Fuzzy Operators Research Articles

A study of Global Equity based on AHP & EW Multi-attribute Decision Model

With the shortage of Earth's resources, asteroid mining has received much attention. However, there is no specific policy to address the impact of asteroid mining on global equity, so this paper proposes a targeted mathematical modeling solution-AHP&EM multi-attribute decision model. First, this paper calculates the weights of these different aspects in the model using entropy weights (EW) and hierarchical analysis (AHP), successfully constructs a global stock valuation model, and finds that the global stock index is gradually improving. In addition, this paper designs a scoring model and evaluates the optimal solution using the Pythagorean hesitant fuzzy operator (PFHS) and concludes that the agency model is most beneficial to the growth of the global equity index, while the equity system and tax planning are most suitable for the current model and most beneficial to the global equity.

Some New Properties of Exponential Trigonometric Convex Functions Using up and down Relations over Fuzzy Numbers and Related Inequalities through Fuzzy Fractional Integral Operators Having Exponential Kernels

The concept of convexity is fundamental in order to produce various types of inequalities. Thus, convexity and integral inequality are closely related. The objectives of this paper are to present a new class of up and down convex fuzzy number valued functions known as up and down exponential trigonometric convex fuzzy number valued mappings (UDET-convex FNVMs) and, with the help of this newly defined class, Hermite–Hadamard-type inequalities (H–H-type inequalities) via fuzzy inclusion relation and fuzzy fractional integral operators having exponential kernels. This fuzzy inclusion relation is level-wise defined by the interval-based inclusion relation. Furthermore, we have shown that our findings apply to a significant class of both novel and well-known inequalities for UDET-convex FNVMs. The application of the theory developed in this study is illustrated with useful instances. Some very interesting examples are provided to discuss the validation of our main results. These results and other approaches may open up new avenues for modeling, interval-valued functions, and fuzzy optimization problems.

Visual Secret Sharing of Gray and Color Images using Fuzzy Random Grids

Problem:Visual secret sharing is a method used to secure images by converting a secret image into multiple shares so that the original image cannot be recognized from individual shares, and no calculations are required during the image decryption, but the original image can be visually seen by stacking the shares. However, one of the significant challenges in this method is the increased size of the shares and the recovered image, which is called pixel expansion. Researchers have proposed several methods to solve this problem, but many of them are limited to binary images, and they cannot handle gray and color images without converting them to binary. Solution:This study proposes a novel fuzzy random grid-based method to directly encrypt gray and color images without any pixel expansions. In this method, fuzzy random grids with decimal values between 0.0 to 1.0 are generated during the encryption stage, and fuzzy operators are used for the decryption stage. Results:The evaluation results demonstrate the ability of the proposed solution in encrypting gray and color images without converting them to binary and without any pixel expansions. The individual shares of the proposed method do not reveal any information from the original image, making it a secure method. The quality of the decrypted images has been evaluated using both subjective and objective evaluation methods such as PSNR and SSIM metrics, which show state-of-the-art results.

Extend Tversky’s Ratio Model to an Asymmetric Similarity Measurement Model with Three Conditional Parameters: 3p-ASM Model

Generally, the similarity between objects is often measured by symmetric operators, such as Cosine, Dice, and Jaccard similarity. However, the ratio model originally proposed by Tversky pointed out that the similarity using the feature matching method tends to be asymmetric. Furthermore, in many practical situations, the existing similarity measures using the feature matching method have some limitations: the calculation formulas are symmetrical, it is not intuitive based on binary features, and it is not easy to calculate based on fuzzy sets. To overcome such limitations, some other asymmetries have proposed to directly combine Tversky’s ratio model with the classical symmetric similarity metric, which in turn leads to the inability to identify different features between the compared objects and affects their similarity accuracy. Therefore, aiming to avoid these, this paper will focus on extending Tversky’s ratio model to a series of 3-parameter asymmetric similarity metrics (3p-ASM), using three conditional parameters to describe both common and different features. First, the set-based 3p-ASM is achieved due to the general and fuzzy set-theoretic operations, when estimating features in left{ 0,1right} and left[ 0,1right] , respectively. Then, considering that the estimated values of features can also be expressed as vectors, it will be extended to the vector-based 3p-ASM. Finally, a vector form of 3p-ASM is compared with existing classical methods and a comparative analysis is performed to demonstrate its effectiveness and validity. It is then applied to the KNN model in order to select the most similar items.

