Fuzzy Function Research Articles

Graph Enhanced Fuzzy Clustering for Categorical Data Using a Bayesian Dissimilarity Measure

Categorical data are widely available in many real-world applications, and to discover valuable patterns in such data by clustering is of great importance. However, the lack of a decent quantitative relationship among categorical values makes traditional clustering approaches, which are usually developed for numerical data, perform poorly on categorical datasets. To solve this problem and boost the performance of clustering for categorical data, we propose a novel fuzzy clustering model in this article. At first, by approximating the maximum a posteriori (MAP) estimation of a discrete distribution of data partition, a new fuzzy clustering objective function is designed for categorical data. The Bayesian dissimilarity measure is formulated in this objective to tackle the subtle relationships between categorical values efficiently. Then, to further enhance the performance of clustering, a novel Kullback–Leibler divergence-based graph regularization is integrated into the clustering objective to exploit the prior knowledge on datasets, for example, the information about correlations of data points. The proposed model is solved by the alternative optimization and the experimental results on the synthetic and real-world datasets show that it outperforms the classical and relevant state-of-the-art algorithms. We also present the parameter analysis of our approach, and conduct a comprehensive study on the effectiveness of the Bayesian dissimilarity measure and the KL divergence-based graph regularization.

Enhanced Local Stabilization of Constrained N-TS Fuzzy Systems With Lighter Computational Burden

The constrained Takagi–Sugeno fuzzy systems with local nonlinear models (N-TS fuzzy systems) are much more practical than the conventional T–S fuzzy models, but their applications are seriously affected by either the great conservatism or the heavy computational burden. In this short article, an enhanced local stabilization of constrained N-TS fuzzy systems is investigated with the purpose of not only reducing conservatism but also relieving computational burden. To do this, a new class of threshold functions are established in order to achieve real-time online assessment of the variation of the normalized fuzzy weighting functions (NFWFs) at different sampling instants, i.e., the one-step-past one and the current one. Thus, a key alternative is proposed for eliminating all the involved terms containing the one-step-past NFWFs while their main information is retained. Since our obtained design criteria are merely dependent on the current NFWFs, the conservatism can be reduced at the expense of lighter computational burden. The benefits of our proposed results are validated by implementing several objective comparisons with those recent results.

Decomposition of a fuzzy function by one-dimensional fuzzy multiresolution analysis

Signal compression and data compression are techniques for storing and transmitting signals using fewer bits as possible for encoding a complete signal. A good signal compression scheme requires a good signal decomposition scheme. The decomposition of the signal can be done as follows: The signal is split into a low-resolution part, described by a smaller number of samples than the original signal, and a signal difference, which describes the difference between the low-resolution signal and the real coded signal. Our paper deals with the proofs of these properties in a fuzzy environment. The proof of one- dimensional multiresolution analysis is given. The concept of fuzzy wavelets is introduced and as a byproduct a special fuzzy space of details of a signal is given and an orthonormal basis of

Combining GRA with a Fuzzy QFD Model for the New Product Design and Development of Wickerwork Lamps

With the popularization of the concept of sustainability in traditional wickerwork, wickerwork lamps have become the most popular production. When customers purchase wickerwork lamp products, the Kansei consensus has become a key factor influencing the communication between manufacturers and customers. Therefore, the purpose of this paper is to explore the product design solutions for wickerwork lamps that meet the emotional satisfaction of users. Firstly, a three-level evaluation grid diagram driven by user attractiveness through Miryoku Engineering is established. Secondly, this paper uses grey relational analysis (GRA) to extract the priority order and its weight values in the perceptual vocabulary to identify the key user needs in product design. In order to effectively deal with the uncertain product evaluation information, the fuzzy quality function deployment (QFD) is used to construct the “emotional demand-design parameter” transformation model and derive the optimal design parameters in the mapping process, thus effectively reducing the ambiguity and uncertainty in the demand transformation process. Based on the experimental results, it is found that the best combination of Texture light transmittance, Simple wickerwork material, Wickerwork primary colours, Cascaded type and Pastoral style could be preferred by customers, thus this proposed method can effectively reduce the ambiguity and uncertainty in the design process. The results of study enable designers to accurately grasp customers’ perceptions of wickerwork lamp products and obtain the best design parameters for wickerwork lamp products.

