Fuzzy Structure Research Articles

Connectedness degrees in (L, M)-fuzzy convex structures

Connectivity is one of the most essential notions in general topology. Convex structures are topological-like structures. Many properties in topological spaces have been generalized to convex structures, such as separation. However, connectivity has not been studied in convex structures yet. In this paper, firstly, based on the consideration to hull operators, separatedness is defined in classical convex structures, and then we provide the concept of connectivity. Secondly, some equivalent characterizations of connectivity are discussed, and we investigate the related properties of connectivity. In additional, through (L, M)-fuzzy convex hull operators, we propose the separatedness degrees of (L, M)-fuzzy convex structures. Furthermore, the notion of connectedness degrees of (L, M)-fuzzy convex structures is introduced. Finally, many properties of connectivity in general convex structures can be generalized to (L, M)-fuzzy convex structures.

A Performance Comparison of Neural Networks and Fuzzy Systems for Time Series Forecasting

Artificial neural networks and fuzzy structures have gained significant popularity in the last decade for time series forecasting. The objective is to conduct a performance comparison of various strategies to determine which ones are more effective for time series forecasting. The dataset provides instruction and evaluates forecasting models, utilizing artificial neural networks and fuzzy architectures. The observation evaluates the overall effectiveness of the forecasting models and the use of the root mean square error and means absolute error measures. This comparison analysis provides initial insights into the efficacy of artificial neural networks and fuzzy structures for predicting time series data. In predicting time series data, this study examines the precision of two renowned artificial intelligence systems, Neural Networks and Fuzzy structures. To evaluate the two algorithms, two distinct types of time series were utilized: a synthetic dataset consisting of 150 variables and a real-world dataset including 129 data points about monetary forecasts. The models' forecasting accuracy, training duration, and generalization abilities were compared. The findings validated that neural network surpassed fuzzy structures in all performance metrics when handling synthetic data. This research emphasizes the capabilities of artificial neural networks and fuzzy structures in addressing complicated forecasting problems. It demonstrates that both techniques may be utilized for predicting future time series values.

Optimal Network Analysis through Vertex Order Coloring of Intuitionistic Fuzzy Graph Operations

Intuitionistic fuzzy graphs (IFGs) are a powerful tool for modeling uncertainty and complex relationships. They offer versatile frameworks for addressing real‐world challenges. In this research, we have introduced intuitionistic fuzzy vertex order coloring (IFVOC) and analyzed the alpha‐strong (), beta‐strong (), and gamma‐strong () vertices through their degree. We explored important theorems based on the types of strong vertices, broadening the scope of our study. We analyzed multiple IFG products to determine the most optimal network based on some important metrics, including the weight and total number of vertices, the chromatic number, and the weight of the graph’s minimum spanning tree. We systematically evaluate different types of IFG products, such as conormal, modular, residue, and maximal, and consider their implications for fuzzy graph structure and connectivity. We have investigated new metrics to measure the presence and importance of vertices in the graph, assessing both their frequency and overall impact. Additionally, we have investigated the impact of product operations on the significance of nodes and the resultant minimum spanning tree, providing insights into the overall robustness and efficiency of each product. We have explored how variations in product operations impact the distribution of vertices and the characteristics of the minimum spanning tree and chromatic number, elucidating the trade‐offs between different product options. We have modeled the product graph as a network to represent complex systems composed of interconnected entities. The outcomes of this research contribute to the advancement of IFG theory and its use in various fields, such as network design, strategic planning, and system analysis.

A novel development to encrypt data communication under t-intuitionistic fuzzy environment.