A Target Threat Assessment Method for Application in Air Defense Command and Control Systems

Introduction. This paper presents a solution for threat assessment of air targets using the fuzzy logic inference method. The approach is based on the Sugeno fuzzy model, which has multiple inputs representing target trajectory parameters and a single output representing the target threat value. A set of IF–THEN fuzzy inference rules, utilizing the AND operator, is developed to assess the input information.Aim. To develop and test an algorithm model to calculate the threat value of an air target for use in real-time automated command and control systems.Materials and methods. An algorithm model was developed using a fuzzy model to calculate the threat value of a target. The model is presented in the form of a flowchart supported by a detailed stepwise implementation process. The accuracy of the proposed algorithm was evaluated using the available toolkit in MATLAB. Additionally, a BATE software testbed was developed to assess the applicability of the algorithm model in a real-time automated command and control system.Results. The efficiency of the proposed fuzzy model was evaluated by its simulation and testing using MATLAB tools on a set of 10 target trajectories with different parameters. Additionally, the BATE software was utilized to test the model under various air defense scenarios. The proposed fuzzy model was found to be capable of efficiently computing the threat value of each target with respect to the protected object.Conclusion. The proposed fuzzy model can be applied when developing tactical supporting software modules for real-time air defense command and control systems.

Research on Green Consumption Based on Visual Evaluation Method—Evidence from Stone Flooring Industry

Blind consumption discovered in the real application of flooring does not produce the visually anticipated impression, leading to additional time costs and stone flooring waste. Consumers cannot clearly articulate their visual imaging needs when purchasing stone flooring. Due to consumers’ lack of understanding of the visual imagery style of decorative stone flooring, manufacturers are unable to produce more visual styles of stone flooring in response to consumer demand, which leads to an unorganized production process and the wasting of stone resources. Additionally, manufacturers are unable to receive feedback on market demand, which makes communication links between sales teams difficult. A total of 40 adjectives were considered the most appropriate in a pool of 110 adjectives for the visual imagery evaluation of stone after ten interior design professionals with experience in decorative stone applications had narrowed the selection. Following this, a general consumer semantic difference method questionnaire survey and questionnaire data factor analysis statistics were used to create 10 sets of visual imagery adjectives for marble flooring, which were then divided into 10 different types of marble flooring. Following the computer simulation drawing with the 10 groups of visual imagery adjectives design questionnaire, the consumers completed the visual imagery evaluation questionnaire survey. They received a 304-question valid questionnaire, and using the triangular fuzzy number operation in fuzzy theory, they arrived at 10 marble floors in the visual imagery evaluation score. In order to clarify the current consumer demand for stone floor imagery, the high sales volume of stone flooring on the market for visual style division, which can guide consumers according to their visual needs for an efficient choice, can enhance the efficiency of communication between consumers and sellers. It can also help enterprises clarify the market consumer demand for orderly production to achieve the purpose of green consumption and to ensure the sustainable development of the decorative stone flooring market.

Picture fuzzy Choquet integral based Einstein operations and its application in selection of the best mobile apps for online education

Picture fuzzy aggregation operators are the standard mathematical tools for the combination of several inputs with respect to attributes into one unique output. The Choquet integral operator has been proven more ideal than traditional aggregation operators in the modelling of interaction phenomena among the attributes in decision-making problems. Firstly, we propose the Choquet integral picture fuzzy Einstein geometric aggregation operator and Choquet integral picture fuzzy Einstein ordered geometric aggregation operator with certain properties of these operators being established. We validate the functioning of the operators with illustrative examples. The proposed operators clearly capture the comprehensive correlative relationships of attributes in a simpler manner. Furthermore, the algorithm for a multi attribute decision-making problem based on proposed operators is given. The application of the proposed operators was explored to deal with the selection of the best mobile apps for online education. Finally, comparisons are conducted to illustrate the discussion and advantages of the proposed operators.