Function approximation reinforcement learning of energy management with the fuzzy REINFORCE for fuel cell hybrid electric vehicles

In the paper, a novel self-learning energy management strategy (EMS) is proposed for fuel cell hybrid electric vehicles (FCHEV) to achieve the hydrogen saving and maintain the battery operation. In the EMS, it is proposed to approximate the EMS policy function with fuzzy inference system (FIS) and learn the policy parameters through policy gradient reinforcement learning (PGRL). Thus, a so-called Fuzzy REINFORCE algorithm is first proposed and studied for EMS problem in the paper. Fuzzy REINFORCE is a model-free method that the EMS agent can learn itself through interactions with environment, which makes it independent of model accuracy, prior knowledge, and expert experience. Meanwhile, to stabilize the training process, a fuzzy baseline function is adopted to approximate the value function based on FIS without affecting the policy gradient direction. Moreover, the drawbacks of traditional reinforcement learning such as high computation burden, long convergence time, can also be overcome. The effectiveness of the proposed methods were verified by Hardware-in-Loop experiments. The adaptability of the proposed method to the changes of driving conditions and system states is also verified.

The KKT Optimality Conditions and Duality for Constrained Programming Problem with Generalized α- Convex Fuzzy Functions

This paper mainly studies the mixed constraint interval programming problem under the generalized convex fuzzy mapping. Firstly, this paper give the concepts of fuzzy mappings, such as quasiconvex, strictly quasiconvex, pseudoconvex and strictly pseudoconvex. Then, the relation of generalized convex fuzzy mapping is studied and some properties are obtained. Finally, the necessary and sufficient KKT conditions are given, and the duality problem is established. The weak duality, strong duality and inverse duality theorem of fuzzy interval programming are proved.

Assessment of GO-Based Protein Interaction Affinities in the Large-Scale Human-Coronavirus Family Interactome.

SARS-CoV-2 is a novel coronavirus that replicates itself via interacting with the host proteins. As a result, identifying virus and host protein-protein interactions could help researchers better understand the virus disease transmission behavior and identify possible COVID-19 drugs. The International Committee on Virus Taxonomy has determined that nCoV is genetically 89% compared to the SARS-CoV epidemic in 2003. This paper focuses on assessing the host-pathogen protein interaction affinity of the coronavirus family, having 44 different variants. In light of these considerations, a GO-semantic scoring function is provided based on Gene Ontology (GO) graphs for determining the binding affinity of any two proteins at the organism level. Based on the availability of the GO annotation of the proteins, 11 viral variants, viz., SARS-CoV-2, SARS, MERS, Bat coronavirus HKU3, Bat coronavirus Rp3/2004, Bat coronavirus HKU5, Murine coronavirus, Bovine coronavirus, Rat coronavirus, Bat coronavirus HKU4, Bat coronavirus 133/2005, are considered from 44 viral variants. The fuzzy scoring function of the entire host-pathogen network has been processed with ~180 million potential interactions generated from 19,281 host proteins and around 242 viral proteins. ~4.5 million potential level one host-pathogen interactions are computed based on the estimated interaction affinity threshold. The resulting host-pathogen interactome is also validated with state-of-the-art experimental networks. The study has also been extended further toward the drug-repurposing study by analyzing the FDA-listed COVID drugs.

Intelligent Height Adjustment Method of Shearer Drum Based on Rough Set Significance Reduction and Fuzzy Rough Radial Basis Function Neural Network