The field of cryptography has grown significantly with the advent of information and communication technologies due to the increasing complexity of cyber threats and rising security requirements. This evolution has come with the creation of new cryptosystems and improvements to current ones. This study is the first to explore the RSA approach in the framework of t-intuitionistic fuzzy subgroups. This technique makes group-based cryptographic operations safer when there are unclear relationships and hesitations. This supports the complex and uncertain nature of subgroup membership, allowing for much more significant representations of the degrees of belonging, non-belonging, and hesitancy for the group elements along parameter 't'. The t-intuitionistic fuzzy RSA technique employs a t-intuitionistic fuzzy subgroup to address cryptosystem ambiguity, fuzziness, and imprecision. Consequently, inaccurate cryptographic data is more effectively represented, manipulated, and protected. Furthermore, this technique enhances the current level of fuzzy cryptography. The t-intuitionistic fuzzy RSA algorithms are of theoretical and practical value, as they significantly contribute towards developing fuzzy cryptography, fuzzy algebraic structures, and decision support systems. In this paper, the notions of t-intuitionistic fuzzy numbers and triangular t-intuitionistic fuzzy numbers are introduced. A new RSA cryptosystem based on a t-intuitionistic fuzzy subgroup is proposed in which the plaintext and the ciphertext are obtained in terms of t-intuitionistic fuzzy numbers and triangular t-intuitionistic fuzzy numbers. In addition, the significance of the concept of the t-intuitionistic fuzzy subgroup is highlighted as a suitable alternative tool to secure the data under consideration. In addition, the practical effect of the proposed methods is also investigated in this study. A mathematical mechanism is presented to implement the t-intuitionistic fuzzy RSA algorithm. Finally, a comparative analysis of the developed technique is presented with some existing methods to showcase the applicability and superiority of the recently developed method.

Q- rung orthopair probabilistic hesitant fuzzy hybrid aggregating operators in multi-criteria decision making problems

With the increase of complex information in applications of decision making problems, the use of probabilistic hesitant fuzzy set structure has expanded. Therefore, this paper aims to present two new operators namely q-rung orthopair probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (q-ROPHHWAG) operator and q-rung orthopair probabilistic hesitant fuzzy hybrid ordered weighted arithmetic and geometric (q-ROPHHOWAG) operator for q>0. The presented operators are better than existing operators in many respects as adding a new parameter, having more flexible structure and presenting comparative analysis in its own. Moreover, we mention from some properties of the proposed operators. In addition to, we give an algorithm and example to indicate effective, reality and flexible of presented method and operators. Then, we solve an example over Pythagorean probabilistic hesitant fuzzy sets with our operators and the results are agreement and the offered operators have superior effect than other operators.

Application of BIM technology in construction project cost refinement control and construction energy consumption control

Abstract In order to solve the problem of accurate cost control management in the process of engineering construction, this paper applies BIM technology to the whole process of cost management, covering the whole life cycle of the project. Through efficient sharing of information on the BIM collaborative platform, it carries out unimpeded process work and achieves refined management. Aiming at the complexity of the information characteristics that affect the cost and uncertainty of information transmission, an algorithm fusion scheme based on NCM-FPN has been designed. The TOPSIS method is used to integrate the case feature attributes into the cost case information database. By combining the clustering algorithm with practical management experience, the knowledge base of engineering cost control strategies can be established, and the logical relationship of strategy matching can be determined. The inverse cloud algorithm is used to establish the feature cloud, determine the fuzzy Petri network structure based on generative rules and design the inference algorithm to establish an intelligent model for strategy matching so as to realize the accurate mapping and rapid response from the target case features to the control strategies. Through the analysis of construction energy consumption, it is concluded that the construction energy consumption of different structure buildings is not the same; the construction energy consumption per unit area of brick structure, steel structure residence and frame office building is 0.1659GJ/m2, 0.2706GJ/m2 and 0.3104GJ/m2 respectively, and the largest is the shear-wall structure residence is 0.3381GJ/m2 for the 2.04 times of the brick structure. Based on BIM technology, the cost of dynamic control engineering for construction projects was reduced by 5.4 million. Therefore, BIM is an important technical means to promote the whole process control of project cost, from empirical control to informationization, standardization, and intelligent control.