Windstorm Hazardous Area Mapping Using Multi-Criteria Evaluation Techniques of Fuzzy Logic Approach

The goal of this study to determine the most exposed area to windstorm event using fuzzy logic approach. Respond to the Sustainable Development Goal (SDG) 11 and 13, Sustainable Cities and Communities and Climate Action, this study was conducted to establish the preparedness in high-risk region. To achieve this goal, the influencing indicator was identified based on previous study. The related indicator comprises of wind speed, temperature, relative humidity, precipitation, slope, population, road, and land use. Fuzzy membership model implemented to aggregating the indicator to standard value 0 to 1. A fuzzy model was used as a method to integrate the constructed index values, and a frequency ratio was used to determine the fuzzy membership value. Different fuzzy operators (AND, OR, SUM, PRODUCT, and GAMMA) are applied to generate windstorm hazard map. The fuzzy gamma (γ) operator, with γ equal to 0.9, was used to create wind hazard map into different zones of five relative sensitivity classes: very high, high, moderate, low, and very low. 10.65% of study area has very high sensitivity towards windstorm hazard which distributed at high area (Banjaran titiwangsa), West Coast area (Pahang and West Johor) and north area (Perlis). In addition, some part in the surrounding region of Peninsular Malaysia were also identified as windstorm hazard due to the dense of urban area such at Johor Bharu and Klang Valley area. 7.20% of the study area has very-low windstorm hazard and is mainly located in the middle part.

Complex spherical fuzzy Aczel Alsina aggregation operators and their application in assessment of electric cars

The multi-criteria decision-making (MCDM) tool is a robust decision-making technique utilized in several fields like networking, risk management, digital analysis, cybercrime investigation, artificial intelligence, waste management enterprises and many other selection criteria. Complex SFS (CSFS) is a new edition of the spherical fuzzy set (SFS) that offers substantial information about any item in terms of amplitude and phase terms in a wider range of real terms. Complex SFS (CSFS) can be an extension of the spherical fuzzy set (SFS). The Aczel-Alsina aggregation tools are more appropriate aggregation operators (AOs), and they are used to conquer the impact of inconsistent and uncertain data. In this paper, we reveal some new approaches based on Aczel-Alsina aggregation tools under consideration of Complex Spherical Fuzzy (CSF) information. These new approaches include the CSF Aczel-Alsina weighted average (CSFAWA) operator, and the CSF Aczel-Alsina ordered weighted average (CSFOWA) operator. In addition to this, we also introduce a list of novel techniques by making use of the theory of Aczel-Alsina aggregation tools such as CSF Aczel-Alsina weighted geometric (CSFAWG) and CSF Aczel-Alsina ordered weighted geometric (CSFOWG) operators. To demonstrate the resilience and efficacy of the approaches that have been mentioned, we will examine a few exceptional examples and remarkable properties of the methodology that we have devised. In addition, a characterization is provided for an approach to the MCDM issue using the CPF information system. We use the example of electric automobiles as a case study to illustrate the uniformity and dependability of the methodology that we have established. This example was chosen because of the high cost of fuel and the present economic challenges that are being encountered by families in the middle class. An empirical case study is also constructed to determine an electric car that is desirable based on the techniques that we have proposed. To evaluate the correctness and superiority of the established strategies, we compare the outcomes of previously used techniques with the AOs currently being provided.

A consensus model with bipolar fuzzy archimedean-dombi operators for group decision-making

A consensus model with bipolar fuzzy archimedean-dombi operators for group decision-making

Intuitionistic fuzzy bimodal topological structures

Two new intuitionistic fuzzy operators from a modal type are defined. Some properties of these operators are studied. Based on them, four new intuitionistic fuzzy modal topological structures are introduced and after this, four intuitionistic fuzzy bimodal topological structures are constructed. All they are examples of modal and bimodal topological structures.