The intelligent adjustment method of the shearer drum is the key technology to improve the intelligent level and safety degree of fully mechanized mining face. This paper proposes a shearer drum intelligent height adjustment model based on rough set significance attribute reduction (AR) and fuzzy rough radial basis function neural network (FRRBFNN) optimized by adaptive immune genetic algorithm (AIGA). The model first selects the parameters of shearer process monitoring based on the importance attribute reduction algorithm of rough set, and establishes the attribute reduction set of shearer operation characteristic parameters and the drum height decision rule base. Next, a fuzzy rough radial basis function neural network determined by the decision rule space is proposed. By introducing the fuzzy rough membership function as the connection weight, the network can accurately describe the complex nonlinear relationship between the working characteristic parameters of the attribute shearer and the drum height, and measure the uncertainty of the coal seam distribution. Finally, to further optimize the performance of FRRBFNN, the adaptive immune genetic algorithm is introduced to optimize its parameters, to build a high-precision shearer drum height prediction system. For the evaluation method of the model, we use three indicators: mean absolute error, mean absolute percentage error, and root mean square error. Based on the measured data in Yujialiang area, Shaanxi Province, the experimental results show that—compared with the FRRBFNN and support vector regression (SVR) models, a gated current neural network (GRU), a radial basis function neural network (RBF), the memory strengthen long short-term memory (MSLSTM) model, and the adaptive fuzzy reasoning Petri net (AFRPN)—the MAE of the AR-AIGA-FRBFNN model for predicting the height of the left and right rollers are 18.3 mm and 17.2 mm, respectively; the MAPE is 0.96% and 0.93%, respectively; and the RMSE is 21.2 mm and 22.4 mm, respectively. The AR-AIGA-FRBFNN model is therefore more effective than the other considered methods.

A Study of Some Properties of Fuzzy Laplace Transform with Their Applications in Solving the Second-Order Fuzzy Linear Partial Differential Equations

In this paper, several results and theorems about the high-order strongly generalized Hukuhara differentiability of function defined via the fuzzy Riemann improper integral (in the sense of Wu) have been established. Then, some properties dealing with the partial derivatives of fuzzy Laplace transform for a fuzzy function of two real variables have been proved. Afterwards, an algorithm of fuzzy Laplace transform for solving second-order fuzzy partial differential equations has been proposed. Finally, two numerical examples, including the heat equation under fuzzy initial conditions, have been studied to justify the efficiency of the algorithm.

Certain Inclusion Properties for the Class of q-Analogue of Fuzzy α-Convex Functions

Recently, the properties of analytic functions have been mainly discussed by means of a fuzzy subset and a q-difference operator. We define certain new subclasses of analytic functions by using the fuzzy subordination to univalent functions whose range is symmetric with respect to the real axis. We introduce the family of linear q-operators and define various classes associated with these operators. The inclusion results and various integral properties are the main investigations of this article.

Density peaks clustering algorithm based on fuzzy and weighted shared neighbor for uneven density datasets

Uneven density data refers to data with a certain difference in sample density between clusters. The local density of density peaks clustering algorithm (DPC) does not consider the effect of sample density difference between clusters of uneven density data, which may lead to wrong selection of cluster centers; the algorithm allocation strategy makes it easy to incorrectly allocate samples originally belonging to sparse clusters to dense clusters, which reduces clustering efficiency. In this study, we proposed the density peaks clustering algorithm based on fuzzy and weighted shared neighbor for uneven density datasets (DPC-FWSN). First, a nearest neighbor fuzzy kernel function is obtained by combining K-nearest neighbor and fuzzy neighborhood. Then, local density is redefined by the nearest neighbor fuzzy kernel function. The local density can better characterize the distribution characteristics of the sample by balancing the contribution of sample density in dense and sparse areas, in order to avoid the situation that the sparse cluster does not have a cluster center. Finally, the allocation strategy for weighted shared neighbor similarity is proposed to optimize the sample allocation at the boundary of the sparse cluster. Experiments are performed on IDPC-FA, FKNN-DPC, FNDPC, DPCSA and DPC for uneven density datasets, complex morphologies datasets and real datasets. The clustering results demonstrate that DPC-FWSN effectively handles datasets with uneven density distribution.