A CONTRIBUTION TO THE STUDY ON CHAOS SPACE IN FUZZY ROUGH ALGEBRAIC TM SYSTEM

This paper introduces a new concept called chaos space in fuzzy rough algebraic TM system. It studies the properties of chaos space and introduces a new system called fuzzy rough chaotic structure space. It emphasizes the properties of chaotic interior and chaotic closure.

Climatic analysis based on interval-valued complex Pythagorean fuzzy graph structure

The Interval-valued Complex Pythagorean Fuzzy Set (IVCPFS), an extension of the Pythagorean Fuzzy Set (PFS), offers a more accurate description of uncertainty than traditional fuzzy sets. It has numerous uses in fuzzy control. In this research study, we show the concept of Interval-Valued Complex Pythagorean Fuzzy Graph Structure (IVCPFGS), as well as the results of some regular IVCPFGS and totally regular IVCPFGS, along with the degree of vertex present. We also discussed the subdivision of an IVCPFGS, the complement IVCPFGS, and the strength of a Path in an IVCPFGS. Finally, we discuss a realworld example based on temperature variation and climatic data analysis in an environment with an interval-valued complex Pythagorean fuzzy framework to demonstrate the applicability of the generated results.

Multi-attribute decision-making using Archimedean aggregation operator in T-spherical fuzzy environment

As an extension of several fuzzy structures such as fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, q-rung ortho-pair fuzzy sets, and T-spherical fuzzy (TSF) sets (TSFSs), are an effective tool for controlling the vagueness of data. Archimedean t-conorm (ATCN) and t-norm (ATN), which consists of the t-conorm (TCN) and t-norm (TN) families, is a crucial approach for fuzzy sets to produce extensive operational rules. In this manuscript, for TSF numbers some core operational laws are initiated based on ATCN and ATN, also some basic characteristics of these operational laws are investigated. Secondly, based on these operational laws TSF Archimedean weighted averaging (TSPFAWA) and TSF Archimedean weighted geometric (TSPFAWG) operators are initiated. Thirdly, we investigated special cases of these aggregation operators and some basic properties. On the behalf of the TSPFAWA and TSPFAWG operators, a novel method for solving multiple attribute decision-making (MADM) problems using TSF information is also devised. Lastly, a numerical example is provided to demonstrate the applicability of the suggested technique, and a comparison analysis is done to demonstrate its advantages.

Selection of best enterprise resource planning system by using Hamy mean operator with complex spherical fuzzy information

Numerous fuzzy structures have been created and studied up to this point in order to investigate objects under ambiguity. Among them, the structure of complex spherical fuzzy set is significant because it can define the four prospective aspects of an expert's viewpoint using the membership degree, non membership degree, abstinence, and rejection in a two-dimensional space. It is never easy to aggregate information, particularly when the input arguments are connected. In order to handle such situations, the goal of this study is to create the idea of the Hamy mean operator because it integrates data in ambiguous environments and takes into account the relationships between the input arguments. In this manuscript, we investigated the notion of Hamy mean and dual Hamy mean operators in the setup of complex spherical fuzzy sets and described their applications for engineering activities. We created the complex spherical fuzzy Hamy mean (CSFHM) and complex spherical fuzzy Dual Hamy mean (CSFDHM) operators and looked into the validity of each. To assess the effectiveness of the enterprise resource planning (ERP) systems using complex spherical fuzzy data, we created the multi attribute decision making technique based on the CSFHM and CSFDHM operators. The impacts of the related parameters are examined using a numerical example to assess the effectiveness of ERP systems. In comparison to conventional aggregation operators, the recommended aggregated results utilizing CSFHM and CSFDHM operators are observed to be reliable because they consider the interdependence of the input data. The suggested operators are compared in this study as well.

