Fuzzy Function Research Articles

An Extended Type-2 Fuzzy Relational Database Model for Aggregate and Grouping Operations

This paper introduces an extended type-2 fuzzy relational database model (ET-2FRDB) for aggregate and grouping operations that can represent and query uncertain and imprecise information in the real world applications. In ET-2FRDB, each fuzzy relation is represented by a type-2 fuzzy set whose membership degree of each tuple is a fuzzy number on [0, 1], the fuzzy aggregate functions, the fuzzy relational algebraic, aggregate and grouping operations are defined as extensions of those in the classical relational database model thereby the membership degree of tuples associated by using the minimum and maximum of fuzzy numbers. Also, some properties of the fuzzy relational algebraic, aggregate and grouping operations in ET-2FRDB are formulated and proven.

LaSNet: An end-to-end network based on steering vector filter for sound source localization and separation

In this paper, we propose a novel time-domain end-to-end network (LaSNet) for solving the problem of multiple sound sources localization (SSL) and separation based on microphone array. The traditional time-frequency (T-F) signal representation is subject to various prior conditions and fails to separate the different sound signal components. Even the data-driven neural network does not develop an effectively integrated approach where localization and separation interplay to serve both challenge. To address the aforementioned issue, we propose a novel approach that involves the implementation of a Separation Driving Localization Network (SDLNet). This framework operates by extracting latent features from a separation network and subsequently employing them in the context of a localization network. Then we propose a simple multi-task network for both SSL and separation. Through the analysis of steering vector filter, we find that the localization and separation problems can be linked by the operation of pseudo-inverse (pinv). To facilitate a synergistic relationship between SSL and sound separation, while also enabling end-to-end network training, we develop a Pinv Module (PM). Fianlly, the Localization and Separation Network (LaSNet) structure of this paper is proposed. Inspired by the overlay mechanism of network, LasNet is extended to a multi-task and multi-layer network, in which separation task is divided into multiple subtasks. A fuzzy separation loss function is introduced for training multi-layer network. Numerical experiments demonstrate that the proposed method has a clearly better advantageous improvement than several well known models. LaSNet has greatly performance improvement in both separation and localization, and achieves at least 32% relative reduction in model size, compared with the baseline models.

Decision Fusion Using Fuzzy Logic Type 1 for Two Aviation Scenarios

In this paper we discuss some aspects of decision fusion using fuzzy logic of type 1 for two aviation scenarios. We study the fuzzy inference system/engine and briefly discuss the MATLAB-GUI based tool developed by the authors to evaluate any existing or new fuzzy implication functions. Two examples: i) formation flight, and ii) flying along an air lane are numerically evaluated and the performance of decision fusion systems incorporating fuzzy logic is illustrated. The results indicate that some existing as well as new implication functions, devised by the authors, work very well for the examples considered. This opens up new possibilities of applications of fuzzy logic based decision fusion to varieties of aerospace/aviation problems in data fusion, decision making, and decision fusion.

System of linear fuzzy differential equations in the space of vector-valued linearly correlated fuzzy numbers

The present paper is concerned with the solution of system of linear fuzzy differential equations where the unknown function is restricted to a vector-valued linearly correlated fuzzy function. First, the concept of the space of vector-valued linearly correlated fuzzy numbers is proposed as an extension to the space of linearly correlated fuzzy numbers. Meantime, the LC-difference and its related properties are also introduced and proved for vector-valued linearly correlated fuzzy numbers, respectively. Second, some analytical properties of vector-valued linearly correlated fuzzy functions such as limit, continuity, and LC-differentiability are examined. Finally, the existence conditions and solutions of the linear fuzzy system are further studied in a special space of vector-valued linearly correlated fuzzy numbers. Some examples are provided to demonstrate the proposed method.

Infinite horizon fuzzy optimal control: optimality does not imply asymptotic stability

In this paper, novel stability result for discrete-time infinite horizon optimal control using fuzzy objective functions is presented. For this class of control, the fuzzy goals and the fuzzy constraints introduced in the fuzzy objective function handle the constraints placed on both the state and the control vectors. We analyze the asymptotic stability of the equilibrium for the infinite horizon fuzzy optimal control law using the minimum aggregation operator. We show that the infinite horizon control with the minimum aggregation operator does not guarantee the asymptotic stability of the equilibrium in general. This is done by deriving an analytical solution of the control law for a simple linear system using a fuzzy dynamic programming approach. An example that shows the novel asymptotic stability result of the equilibrium for discrete-time infinite horizon optimal control with fuzzy objective function problem is given.