MULTIVARIATE FUZZY APPROXIMATION BY NEURAL NETWORK OPERATORS ACTIVATED BY A GENERAL SIGMOID FUNCTION

Here is studied in detail the multivariate fuzzy approximation to the multivariate unit by multivariate fuzzy neural network operators activated by a general sigmoid function. These operators are multivariate fuzzy analogs of earlier studied multivariate Banach space valued ones. The derived results generalize earlier Banach space valued ones into the fuzzy level. Here the high order multivariate fuzzy pointwise and uniform convergences with rates to the multivariate fuzzy unit operator are given through multivariate fuzzy Jackson type inequalities involving the multivariate fuzzy moduli of continuity of the mth order (m ≥ 0) H-fuzzy partial derivatives, of the involved multivariate fuzzy number valued function. The treated operators are of averaged, quasi-interpolation, Kantorovich and quadrature types at the multivariate fuzzy setting.

Similarity measures of neutrosophic fuzzy soft set and its application to decision making

ABSTRACT Complex data analysis should be done in the most accurate way in order to express the uncertain environments in the most ideal way. In addition, mathematical models that can best express the membership degrees that represent the objects are preferred for these data analyses. Taking these situations into account, this study proposes the concept of single-valued neutrosophic fuzzy soft set, which can be expressed with four different membership degrees of each object that provides a parameter, with the contribution of the parameterisation tool. Some important results are obtained by examining some single-valued neutrosophic fuzzy soft set-based theoretical operations. In addition, distance measures between two single-valued neutrosophic fuzzy soft sets. Then, similarity measurements based on these distance measurements are studied. In this way, a determination has been made for the analysis of the decision-making processes for the determination of the interaction between two single-valued neutrosophic fuzzy soft sets.

New q-rung orthopair fuzzy distance-similarity operators with applications in investment analysis, pattern recognition, clustering analysis, and selection of robot for smart manufacturing

New q-rung orthopair fuzzy distance-similarity operators with applications in investment analysis, pattern recognition, clustering analysis, and selection of robot for smart manufacturing

Application of Intuitionistic Fuzzy Topological Operators in Spatial Objects Modeling

The concept of topology is widely used in mathematical modeling of spatial objects and in GIS. One such application of fuzzy topological operators, detecting areas affected by Mikania micrantha, was studied by Shi and Liu. The precision of the results was evaluated by applying the intuitionistic fuzzy pre-interior and pre-clouser operators defined by the author to the data included in this study.
 With this application example, it has been shown that the newly defined operators give results closer to the real bounds.

Representations of L-fuzzy rough approximation operators

In recent years, there has been tremendous interest in developing lattice-valued rough set theory. In this framework, we primarily take into account the following two problems. Firstly, we include the well-known intuitionistic, interval-valued, neutrosophic and Pythagorean fuzzy rough sets into the framework of lattice-valued rough sets. Specifically, the four kinds of rough sets can be considered as special lattice-valued rough sets. Secondly, based on a completely distributive lattice L, we provide representations of the upper and lower L-fuzzy rough approximation operators by using four kinds of cut sets of an L-fuzzy set and an L-fuzzy relation, which generalizes the existing results in the case that L=[0,1]. In particular, we show that representations of intuitionistic and interval-valued fuzzy rough approximation operators provided by Zhou and Sun are special examples of our proposed representations.

An approach to multi-attribute decision making based on intuitionistic fuzzy rough Aczel-Alsina aggregation operators

A concept of intuitionistic fuzzy rough set based on approximations plays a vital role in coping with uncertainty. Aczel-Alsina t-norm and t-conorm are the most flexible operational laws based on the parameter for fuzzy frameworks. In multi-attribute group decision-making (MAGDM), the aim of this article is to develop some tools based on norm operations for the information fusion. In this article, intuitionistic fuzzy rough Aczel-Alsina weighted geometric operators are developed and studied their properties. Based on these operators, MAGDM algorithm is presented. The developed aggregation operators (AOs) are compared with some existing AOs, and their significance is discussed.

