjective knowledge of experts or of numerical information has focused on control and pattern classification systems in recent years. One of the main challenges in designing a type-2 fuzzy logic system (FLS) is how to estimate the parameters of the type-2 fuzzy membership function (T2MF) and the footprint of uncertainty (FOU) from imperfect and noisy datasets. This paper presents an automatic approach to learn and tune Gaussian interval type-2 membership functions (IT2MFs) with application to multidimensional pattern classification problems. T2MFs and their FOUs are tuned according to the uncertainties in the training dataset by a combination of genetic algorithm (GA) and cross-validation techniques. In our GA-based approach, the structure of the chromosome has fewer genes than other GA methods, and chromosome initialization is more precise. The proposed approach addresses the application of the interval type-2 fuzzy logic system (IT2FLS) for the problem of nodule classification in a lung computer-aided detection system. The designed IT2FLS is compared with its type-1 fuzzy logic system (T1FLS) counterpart. The results demonstrate that the IT2FLS outperforms the T1FLS by more than 30% in terms of classification accuracy.

Sliding mode type‐2 neuro‐fuzzy power control of grid‐connected DFIG for wind energy conversion system

This study presents an adaptive sliding mode type-2 neuro-fuzzy controller for power control of doubly fed induction generators (DFIGs). DFIG-based wind turbine system is variable-speed constant-frequency wind energy conversion system. In this proposed control scheme, in order to enhance its performance, sliding mode control (SMC) theory is used for online training the parameters of type-2 fuzzy system membership functions. To regulate the antecedent and consequent part parameters, the SMC adaptive technique is used according to the controller inputs. These inputs are active and reactive power errors and their time derivative, which applied to the structure of T2NF system. The proposed controller employs an interval type-2 fuzzy system because of the uncertainties of the wind speed and variation in parameters in the wind power conversion system. The simulations carried out for a DFIG-based 1.5 MW wind turbine. The results of simulation are compared with the classical proportional-integral controller to confirm the effectiveness of this control scheme. This comparison is carried out between the cut-in and rated region wind speeds. The results of simulation show that the proposed control scheme has better performance to track the peak power and is more robust to machine parameter variations.

Toward a development of general type-2 fuzzy classifiers applied in diagnosis problems through embedded type-1 fuzzy classifiers

Nowadays, with the emergence of computer-aided systems, diagnosis problems are one of the most important application areas of artificial intelligence. The present paper is focused on a specific kind of computer-aided diagnosis system based on General Type-2 Fuzzy Logic. The main goal is the generation of General Type-2 Fuzzy Classifiers that can handle the data uncertainty. The concept of embedded Type-1 Fuzzy membership functions has been proposed to be used in the design of General Type-2 Fuzzy Classifiers. A methodology for generating the embedded Type-1 fuzzy membership functions is introduced, and the subsequent approach for developing the Footprint of Uncertainty of the General Type-2 Fuzzy Classifier is presented. On the other hand, the proposed approach performance is evaluated by the experimentation with different diagnosis benchmark problems. In addition, a statistical comparison with respect to another existing approach of General Type-2 Fuzzy classifiers is presented.

Type-2 Fuzzy PCA Approach in Extracting Salient Features for Molecular Cancer Diagnostics and Prognostics.

Machine learning is becoming a powerful tool for cancer diagnosis and prognosis based on classification using high dimensional molecular data. However, extracting classification features from high-dimensional datasets remains a challenging problem. Principal component analysis (PCA) is a widely used method for dimensionality reduction. However, it is well-known that PCA and most PCA-based feature extraction methods are sensitive to noise, which may affect the accuracy of the subsequent classification. To address this problem, here we have proposed a robust fuzzy principal component analysis (PCA) with interval type-2 (IT-2) fuzzy membership functions for feature extraction. We have tested the performance of three widely used classifiers using the features extracted by proposed approaches and other feature extraction methods - PCA-based feature extraction methods (i.e. conventional PCA and fuzzy PCA), linear discriminant analysis (LDA), and support vector machine recursive feature elimination (SVM-RFE). The proposed feature extraction approaches showed better performance on cancer transcriptome and proteome datasets.