Optimizing Resource Swap Functionality in IoE-Based Grids Using Approximate Reasoning Reward-Based Adjustable Deep Double Q-Learning

The Energy Router (ER) concept as a compact intelligent power electronic device has been proposed as the core of the Internet of Energy (IoE), maximizing energy efficiency, minimizing loss and costs, and addressing growing electricity demand. However, optimizing electricity routing in the residential sector has not been well investigated. Moreover, complex modeling of the energy components besides the uncertain environment made the conventional methods impotent in tackling these problems. Consequently, this research proposes a novel algorithm titled Approximate Reasoning Reward-based Adaptable Deep Double Q-Learning (A2R-ADDQL) that is introduced specially to optimize electricity routing in residential units. As a result, both overestimation and underestimation biases are reduced comparing other deep Q-Learning-based algorithms. Moreover, the sample complexity of the model is decreased due to utilizing a fuzzy approximate reasoning reward function. Ultimately, the proposed algorithm is assessed on a real-world dataset evaluating the findings in several benchmarks. The results indicate that the proposed model is unbiased while convergence speed is higher than other analyzed techniques. Additionally, monthly average cost and power loss are lowered by 24.9% and 29.1% more than other techniques. Finally, the proposed algorithm reduces greenhouse gases emission by 3.91 kg per month.

Deep fuzzy mapping nonparametric model for real-time demand estimation in water distribution systems: A new perspective.

Hydraulic modeling has been recognized as a valuable tool for improving the design, operation, and management of water distribution systems (WDSs) as it allows engineers to simulate and analyze behaviors of WDSs in real time and help them make scientific decisions. The informatization of urban infrastructure has motivated the real-time fine-grained control of WDSs, making it one of the hotspots in recent years, thereby putting higher requirements on WDS online calibration in terms of efficiency and accuracy, especially when dealing with large-complex WDSs. To achieve this purpose, this paper proposes a novel approach (i.e., deep fuzzy mapping nonparametric model (DFM)) from a new perspective for developing a real-time WDS model. To our knowledge, this is the first work that considers uncertainties in modeling problems using fuzzy membership functions and establishes the precise inverse mapping from pressure/flow sensors to nodal water consumption for a given WDS based on the proposed DFM framework. Unlike most traditional calibration methods that require time to optimize model parameters, the DFM approach has a unique analytical solution derived through rigorous mathematical theory, thus the DFM is computationally fast as a result of sensibly handling the problems whose solutions typically require iterative numerical algorithms and large computational time. The proposed method is applied to two case studies and the results obtained show that it can produce a real-time estimation of nodal water consumption with higher accuracy, computational efficiency, and robustness relative to traditional calibration methods.

A Modeling Approach with Defective Products Reduces the Production and Unpredictability through Matlab Programming

Abstract: Analyses a standardized item with a flawed production process' limited replenishing modelling techniques. A predetermined percentage or an arbitrary amount of the things generated throughout this technique are flawed. The renewal rate is regarded as a component. A surcharge above the manufacturing costs determines the command's cost of goods sold. And use a horizontal stripe integer programming strategy for improvement; it is advised that the commodity be produced at its most profitable level. The inventory management process used both the crispness and imprecise models to repair broken goods. The proposed model is solved by the Nonlinear Mathematics Engineering Lagrangian Method, which uses a Trapezoidal Fuzzy Number to discover the lowest pricing. The purpose of this study is to advocate the Lagrangian methodology as a means of lowering defective products in production management. The distorted produced inventory framework optimal solution, which integrates the defective entire value in the appropriate course of action, is corrected using a modified version of the KuhnTucker Technique for promoting equity. The optimal evaluation of the various fuzzy function membership functions is demonstrated with the aid of a mathematical model developed utilising properly analysing. The objective of this study is to utilize the Lagrangean and Kuhn-Tucker methods to discover the ideal method for some of these models. Ultimately, a simulation results is provided to illustrate the individuality found in both the crisp and fuzzy inventory management systems. The expenses made to prevent or reduce the number of issues that originally arose in the Matlab programming functions