Evaluating the interconnection performance of cross-regional road infrastructures based on an integrated micro-pattern approach with fuzzy linguistic operators

The dilemma of invalidating cross-regional road infrastructures (CRRIs) seriously impedes the flow of resources and affects its interconnection performance. However, the relations between the key driving force and referential improvement paths remain unclear, correspondingly, the combination set of options for improving CRRI interconnection is a major uncertainty embedded in the cross-regional collaboration period. To address this issue, this paper proposes an integrated case-based reasoning and fuzzy adversarial interpretive structure modeling (CBR-FAISM) framework to uncover micro-structural situational elements, match similar historical cases, and reveal the interactive mechanism of CRRI operation, in which the black box can be opened to find referential and reasonable solutions. The proposed framework was validated with Hong Kong–Zhuhai–Macao Bridge (HZMB) case. The findings indicatedthat the top five impact factors are mainly induced by governments and operators. The results also show that the improvement paths are period-oriented and should be done in the following order: communication links and feeder lines in the early period, collaboration in the middle period, micro-feeder mode in the mid-late period, and service level in the later period. This is the most significant insight of the proposed framework, which broadens the micro and macro understanding of regional transportation development.

APPLICATION OF FUZZY LOGIC IN THE ROBOT CONTROL FOR MECHANICAL PROCESSING

Robot application in mechanical machining is growing day by day because it has many advantages over conventional machines such as high flexibility, large working space, and high repeatability. Many degrees of freedom of motion give robots the ability to perform complex technological operations, but also because of that, methods of controlling robots based on dynamic models have difficulties. Applying fuzzy logic to robot control can partially or completely exclude the calculation of the robot's dynamic model as well as overcome other uncertainties of the whole technological system. The variables and parameters of the fuzzy logic-based controller are modeled in a linguistic form, called linguistic variables, and are defined by the linguistic semantic values. Fuzzy rules are an important basis for the performance of operations defining the control quantities of the controller. Fuzzy rules are constructed by natural human inference and are based on expert intelligence. The main tasks of applying fuzzy logic control include “Fuzzification” to determine fuzzy parameters in the form of fuzzy sets of input-output data; “Fuzzy Rules and Fuzzy Inference Mechanism” to perform fuzzy operations defining control quantities, and finally “Defuzzification” to convert control quantities from linguistic values to physical values for controller operation. There have been many types of research on applying fuzzy logic to control robots in general, but the percentage of fuzzy control research work for mechanical machining robots is still limited.
 The article is based on published works on fuzzy control for robots in general and mechanical processing robots to analyze the applicability of fuzzy control for mechanical machining robots. The article provides detailed information on fuzzy controller design, on determining input and output variables, proportional mapping to determine the number of fuzzy sets and the corresponding type of membership function. The construction of fuzzy rule base system and fuzzy inference mechanism is presented, and finally defuzzification. Prospects for the use of methods to perfect and develop fuzzy control systems for mechanical machining robots are also presented. Collectively, the information in this document is intended to guide the implementation of fuzzy logic-based controller designs for application to machining robots, as well as to general robot control.

Performance Evaluation of Healthcare Supply Chain in Industry 4.0 with Linear Diophantine Fuzzy Sine-Trigonometric Aggregation Operations

The concept of linear Diophantine fuzzy set (LDFS) theory with its control parameters is a strong model for machine learning and data-driven multi-criteria decision making (MCDM). The sine-trigonometric function (STF) has two significant features, periodicity and symmetry about the origin that are very useful tools for information analysis. Keeping in view the characteristics of both STF and LDFS theory, this article introduces the sine-trigonometric operations for linear Diophantine fuzzy numbers (LDFNs). These operational laws lay a foundation for developing new linear Diophantine fuzzy sine-trigonometric aggregation operators (LDFSTAOs). The integration of Industry 4.0 technology into healthcare has the potential to revolutionize patient care. One of the most challenging tasks is the selection of efficient suppliers for the healthcare supply chain (HSC). The traditional suppliers are not efficient in accordance with Industry 4.0, with particular uncertainties. A new MCDM framework is presented based on LDFSTAOs to examine the HSC performance in industry 4.0. A credibility test, sensitivity analysis and comparative analysis are performed to express the novelty, reliability, and efficiency of the proposed methodology.