Hybrid Type-2 Fuzzy Based Channel Estimation for MIMO-OFDM System with Doppler Offset Influences

The channel estimation methods track and predict the variation in channel characteristics, so that the original signal can be obtained after nullifying the channel induced influences. The channel estimation methods impact the overall performance of the MIMO-OFDM system. When the communicating nodes are mobile, a complete estimation of the fast time varying channel is accomplished if the Doppler offset is evaluated along with the channel gain. However, most of the channel estimation approaches proposed in literature for MIMO-OFDM systems assume that the Doppler offset contributed by highly mobile communicating nodes is already known to the receiver. The estimation of the Doppler offset with the channel coefficients renders the channel estimation problem non linear. In this paper, the issue of this non linear channel estimation for high mobility communicating nodes with associated dynamic Doppler offset in a MIMO-OFDM system is addressed. In order to obtain complete information of the channel which includes the channel coefficients and the associated Doppler offsets, a hybrid interval type-2 fuzzy aided Kalman filter for channel estimation is proposed. The type-2 fuzzy based membership functions are used here opposed to the type-1 fuzzy membership functions because the type-2 fuzzy membership functions are capable of effective modeling even under high degree of uncertainties. Furthermore, a detailed computational complexity analysis of the proposed algorithm is presented which shows that the algorithm has moderate computational complexity and has good performance in fast time varying channel conditions with high node mobility in a MIMO-OFDM system.

Interval type-2 fuzzy set and human vision based multi-scale geometric analysis for text-graphics segmentation

This paper presents a novel method for texture-based text-graphic segmentation in a text embedded image. In the method, features are computed applying Multi-scale Geometric Analysis(MGA). The MGA of the image is done by Nonsubsampled contourlet transform(NSCT). The NSCT sub-bands help to generate the features which represent textures of the text portions and graphics portions of the image. In a segmentation process, the uncertainties arise mainly for two reasons: one is the ambiguity in gray level and other is the spatial ambiguity. Here the uncertainties are managed by interval type2 fuzzy set (IT2FS). The human vision model called human psychovisual phenomenon (HVS) is incorporated in the process for generating the interval type-2 fuzzy membership functions (IT2FMF). The efficiency of the proposed scheme is measured on the benchmark dataset. The robustness and performance bound of the proposed technique under noise corruption are measured statistically using modified Cramer-Rao bound. We found that effectiveness of the features by NSCT in combination with the IT2FS are quite promising in comparison to the state-of-the-arts methods.

Parameter optimization of interval Type-2 fuzzy neural networks based on PSO and BBBC methods

Interval type-2 fuzzy neural networks (IT2FNNs) can be seen as the hybridization of interval type-2 fuzzy systems (IT2FSs) and neural networks (NNs). Thus, they naturally inherit the merits of both IT2FSs and NNs. Although IT2FNNs have more advantages in processing uncertain, incomplete, or imprecise information compared to their type-1 counterparts, a large number of parameters need to be tuned in the IT2FNNs, which increases the difficulties of their design. In this paper, big bang-big crunch (BBBC) optimization and particle swarm optimization (PSO) are applied in the parameter optimization for Takagi-Sugeno-Kang (TSK) type IT2FNNs. The employment of the BBBC and PSO strategies can eliminate the need of backpropagation computation. The computing problem is converted to a simple feed-forward IT2FNNs learning. The adoption of the BBBC or the PSO will not only simplify the design of the IT2FNNs, but will also increase identification accuracy when compared with present methods. The proposed optimization based strategies are tested with three types of interval type2 fuzzy membership functions (IT2FMFs) and deployed on three typical identification models. Simulation results certify the effectiveness of the proposed parameter optimization methods for the IT2FNNs.

