Fuzzy Function Research Articles

Increasing the accuracy of electricity accounting by digitalinformation-measuring systems

Significant non-technological losses of electricity are observed in 0.38 kV distribution networks, which lead to financial dam-ages of energy supply companies. The reason for their occurrence is the deficiencies in the accountingunits functioning inthe re-duced load mode, which occurs during the downtime of the main technological equipment. The purpose of the study is to increase the accuracy of electricity measurement by a commercial accountingunit in the reduced load mode based on mathematical modeling of measurement uncertainty. Evaluation of regression parameters for the static characteristics of measuring current transformersin the reduced load mode is carried out using the covariance analysis methods and analysis of regression residuals. Estimation of the non-random uncertainty of electricity measurementby one measuring channel of theaccountingunit was carried out using the fuzzy set theory. The polynomial approximation of the experimental values of the membership function for the measured quantity was carried out according to the maximum norm method. The least square method was used to approximate the boundaries of fuzzy functions. As a result of research, a universal static characteristic of a measuring current transformer of a certain accuracy class was obtained at a reduced primary current. It was established that the sample estimates uncertainty of the current transformer error of the 0.5 S accura-cy class changes from ±11.7% to ±1.7%. The uncertainty of electricity measurement by the commercial accountingunit in the re-duced load mode is proposed to be estimated by a fuzzy function. The developed mathematical model takes into account the depend-ence of the fuzzy interval boundaries, which characterizes the measurement result, on the phase currents asymmetric values. Compar-ison of the analytically obtained membership function for the relative deviations of the readings of the accountingunits with the em-pirically obtained value of such a deviation made it possible to establish the limitvalue of the confidence level, which was not less than 0.54 at the minimum permissible value of 0.4 of the adequacy criterion. This confirms the adequacy of the results of mathemati-cal modeling with experimental data. Estimating the electricity metering uncertainty with a fuzzy interval increases the accuracy of the measurement, as it allows clarifyingthe monthly electricity consumption by taking into account the energy that was consumed during the reduced load mode

A model reconstruction approach for control synthesis of Takagi-Sugeno fuzzy systems

This paper investigates the control synthesis for Takagi-Sugeno (TS) fuzzy systems via a model reconstruction approach. Firstly, based on a nonparallel distributed compensation (NPDC) control scheme and a fuzzy Lyapunov function candidate (FLF), LMI-based synthesis conditions are derived to guarantee the asymptotic stability of the closed-loop TS fuzzy system. Then the operation domain of the premise variables is divided into several subregions to provide more flexibility in control design. And a new local model reconstruction method is proposed to transform the time-derivative of the FLF into new fuzzy forms with transformed membership functions in each subregion. This enables better exploitation of information on membership functions, resulting in relaxed conditions for both stabilization and robust H∞ control. Two simulation examples are provided to verify the advantages of the proposed TS fuzzy control approach.

Fuzzy Structured Element Integrated Decision of Metamorphism on Coal Dust Ignition Hazard Rating

To discuss the coal dust ignition hazard rating of different metamorphism, the fuzzy structure element integrated decision model about “no danger”, “weak danger”, “general danger”, and “strong danger” of coal dust ignition is established. 40 kinds of coal samples are selected to carry out coal quality analysis test, overpressure test, temperature test, flame propagation properties test and particle size distribution test. Based on this, coal dust ignition hazard rating decision-making index system is built. The triangular structure element is added to fuzzy comprehensive decision model, by sequencing weighted Hamming distance between fuzzy index value function and fuzzy maximal function, the coal dust ignition hazard rating of different coal quality can be decided. The result shows that: with increasing metamorphic grade, coal dust ignition hazard rating is decreasing, which provides study basis for relation between metamorphism and ignition hazard rating.

Local Stabilization of Constrained N-TS Fuzzy Systems Based on a Weighted Ranking Protocol

In this article, relaxed local stabilization criteria of constrained N-TS fuzzy systems are provided by developing a weighted ranking protocol. Different from the recent criteria reported in the literature, a set of operating modes is produced by employing the weighted ranking information of the available normalized fuzzy weighting functions. With regard to each enabled operating mode, its proprietary boundary information constraint is fully considered by means of introducing a class of cascade-type free variables, and thus the conservatism can be reduced to a large extent than before. More importantly, the applied variable weights for adjusting the range of different operating modes play an important role in further enlarging the estimated attraction regions. Finally, the superiority of the proposed approach is tested and verified by giving several comparisons on two key indicators for the same benchmark example.