An algorithmic multiple attribute decision-making method for heart problem analysis under neutrosophic hypersoft expert set with fuzzy parameterized degree-based setting

A fuzzy parameterized neutrosophic hypersoft expert set (FpNHse-set) is one of the family members of fuzzy parameterized structures and a valuable extension of the neutrosophic soft expert set as well as the neutrosophic hypersoft set. This structure involves a multi-argument approximate function that has the ability to change the sub-characteristic pairs in the form of power set of universe. The main function of this structure is the classification of each character into sub-characteristic valued sets. Due to this prominent property, this mathematical structure is useful for uncertainties and also helps make the decision-making process more adaptable and dependable. By using the algebraic and basic ideas of the FpNHse-sets, a useful strategy, especially for medical diagnosis, known as Sanchez’s method has been used in this study. To see a reformed process for the medical diagnosis of heart disease, a useful combination of FpNHse-set and a modified Sanchez’s method has been made in this context. By using the real data from the Cleveland data set for heart disease, the implementation of the reform process has been made to see its veracity. Finally, a clear comparison of the used study with its existing studies has been made for the purpose of benefits.

Domination in Plithogenic product fuzzy graphs

Abstract The notion of Plithogenic vertex domination and Plithogenic edge domination in Plithogenic product fuzzy graphs (PPFGs) has been newly introduced and discussed based on P-weights of P-vertices and P-edges respectively with properties, results and examples. Plithogenic vertex domination number and Plithogenic edge domination number for a Plithogenic product fuzzy graph (PPFG), and the bounds and algorithms for and the maximum and minimum values and algorithms for the same are also investigatedthe same are also investigated. Perfect Plithogenic vertex domination and perfect Plithogenic edge domination are presented as special cases of Plithogenic vertex domination and Plithogenic edge domination respectively. It is observed that the P-vertex (P-edge) with the maximum P-weight exists in every Plithogenic vertex (edge) dominating set of a Plithogenic product fuzzy graph. The novelty in these ideas of domination is that a better perception of reality can be obtained through the analysis of both, Plithogenic vertex domination and Plithogenic edge domination, in any Plithogenic product fuzzy graphical structure.

Picture Fuzzy Subgroup

Picture fuzzy subgroup of a crisp group is established here and some properties connected to it are investigated. Also, normalized restricted picture fuzzy set, conjugate picture fuzzy subgroup, picture fuzzy coset, picture fuzzy normal subgroup and the order of picture fuzzy subgroup are defined. The order of picture fuzzy subgroup is defined using the cardinality of a special type of crisp subgroup. Some corresponding properties are established in this regard. Significant Statement. Subgroup is an important algebraic structure in the field of Pure Mathematics. Study of different properties of subgroup in fuzzy sense is an interesting fact to the readers because fuzzy sense is the extension of classical sense. Readers can easily observe how the properties of subgroup hold in fuzzy sense like classical sense. Picture fuzzy sense is the generalization of fuzzy sense. In other words, picture fuzzy sense can be treated as advanced fuzzy sense. Readers will be interested to study how the properties of subgroup hold when the number of components increases in fuzzy environment. Our study is actually the study of an important type of advanced fuzzy algebraic structure.

Evolution of irradiation damage in tungsten matrix and Y2O3 phase after low energy helium plasma exposure

Tungsten is the preferred material for the first wall. In this paper, W-0.5 %wt Y2O3 was selected for the exposure test of helium plasma, so that fuzz tendrils of considerable thickness were formed on its surface. By using ultrasonic dispersion, the tendril dispersion was obtained and observed through TEM. The fuzz tendrils on the W matrix surface were seen to have a complete tungsten crystal structure, along with bubbles of different sizes. The outer layer of the tendril is composed of an amorphous material, which is visible on the surface of the fuzz tendril. This is likely due to the subsequent of helium plasma exposure damage. Fuzz tendrils only appeared on the W matrix, whereas Y2O3 particles created nano-protrusions and samll cracks on the surface. The nano-protrusion morphology and EDS analysis, including the lack of Y in fuzz tendrils, indicate that Y2O3 particles were unable to form a fuzzy structure. It is evident that the defects distribution of W matrix and Y2O3 particles is altered due to helium plasma exposure. Near the surface of Y2O3 particles, fewer but larger bubbles were observed, whereas further away, smaller but denser bubbles were seen. In W matrix, bubbles were formed at a deeper level and were larger than the deepest bubbles in Y2O3 particles, likely caused by the lower migration energy. The different responses of W matrix and Y2O3 particles to helium plasma exposure have combined to further reveal the potential of increasing the plasma exposure resistance of plasma-oriented tungsten based materials.