Advanced Fuzzy Sets and Genetic Algorithm Optimizer for Mammographic Image Enhancement

A well-researched field is the development of Computer Aided Diagnosis (CADx) Systems for the benign-malignant classification of abnormalities detected by mammography. Due to the nature of the breast parenchyma, there are significant uncertainties about the shape and geometry of the abnormalities that may lead to an inaccurate diagnosis. These same uncertainties give mammograms a fuzzy character that is essential to the application of fuzzy processing. Fuzzy set theory considers uncertainty in the form of a membership function, and therefore fuzzy sets can process imperfect data if this imperfection originates from vagueness and ambiguity rather than randomness. Fuzzy contrast enhancement can improve edge detection and, by extension, the quality of related classification features. In this paper, classical (Linguistic hedges and fuzzy enhancement functions), advanced fuzzy sets (Intuitionistic fuzzy set (ΙFS), Pythagorean fuzzy set (PFS), and Fermatean fuzzy sets (FFS)), and a Genetic Algorithm optimizer are proposed to enhance the contrast of mammographic features. The advanced fuzzy sets provide better information on the uncertainty of the membership function. As a result, the intuitionistic method had the best overall performance, but most of the techniques could be used efficiently, depending on the problem that needed to be solved. Linguistic methods could provide a more manageable way of spreading the histogram, revealing more extreme values than the conventional methods. A fusion technique of the enhanced mammography images with Ordered Weighted Average operators (OWA) achieves a good-quality final image.

Fractional derivatives of fuzzy complex-variable functions and application to fuzzy fractional complex differential equations

In this paper, through theory of fuzzy complex analysis, we introduce some representations of r-cuts of trivial fuzzy zero, nontrivial fuzzy zero and fuzzy complex numbers in polar form on complex plane and establish some of their basic properties. Based on this, the addition and scalar multiplication operations of fuzzy complex numbers are established and the calculus of fuzzy complex-variable functions is studied. Moreover, we introduce a notion of fuzzy Ortigueira fractional derivative of fuzzy complex-variable functions and develop a theory of fuzzy fractional calculus on complex plane including some geometric features. As applications, the existence and uniqueness theorem of solutions for nonlinear fuzzy fractional complex-variable differential equations is established and some examples are provided.

Assessing alternatives of including social robots in urban transport using fuzzy trigonometric operators based decision-making model

Current trends point to a not-too-distant future with qualitatively advanced interactions between humans and social robots. It is critical to consider the possibility of forming meaningful social relationships with robots when defining the future of human-robot interactions, as well as studying how these interactions will evolve to the point where humans are unable to distinguish between humans and robots in urban transportation. In this study, the advantages of using social robots in urban transportation are prioritized by using a multi-criteria decision-making tool, which consists of two consecutive stages, namely: i) a novel fuzzy sine trigonometry based on the logarithmic method of additive weights (fuzzy ST-LMAW) that is proposed to calculate the criteria weights; ii) a nonlinear fuzzy Aczel-Alsina function based the weighted aggregate sum product assessment (fuzzy ALWAS-WASPAS) that is developed to select and rank the alternatives. The proposed model enables flexible nonlinear processing of complex and uncertain information encountered in real applications. A case study is developed to rank three alternatives with twelve sub-criteria grouped into four aspects using the proposed method. The results show that the most advantageous alternative is to replace people with social robots as safety drivers in level four autonomous vehicles due to their possible impact on transportation.

An Algorithm for the Solution of Second Order Linear Fuzzy System With Mechanical Applications

In this paper, we consider homogeneous and non-homogeneous second order linear fuzzy systems under granular differentiability. The concept of continuous n-dimensional fuzzy functions on the space of n-dimensional fuzzy numbers are introduced. Developed an algorithm for the solution of a non-homogeneous second order linear fuzzy system under granular differentiability. The proposed algorithm is applied to solve some well-known mechanical problems with fuzzy uncertainty.