A Choquet integral-based TODIM method for q-rung trapezoidal fuzzy numbers and its application in group decision-making

PurposeThe purpose of this paper is to develop a multi-attribute group decision-making (MAGDM) method under the q-rung orthopair trapezoidal fuzzy environment, which calculates the interaction between the criteria depending on the proposed q-rung orthopair trapezoidal fuzzy aggregation Choquet integral (q-ROTrFACI) and employ TODIM (an acronym in Portuguese of Interactive and Multi-criteria Decision Making) to consider the risk psychology of decision-makers, to determine the optimal ranking of alternatives.Design/methodology/approachIn MAGDM, q-rung orthopair trapezoidal fuzzy numbers (q-ROTrFNs) are efficient to indicate the quantitative vagueness of decision-makers. The q-ROTrFACI operator is defined and some properties are proved. Then, a novel similarity measure is developed by fusing the area and coordinates of the q-rung orthopair trapezoidal fuzzy function. Based on the above, a Choquet integral-based TODIM (CI-TODIM) method to consider the risk psychology of decision-makers is proposed and two cases are provided to prove superiority of the method.FindingsThe paper investigates q-ROTrFACI operator to productively solve problems with interdependent criteria. Then, an approach is proposed to determine the center point of q--ROTrFNs and a q-rung orthopair trapezoidal fuzzy similarity is constructed. Furthermore, CI-TODIM method is devised based on the proposed q-ROTrFACI operator and similarity in q-rung orthopair trapezoidal fuzzy context. The illustration example of business models' solutions and hypertension health management are given to demonstrate the effectiveness and superiority of proposed method.Originality/valueThe paper develops a novel CI-TODIM method that effectively solves the MAGDM problems under the premise of fully considering the priority of criteria and the risk preference of decision-makers, which provides guiding advantages for practical decision-making and enriches the application of decision-making theory.

Satellite Network Transmission of Cooperative Relay Superimposed Signal Reconstructed in Spatial Dimension

In order to save frequency resources, a new remote sensing satellite service can gradually adopt relay cooperation transmission to realize the same frequency and common channel transmission of multiple data. To solve the problem of mutual interference between messages, this study proposes a universal model of relay cooperative channel transmission, and the separation mechanism of heterogeneous signals for simultaneous unicast and multicast transmission is also studied. In this study, a signal space is used to reconstruct the degrees of freedom, and an orthogonalized spatial alignment direction is designed to obtain the equivalent parallel transmission channel. We also propose a constellation point remapping scheme under the optimal constraint of spatial separation of transmission signals. Furthermore, we merge constellation points to solve the problem of fuzzy mapping of physical layer network coding. The simulation results show that the co-channel transmission with interference suppression can be realized when the equivalent degrees of freedom of the signal intersection subspace is not less than dpK(K−1)+dcK. The Euclidean distance between constellation points is increased by constructing orthogonal signal spatial alignment directions, which brings an additional BER performance gain of 2 dB. If the signal alignment direction and channel quality are jointly designed, the transmission quality can be further improved.

The boundedness, global Mittag-Leffler sability and S-asymptotic ω-periodic of fractional-order fuzzy inertial neural networks with delays

The boundedness, global Mittag-Leffler stability (GMLS), and S-asymptotic ω-periodic of fuzzy fractional-order inertial neural networks (FINN) with delays are discussed. Using the properties of Riemann-Liouville fractional-order calculus, variable substitutions and the property of fuzzy functions are adopted to get the boundedness, the GMLS, and the S-asymptotic ω-periodic of the system. Furthermore, a numerical example is given to demonstrate the theorems.

On Fuzzy Spiral-like Functions Associated with the Family of Linear Operators

At the present time, the study of various classical properties of the geometric function theory using the concept of a fuzzy subset remains limited. In this article, our main aim is to introduce the subclasses of spiral-like functions of complex order in terms of the fuzzy notion and we generalize these subclasses by applying a family of linear operators. The relationships between the newly defined subclasses are examined. In addition, we show that these subclasses are preserved under the well-known Bernardi integral operator.

A Fuzzy Lyapunov Function Approach for Fault Estimation of T–S Fuzzy Fractional-Order Systems Based on Unknown Input Observer

This article discusses the fault estimation (FE) problem of nonlinear fractional-order (FO) systems subject to faults and unknown inputs through the T–S fuzzy approach. A novel fuzzy FO unknown input observer is well synthesized to not only achieve the desired FE but also decouple the unknown input in contrast to the traditional integer-order observer design technique. It is worth pointing out that the provided FE scheme can reconstruct the fault signal appearing in both input and output equations simultaneously. Furthermore, by resorting to linear matrix inequalities, the stability criteria of observation error dynamics are first formulated based on general quadratic Lyapunov functions, which are further extended via fuzzy Lyapunov functions containing the information of membership functions. Finally, the performance of theoretical results is verified through two elaborate examples.