FUZZY PRE β-OPEN SET AND ITS APPLICATIONS

This paper deals with a new type of fuzzy open-like set, viz., fuzzy pre β-open set, the class of which is strictly larger than that of fuzzy preopen set [7]. Using fuzzy pre β-open set as a basic tool, here we introduce fuzzy pre β-regular space in which fuzzy open set and fuzzy pre β-open set coincide. Here we introduce two new types of functions, viz., fuzzy pre β-continuous function, fuzzy pre β-irresolute function. The applications of these two functions on fuzzy pre β-regular space are discussed here

Multi-Objective Collaborative Control Method for Multi-Axle Distributed Vehicle Assisted Driving

For human–machine collaborative driving conditions, a hierarchical chassis multi-objective cooperative control method is proposed in this paper. Firstly, based on the phase plane theory, vehicle dynamics analysis is carried out to complete the definition of vehicle stability region. Secondly, based on the linear time-varying (LTV) system model, a cooperative control strategy combining fuzzy control with model predictive control (MPC) is proposed in the upper layer. In this strategy, the assisted driving weight adjustment coefficient and the stability weight adjustment coefficient are obtained by fuzzy mapping combining human–machine cooperation index and the vehicle stability region, respectively, and the optimization objectives of MPC are designed based on the above coefficients. In the lower layer torque allocation strategy, the stability weight adjustment coefficient is introduced to achieve multi-objective optimization of tire load rate and energy efficiency. For energy efficiency optimization, an optimal energy efficiency point-based tracking method is proposed to avoid nonlinearity caused by the introduction of motor loss models. Simulation analysis results show that the proposed strategy can effectively alleviate human–machine conflicts and improve vehicle handing stability. It also can achieve smaller tire load rate optimization through torque allocation and can reduce energy consumption by approximately 8% compared with the inter-axle torque allocation strategy. This study helps to promote the improvement of the comprehensive performance of assisted driving vehicles in human–machine cooperation, handling stability, and energy-saving torque distribution.

An Underground Mine Ore Pass System Optimization via Fuzzy 0–1 Linear Programming with Novel Torricelli–Simpson Ranking Function

In this work, we propose a 3D dynamic optimization model that enables the design of an underground mine ore pass system with uncertainties. Ore transportation costs and ore pass development costs are quantified by triangular fuzzy numbers. Transportation costs are treated as production costs, and they vary over the duration of mining operation, while development costs of ore passes are treated as an investment, and they are treated as constant. The developed model belongs to the class of fuzzy 0–1 linear programming models, where the fuzzy objective cost function achieves a minimum value, with respect to given set of techno-dynamic constraints. Searching for optimal value in the fuzzy environment is a hard task, and because of that, we developed a new ranking function which transforms the fuzzy optimization model into a crisp one. A triangular fuzzy number can be presented as a triangular graph G(V,E) composed of vertices and edges. The x-coordinate of the Torricelli point of a triangular graph presents the crisp value of a triangular fuzzy number. The use of this model lets us know the optimal number of ore passes, optimal location of ore passes, and optimal dynamic ore transportation plan.

Application of nanotechnology in breast cancer screening under obstetrics and gynecology through the use of CNN and ANFIS

Breast cancer is the leading reason of death among women aged 35 to 54. Breast cancer diagnosis still presents significant challenges, and preventing the disease's most severe symptoms requires early detection. The role of nanotechnology in the tumor-treatment has recently attracted a lot of interest. In cancer therapies, nanotechnology plays a major role in the medication distribution process. Nanoparticles have the ability to target tumors. Nanoparticles are favorable and maybe preferable for usage in tumor detection and imaging due to their incredibly small size. Quantum dots, semiconductor crystals with increased labeling and imaging capabilities for cancer cells, are one of the particles that have received the most research attention. The design of the research is cross-sectional and descriptive. From April through September of 2020, data were gathered at the State Hospital. All pregnant women who came to the hospital throughout the first and second trimesters of the research's data collection were included in the study population. 100 pregnant women between the ages of 20 and 40 who had not yet had a mammogram comprised the research sample. 1100 digitized mammography images are included in the dataset, which was obtained from a hospital. Convolutional neural networks (CNN) were used to scan all images, and breast masses and mass comparisons were made using the malignant-benign categorization. The adaptive neuro-fuzzy inference system (ANFIS) then examined all of the data obtained by CNN in order to identify breast cancer early using inputs based on the nine different inputs. The precision of the mechanism used in this technique to determine the ideal radius value is significantly impacted by the radius value. Nine variables that define breast cancer indicators were utilized as inputs to the ANFIS classifier, which was then used to identify breast cancer. The parameters were given the necessary fuzzy functions, and the combined dataset was applied to train the method. Testing was initially performed by 30% of dataset that was later done with the real data obtained from the hospital. The accuracy of the results for 30% data was 84% (specificity =72.7%, sensitivity =86.7%) and the results for the real data was 89.8% (sensitivity =82.3%, specificity =75.9%), respectively.