Influence of the Fuzzy Function on the Estimation of the Fuzzy Sample Entropy with Fixed Tolerance Values for the Evaluation of Surface EMG Muscle Activity.

Fixed sample entropy (fSampEn) is a technique that has demonstrated superior performance to other amplitude estimators for assessing respiratory muscle electromyographic activity. This technique is based on the calculation of sample entropy (SampEn) using fixed tolerance thresholds. Fuzzy entropy (FuzzyEn) introduces an improvement to the SampEn algorithm based on the use of a fuzzy measure to evaluate the similarity between vectors. However, several fuzzy functions have been used to calculate the FuzzyEn, and not all of them allow an effective comparison with the SampEn calculation parameters. In the present work, an analysis of the different fuzzy functions previously used has been carried out and a new sigmoid fuzzy function for the calculation of FuzzyEn with fixed tolerance thresholds (fFuzzyEn) has been proposed. The results show that the proposed fuzzy function outperformed both fSampEn and previously proposed FuzzyEn-based algorithms. These results suggest that fFuzzyEn could improve the assessment of muscle activity providing potentially useful diagnostic information.Clinical Relevance- This sets out the appropriate use of the fuzzy function for the estimation of the fuzzy sample entropy with fixed tolerance thresholds (fFuzzyEn). The use of fFuzzyEn could improve methods for detecting the onset and offset of respiratory electromyographic (EMG) signals, as well as the assessment of EMG activation level.

Fuzzy g ̃-Continuous Functions and Fuzzy g ̃-Irresolute Continuous Functions in Fuzzy Topological Spaces

In present of this paper, new classes of generalized fuzzy continuous functions called fuzzy -continuous functions and fuzzy -irresolute continuous functions are defined and studied. Also, several examples are given.

The slightly altruistic equilibrium in the one-leader-follower games with fuzzy mapping

This paper constructs a one-leader-follower game with fuzzy mapping (OLFFG), and studies the existence of equilibrium point of OLFFG. First, we introduce the definition of fuzzy equilibrium point and slightly altruistic fuzzy equilibrium point of OLFFG. Furthermore, we prove that the existence of fuzzy equilibrium point and slightly altruistic fuzzy equilibrium point of OLFFG by the nonlinear analysis theory. Finally, it is proved that if the essential equilibrium point of OLFFG exists, it must be the slightly altruistic fuzzy equilibrium point.

Fuzzy‐model‐based robust control of Markov jump nonlinear systems with incomplete transition probabilities and uncertain packet dropouts

AbstractInterval type‐2 fuzzy Markov jump systems (IT2FMJSs) have received much attention because they can well describe complex nonlinear systems with uncertainties and stochastic system mode switching. However, the transition probabilities of fuzzy MJSs (FMJSs) have been assumed to be completely known, limiting real‐world applications of existing results. Different from the previous studies, transition probabilities between system modes switching are partially unknown, and packet dropouts of data transmission are uncertain in this study. Compared with the previous studies, the main advantages of this work are as follows: (1) To analyze stochastic stability and reduce conservatism of existing approaches, a novel Lyapunov function that depends on both system mode and fuzzy basis function is constructed; (2) the existence of a mode‐dependent and fuzzy‐basis‐dependent state feedback controller is revealed; (3) stochastic stability of closed‐loop system with a desired performance is established, and the problem of incomplete transition probabilities and uncertain packet dropouts has been completely addressed. An illustrative example of a robot arm is used to demonstrate the effectiveness and practicality of the proposed control strategy. By virtue of the proposed strategy, the effects of incomplete transition probabilities and uncertain packet dropouts on IT2FMJSs have been completely alleviated.

Financial risk assessment management of state-owned enterprises based on cloud accounting in the era of big data

Abstract To solve the financial risk problem of enterprise financing difficulties and large financing amounts in the era of big data, this paper constructs a financial risk assessment model and evaluates the indexes of enterprise financial risk by combining it with cloud accounting products. Firstly, we assign and determine the weights, use the evidence theory to develop the enterprise financial risk evaluation, and determine the weights of each risk evaluation index. Secondly, we set up a fuzzy evaluation language set, calculate the maximum value of the fuzzy rubric affiliation function for the risk indicators of state-owned enterprises under cloud accounting, pre-process the obtained data, determine the specific indicator weights with the help of fuzzy hierarchical analysis, and carry out consistency tests on them. Finally, the relative importance of each indicator is calculated among the model factors to obtain the overall risk score of cloud accounting enterprise finance. The experimental results show that the risk level measured according to the steps of the cloud accounting risk assessment system, the data confidentiality risk score is 76.14, the cloud accounting product risk is 85.96, the service risk is 72.88, and only one item is higher risk. This shows that the use of cloud accounting financial risk control measures can improve the quality of financial risk management of enterprises.