An Event-Triggered Predefined Time Decentralized Output Feedback Fuzzy Adaptive Control Method for Interconnected Systems

This article investigates the event-triggered predefined time output feedback control design problem for nonlinear interconnected systems with nonstrict feedback control structures. Compared with the existing event-triggered output feedback control design schemes, the most significant contribution of this article is that the system stability time can be preset directly. Fuzzy logic systems (FLSs) and FLSs-based state observer deal with unknown nonlinear dynamics and unmeasured states. Combining with dynamic surface control technology and event-triggered mechanism based on switching threshold strategy, an event-triggered predefined time decentralized output feedback control method is proposed, in which a predefined time filter is designed to solve the computational complexity problem. In addition, the algebraic loop problem and control singular problem are also solved, respectively, by applying the property of fuzzy basis function and L’Hospital’s rule. Utilizing the predefined time Lyapunov stability theory, the system stability analysis is given. Finally, the effectiveness and practicability of the proposed control method are verified by practical system simulation cases.

Timestamp Feature Variation based Weather Prediction Using Multi-Perception Neural Classification for Successive Crop Recommendation in Big Data Analysis

The recent generation has a lot of information for analysing growth in future prediction. Especially India is an extensive agricultural resource for the world's expansive economic growth. But in extensive data analysis, a problem for the recommendation of the seasonal crop is tedious because of improper feature analysis due to varying periods in weather conditions. So time variation-based big data analysis is essential for research improvement. To resolve this problem, we propose a Timestamp feature variation-based weather prediction using multi-perception neural classification (TFV-MPNC) for successive crop recommendation in big data analysis. Initially, the pre-processing was carried out to prepare the redundant noise dataset for fast prediction. Initially, the Preprocessing ensures the Contemporary Forecasting rate (CFR) for predicting the previous deficiency rate. Based on that Time stamp feature analysis (TSFA). The Dense region harvest rate (DRHR) was evaluated, and features were decision using Fuzzy intensive decision Function (FIDF), selected the scaled features and trained with multi-perception neural classification (MPNN). The proposed system produces higher forecasting by prediction features as well supportive to the weather dependences related to higher classification rate in precision, and recall has the best classification result.

Sustainable E-scooter parking operation in urban areas using fuzzy Dombi based RAFSI model

Over the last five years, e-scooters have gradually become commonplace in most urban areas. However, shortcomings in infrastructure provision, especially with parking, make it awkward to use these vehicles. This study presents a novel hybrid fuzzy multi-criteria decision-making model for determining optimal e-scooter parking locations by combining the Logarithmic Methodology of Additive Weights (LMAW) and the RAFSI (Ranking of Alternatives through Functional mapping of criterion sub-intervals into a Single Interval) methods. In the first stage, the fuzzy Aczel-Alsina function based LMAW approach is used to address the uncertainty of experts’ opinions in the decision process and to calculate the weights of the twelve criteria. Afterward, fuzzy Dombi based RAFSI is applied to obtain the ranking of e-scooter parking locations. A case study is presented to propose a solution for the operation of e-scooter parking by taking into consideration three different alternatives based on four different aspects and twelve criteria. According to the findings, the third option, which is a hybrid operation with geo-fencing hubs in primary catchment areas of public transportation, is the most practical choice for a sustainable operation of e-scooter parking. This option also has the potential to be the most environmentally friendly.

Solution for a System of First-Order Linear Fuzzy Boundary Value Problems

In this paper, we consider homogeneous and non-homogeneous system of first order linear fuzzy boundary value problems (SFOLBVPs) under granular differentiability. Using the concept of horizontal membership function, we introduced the notion of first order granular differentiability for n-dimensional fuzzy functions. We present granular integral and its properties. Theorems on the existence and uniqueness of solutions for homogeneous and non-homogeneous SFOLFBVPs are proved. We develop an algorithm for solution of non-homogeneous SFOLBVPs under granular differentiability. We provide some examples to illustrate the validity of the proposed algorithm.