A Three-Stage Nonparametric Kernel-Based Time Series Model Based on Fuzzy Data

In this paper, a nonlinear time series model is developed for the case when the underlying time series data are reported by LR fuzzy numbers. To this end, we present a three-stage nonparametric kernel-based estimation procedure for the center as well as the left and right spreads of the unknown nonlinear fuzzy smooth function. In each stage, the nonparametric Nadaraya–Watson estimator is used to evaluate the center and the spreads of the fuzzy smooth function. A hybrid algorithm is proposed to estimate the unknown optimal bandwidths and autoregressive order simultaneously. Various goodness-of-fit measures are utilized for performance assessment of the fuzzy nonlinear kernel-based time series model and for comparative analysis. The practical applicability and superiority of the novel approach in comparison with further fuzzy time series models are demonstrated via a simulation study and some real-life applications.

An effective method for salt and pepper noise removal based on algebra and fuzzy logic function

An effective method for salt and pepper noise removal based on algebra and fuzzy logic function

FMap: A fuzzy map for scheduling elephant flows through jumping traveling salesman problem variant toward software‐defined networking‐based data center networks

SummaryNowadays data center networks (DCNs) should handle the ever‐growing load generated by diverse applications. It particularly occurs under concurrent flow requests and so‐called mice flows (MFs): elephant flows (EFs) ratio. Concentrating on a binary vision over flow size classification (EF or MF) results in subsequent unpredicted load imbalance due to neglecting EF's distinctions including a wide range of sizes. As a result, some EFs might utilize a path owing qualities beyond the given EF's demands, while another EF with higher requirements is attending to use an over‐utilized path. This article proposes FMap, a fuzzy map for scheduling EFs through our proposed variant of traveling salesperson problem (TSP) toward DCNs. FMap represents a novel EF scheduling scheme that integrates flow prioritization and routing decisions under the event pf parallel incoming flows besides the cooperation of the controller and OpenFlow switches in software‐defined networking (SDN) paradigm. FMap adopts fuzzy inference process to overcome the vagueness over EF's resource allocation. Mainly, FMap proposes a new variant of TSP (optimized by genetic algorithm) which enables EF's group forwarding with a minimum cost. FMap reduces the total hop count of EFs through considering a single optimal path for delivering groups of EFs that contain a same tag (priority). The outstanding results represent a major improvement as compared with equal cost multiple path, Hedera, Sonoum, and Size‐KP‐PSO. Particularly, the results illustrate an outperforming by 3.76×, 0.21×, 0.15×, 0.03×, and 0.03× in terms of total hop count, EFs FCT, packet loss, goodput, and received packets as compared with Size‐KP‐PSO, respectively.

Non-Probabilistic Reliability Analysis of Slopes Based on Fuzzy Set Theory

Aimed at the problem of fuzzy uncertainty of geotechnical parameters in slope stability analysis, a non-probabilistic reliability analysis method for slopes based on fuzzy set theory is proposed. Geotechnical parameters are described as fuzzy numbers, which are transformed into interval numbers at different cut set levels by taking fuzzy sets. The corresponding non-probabilistic reliability indexes and failure degrees of the slope are calculated by the non-probabilistic reliability analysis method based on the ellipsoidal model, and then the overall failure degree of the slope is obtained by weighted average to judge the stability state of the slope. The feasibility of the method was verified by a case analysis. The results show that the type and shape parameters of the fuzzy affiliation function of geotechnical parameters have a great influence on the non-probabilistic reliability of the slope. The slope failure degrees obtained from trapezoidal fuzzy numbers were larger, the slope failure degrees obtained from triangular fuzzy numbers and normal fuzzy numbers were medium, and the slope failure degrees obtained from lognormal fuzzy numbers were smaller. When considering soil parameters as triangular fuzzy numbers, normal fuzzy numbers, or lognormal fuzzy numbers, with the reduction of the shape parameters, the non-probabilistic reliability indexes of the slope increased while the failure degrees decreased. Additionally, adopting the overall failure degree to evaluate the stability of the slope can effectively solve the problem where the calculation results are too conservative (if the non-probabilistic reliability index is greater than 1) to judge the stability state of the slope in the traditional non-probabilistic reliability method.