Supervised Classification High-Resolution Remote-Sensing Image Based on Interval Type-2 Fuzzy Membership Function

Because of the degradation of classification accuracy that is caused by the uncertainty of pixel class and classification decisions of high-resolution remote-sensing images, we proposed a supervised classification method that is based on an interval type-2 fuzzy membership function for high-resolution remote-sensing images. We analyze the data features of a high-resolution remote-sensing image and construct a type-1 membership function model in a homogenous region by supervised sampling in order to characterize the uncertainty of the pixel class. On the basis of the fuzzy membership function model in the homogeneous region and in accordance with the 3σ criterion of normal distribution, we proposed a method for modeling three types of interval type-2 membership functions and analyze the different types of functions to improve the uncertainty of pixel class expressed by the type-1 fuzzy membership function and to enhance the accuracy of classification decision. According to the principle that importance will increase with a decrease in the distance between the original, upper, and lower fuzzy membership of the training data and the corresponding frequency value in the histogram, we use the weighted average sum of three types of fuzzy membership as the new fuzzy membership of the pixel to be classified and then integrated into the neighborhood pixel relations, constructing a classification decision model. We use the proposed method to classify real high-resolution remote-sensing images and synthetic images. Additionally, we qualitatively and quantitatively evaluate the test results. The results show that a higher classification accuracy can be achieved with the proposed algorithm.

Analysis of Data Generated From Multidimensional Type-1 and Type-2 Fuzzy Membership Functions

Due to the numerous applications that utilize different types of fuzzy membership functions (MFs), it may sometimes be difficult to choose an appropriate MF for a particular application. In this paper, we establish preliminary guidelines to direct this selection by proposing a three-stage method. In the “forward” stage, different MFs, such as crisp MFs, type-1 (T1) fuzzy MFs, and type-2 (T2) fuzzy MFs, are generated from multidimensional data sets. Next, in the “reverse” stage, data is generated back from these MFs by considering different bin sizes. In doing so, various data sets may be generated for different applications which require fuzzy data. Finally, for the “similarity analysis” stage, we propose an iterative algorithm that makes use of the results of Wilcoxon signed rank (WSR) and Wilcoxon rank sum (WRS) tests to compare the original data and the generated data. From the results of these tests, recommendations concerning the suitability of MFs for a specific application may be suggested by observing the accuracy of representation and the requirements of the application. With this analysis, the objective is to gain insight on when T2 fuzzy sets may be considered to outperform T1 fuzzy sets, and vice versa. Several examples are provided using synthetic and real data to validate the iterative algorithm for data sets in various dimensions.

Diagnosis of Lung Disorder Using Immune Genetic Algorithm and Fuzzy logic to Handle Incertitude

In this paper, we present an immune based fuzzy-logic approach for computer-aided diagnosis scheme in medical imaging. The scheme applies to lung CT images and to detect and classify lung nodules. Classification of lung tissue is a significant and challenging task in any computer aided diagnosis system. This paper presents a technique for classification of lung tissue from computed tomography of the lung using the Gaussian interval type-2 fuzzy logic system. The type-2 Gaussian membership functions (T2MFs) and their footprint of uncertainty (FOU) are tuned by immune, genetic algorithm, which is the combination of immune genetic algorithm (GA) and local exploration operator. An immune, genetic algorithm estimates the parameters of the type-2 fuzzy membership function (T2MF). By using immune, genetic algorithm, converging speed is increased. The proposed local exploration operator helps in finding the best Gaussian distribution curve of a particular feature which improves the efficiency and accuracy of the diagnosis system.

A New Method for Parameterization of General Type-2 Fuzzy Sets

ABSTRACTIn this paper a new method for the parameterization of general type-2 fuzzy membership functions. The proposed method describes the methodology, equations and pseudo-code for building a set of general type-2 membership functions, which are a combination of two Gaussian-type primary membership functions (Gaussian with uncertain mean, and Gaussian with uncertain standard deviation), with multiple combinations of secondary membership functions (Gaussian, double Gaussian, general bell and trapezoidal). In addition, several application cases are used to illustrate the advantages of the proposed parameterization of general type-2 fuzzy sets; where the membership functions are designed using the parameterization approach and the general type-2 inference system is approximated using the α-planes theory. Simulation results illustrate that the parameterization offers an efficient way to represent these fuzzy sets. The main idea of the approach is to facilitate the use of general type-2 fuzzy systems in real world applications. The main contribution is a proposed new form of parameterizing general type-2 fuzzy sets that simplifies the efficient design of this type of sets.