Multi-objective sustainable supply chain network optimization based on chaotic particle-Ant colony algorithm.

For the optimal design of the sustainable supply chain network, considering the comprehensiveness of the problem factors, considering the three aspects of economy, environment and society, the goal is to minimize the establishment cost, minimize the emission of environ-mental pollution and maximize the number of labor. A mixed integer programming model is established to maximize the efficiency of the supply chain network. The innovation of this paper, first, is to consider the impact of economic, environmental and social benefits in a continuous supply chain, where the environmental benefits not only consider carbon emissions but also include the emissions of plant wastewater, waste and solid waste as influencing factors. Second, a multi-objective fuzzy affiliation function is constructed to measure the quality of the model solution in terms of the overall satisfaction value. Finally, the chaotic particle ant colony algorithm is proposed, and the problem of premature convergence in the operation of the particle swarm algorithm is solved. Experimental results show that the PSCACO algorithm proposed in this paper is compared with MOPSO, CACO and NSGA-II algorithms, and the convergence effect of the algorithm is concluded to be more effective to verify the effectiveness and feasibility of chaotic particle ant colony algorithm for solving multi-objective functions, which proposes a new feasible solution for the supply chain management.

A novel few-sample wind power prediction model based on generative adversarial network and quadratic mode decomposition

With the emergence of various new power systems, accurate wind power prediction plays a critical role in their safety and stability. However, due to the historical wind power data with few samples, it is difficult to ensure the accuracy of power system prediction for new wind farms. At the same time, wind power data show significant uncertainty and fluctuation. To address this issue, it is proposed in this research to build a novel few-sample wind power prediction model based on the least-square generative adversarial network (LSGAN) and quadratic mode decomposition (QMD). Firstly, a small amount of original wind power data are generated to improve the data by least-square generative adversarial network, which solves the error in prediction with limited sample data. Secondly, a quadratic mode decomposition method based on ensemble empirical mode decomposition (EEMD) and variational mode decomposition (VMD) is developed to address the instability of wind power data and extract hidden temporal characteristics. Specifically, ensemble empirical mode decomposition decomposes the data once to obtain a set of intrinsic mode functions (IMFs), and then variational mode decomposition is used to decompose the fuzzy irregular IMF1 function twice. Finally, a bidirectional long short-term memory network (BiLSTM) based on particle swarm optimization (PSO) is applied to predict wind power data. The LSGAN-QMD-PSO-BiLSTM model proposed in this research is verified on a wind farm located in Spain, which indicates that the proposed model achieves the lowest root mean square error (RMSE) and mean absolute error (MAE) errors of 100.6577 and 66.5175 kW, along with the highest R2 of 0.9639.

Decoding Culture: Tools for Behavioral Strategists

It is uncontroversial for strategy scholars that culture matters for both strategy formulation and execution. Yet, the diversity of approaches and concepts for thinking about culture can prove daunting for operationalizing this insight. We introduce the concept of a “code”—a fuzzy mapping between two distinct sets of cognitive constructs—as a fundamental construct to study culture. The concept of a code, and the distinction between using a code versus expectations about the code others use, can be applied to study many different elements of culture both in terms of theorizing about them with precision and for empirical applications. Furthermore, we argue that a code-based perspective on culture is particularly useful from the normative, design-oriented stance that is characteristic of strategy. Using an example of creating stakeholder alignment around the problem of sustainability, a first-order challenge for business and society today, we show that the perspectives of culture as shared values and culture as a toolkit point to different interventions that are each likely to work under different conditions. Funding: P. Puranam thanks The Desmarais Fund at INSEAD for supporting the Organizations & Algorithms project.