A fuzzy nonparametric regression model based on an extended center and range method

When dealing with nonparametric regression problems, kernel-based methods are often employed. In this paper, we investigate nonparametric regression problems with fuzzy responses and exact predictors by implementing an extended center and range method within a three-stage procedure. For this purpose, we utilize the Nadaraya–Watson estimator for estimating the unknown fuzzy smooth function. In each stage, the unknown bandwidth is determined with the help of a generalized cross validation criterion. To evaluate and to compare the performance of our proposed fuzzy nonparametric regression model with established regression models, different goodness-of-fit criteria are considered. Finally, we investigate the practical applicability and show the superiority of the proposed regression model by means of a simulation study and real data applications.

The resolution of q-rung orthopair fuzzy set based three-way group conflict analysis

In social life, conflict situations occur frequently all the time. To analyse a conflict situation, not only the intrinsic reason of the conflict but also the resolution of the conflict should be given. In this paper, we propose a combine conflict analysis model under q-rung fuzzy orthopair information system that contain conflict resolution, which is called discern function-based three-way group conflict analysis. Firstly, we propose three novel form conflict distances which are induced by discern functions, and examine their properties, then the comprehensive conflict distances are given based on the normality and symmetry they share. Thus, the conflict analysis and resolution method in our model can be directly gained based on these novel form conflict distances. Secondly, from the view of group decision, the comprehensive q-rung fuzzy loss function is attained by aggregating a group of q-rung fuzzy loss functions through the q-rung orthopair fuzzy weighted averaging operator in the procedure of conflict resolution. Finally, we employ an example of the governance of a local government to demonstrate the process of finding an optimal feasible strategy in our model.

An improved entropy function for the intuitionistic fuzzy sets with application to cloud vendor selection

This study proposes a novel entropy function for the intuitionistic fuzzy sets to improve the existing fuzzy entropy measure. We introduce an attitude-based entropy measure by methodically calculating the experts’ attitude values through variance approach. We discuss several important properties and present an example to demonstrate the applicability and efficacy of the proposed method. An illustrative example exhibits the effectiveness of the proposed intuitionistic fuzzy entropy functions and measures. We further show the superiority of the proposed intuitionistic fuzzy entropy measures over the existing measures.

Identification of suitable location to cultivate grape based on disease infestation using multi-criteria decision-making (MCDM) and remote sensing

This study aims to identify suitable regions for grape cultivation and the areas where diseases are likely to occur in Fars Province, Iran. The study employs a multi-criteria decision-making (MCDM) model based on the Analytic Hierarchy Process (AHP) and fuzzy logic methods, taking into account the ecological requirements of grape plants. Fourteen essential parameters for grape cultivation are prepared, and interpolation maps are created for each parameter. Fuzzy maps are generated by defining membership functions, and AHP is utilized to compare and determine the importance of each factor to produce a final map of grape cultivation land suitability. The study reveals that grape cultivation is most suitable in the southern regions of Fars Province. Furthermore, the research identifies the areas where Powdery mildew, Gray mold, and GFLV diseases may occur based on rainfall and temperature levels. The study recommends against grape cultivation in the southern region due to the possibility of these diseases developing. The study employs a highly accurate regression method (R2 = 0.968 and F = 0.00001) and principal component analysis (PCA) to determine that land suitability class strongly correlates with Tmin, NDVI, LST, Total disease, Tmean, and RH. By identifying the areas suitable for grape cultivation and where pests may flourish, the necessary management can be implemented to ensure maximum harvest in the best suitable locations for grape planting.

Multiple interval delay-dependent finite-time control of fuzzy stochastic systems

This work is concerned with multiple interval delay-dependent stochastic finite-time boundedness as well as input-output finite-time mean square stabilization for fuzzy plants against state constraints as well as input constraints. Nonlinear dynamics, intermittent actuator faults, exogenous disturbances, model uncertainties and intermittent sensor faults appear in the multiplicative form in these systems. The switching between the faulty and healthy conditions is described via semi-Markov chain. First, a semi-Markovian fault-tolerant controller is researched. Next, the closed-loop model is gathered. The issue of robust stochastic finite-time boundedness as well as input-output finite-time mean square stabilization against H∞ performance is realized via fuzzy stochastic Lyapunov function. Meanwhile, sufficient conditions are presented with linear matrix inequalities. At last, this validity of this approach in this paper is proved by two examples.

Some connections between the generalized Hukuhara derivative and the fuzzy derivative based on strong linear independence

This article investigates some connections between the notions of the generalized Hukuhara derivative and the Ψ-derivative of fuzzy number-valued functions. The concept of Ψ-differentiability is defined on a fuzzy number-valued function φ in the form of φ(x)=ϱ1(x)A1+…+ϱn(x)An, where ϱ1,…,ϱn are n real-valued functions defined on an interval [a,b] and {A1,…,An} is a strongly linearly independent subset of fuzzy numbers. The Ψ-derivative of φ at some x is φ′(x)=ϱ1′(x)A1+…+ϱn′(x)An whenever the derivatives ϱ1′(x),…,ϱn′(x) exist. This article provides conditions for these two notions of derivatives of such functions to coincide. Moreover, under some weak conditions, we show that an arbitrary continuously gH-differentiable function defined on an interval [a,b] and its gH-derivative can be uniformly approximated as closely as desired by a Ψ-differentiable function and its Ψ-derivative, respectively. Finally, we apply these results to obtain numerical and analytical solutions of a simple fuzzy decay model described by a fuzzy initial value problem under gH-derivative.

Metaverse integration alternatives of connected autonomous vehicles with self-powered sensors using fuzzy decision making model

Using self-powered sensors, traffic data may be collected continuously, efficiently, and sustainably once connected autonomous vehicles (CAVs) are a part of metaverse technology. Metaverse self-powered sensors can capture uninterrupted data that allow for activities such as the management of the traffic network, the optimization of transportation facilities, and the management of urban and intercity journeys to be performed. In addition, metaverse technology creates a new field of study. Evaluating the systems involved in current transportation activities together with the metaverse can increase the efficiency and sustainability of transportation. The main purpose of this study is to prioritize four alternatives of CAVs in metaverse with self-powered sensors using a novel decision making model. The proposed hybrid decision making framework includes two stages. In the first stage the fuzzy full consistency method (fuzzy FUCOM) is applied to find the weighting coefficients of criteria. In the second stage, a fuzzy non-linear model based on fuzzy Aczel-Alsina functions (fuzzy Aczel-Alsina weighted assessment - ALWAS method) is defined to rank the alternatives. Four alternatives are defined and evaluated using twelve different criteria under four headings, namely, technical advancement, environmental, implementation, and financial aspects. A case study has been created for the experts to evaluate the alternatives most effectively. The results of the study indicate that using self-powered sensors for integrating real-time traffic management in the metaverse is the most advantageous alternative.

An efficient spherical fuzzy MEREC-CoCoSo approach based on novel score function and aggregation operators for group decision making.

The major objective of the current investigation is to build an integrated multiple criteria group decision-making (MCGDM) methodology based on combined compromise solution (CoCoSo) andspherical fuzzy set for determining the optimal solar power station. To begin with, an innovative spherical fuzzy score function is brought forward to strengthen the efficiency of the comparison for spherical fuzzy number (SFN). Secondly, several newly operational laws for SFN are defined and some novel aggregation operation based on them are propounded. The corresponding excellent properties of the novel operators are also explored at length. Further, the spherical fuzzy method on the removal effects of criteria (MEREC) technique is presented by the proposed score function to work out the importance of the criteria. Lastly, an MCGDM approach is propounded based on improved spherical fuzzy CoCoSo to obtain the ranking of the solar power station locations. The feasibility and practicability of the proposed SF-MEREC-CoCoSo method are investigated through the comparison study with the extant methods. The sensibility analysis is also executed to discuss the robustness and stability of the propounded methodology.