A novel fuzzy TOPSIS method based on T-spherical fuzzy Aczel–Alsina power Heronian mean operators with applications in pharmaceutical enterprises’ selection

One of the most significant and complete approaches to accommodate greater uncertainty than current fuzzy structures is the T-Spherical Fuzzy Set (TSPFS). The primary benefit of TSPFS is that current fuzzy structures are special cases of it. Firstly, some novel TSPF power Heronian mean (TSPFPHM) operators are initiated based on Aczel–Alsina operational laws. These aggregation operators (AOs) have the capacity to eliminate the impact of uncomfortable data and can simultaneously consider the relationships between any two input arguments. Secondly, some elementary properties and core cases with respect to parameters are investigated and found that some of the existing AOs are special cases of the newly initiated aggregation operators. Thirdly, based on these AOs and Aczel–Alsina operational laws a newly advanced technique for order of preference by similarity to ideal solution (TOPSIS)-based method for dealing with multi-attribute group decision-making (MAGDM) problems in a T-Spherical fuzzy framework is established, where the weights of both the decision makers (DMs) and the criteria are completely unknowable. Finally, an illustrative example is provided to evaluate and choose the pharmaceutical firms with the capacity for high-quality, sustainable development in the TSPF environment to demonstrate the usefulness and efficacy. After that, the comparison analysis with other techniques is utilized to demonstrate the coherence and superiority of the recommended approach.

A novel fuzzy extended state observer-based control for electro-optical tracking system with disturbances and measurement noises: Design, analysis and experiments

In the electro-optical tracking system (ETS), the stability of line-of-sight (LOS) is usually limited by low and medium-frequency disturbances and measurement noises. Conventionally, the active disturbance rejection control (ADRC) strategy is an effective method to improve the stability of LOS; however, it is limited by the fixed observer bandwidth, which is the parameter of the extended state observer (ESO). Besides that, for conventional ESO, the conflict exists between disturbance rejection ability and noise attenuation ability. In this paper, this problem is tackled by transforming the ESO which is the core element of ADRC, into a novel fuzzy self-tuning observer structure. The proposed method is experimentally validated to effectively ensure the stability of the LOS after obtaining an optimal trade-off between disturbance rejection ability and noise attenuation ability.

Improved Gorilla Troops Optimizer-Based Fuzzy PD-(1+PI) Controller for Frequency Regulation of Smart Grid under Symmetry and Cyber Attacks

In a smart grid (SG) system with load uncertainties and the integration of variable solar and wind energies, an effective frequency control strategy is necessary for generation and load balancing. Cyberattacks are emerging threats, and SG systems are typical cyber-attack targets. This work suggests an improved gorilla troops optimizer (iGTO)-based fuzzy PD-(1+PI) (FPD-(1+PI)) structure for the frequency control of an SG system. The SG contains a diesel engine generator (DEG), renewable sources like wind turbine generators(WTGs), solar photovoltaic (PV), and storage elements such as flywheel energy storage systems (FESSs) and battery energy storage systems (BESSs) in conjunction with electric vehicles (EVs). Initially, the dominance of the projected iGTO over the gorilla troops optimizer (GTO) and some recently suggested optimization algorithms are demonstrated by considering benchmark test functions. In the next step, a traditional PID controller is used, and the efficacy of the GTO method is compared with that of the GTO, particle swarm optimization (PSO), and genetic algorithm (GA) methods. In the next stage, the superiority of the proposed FPD-(1+PI) structure over fuzzy PID (FPID) and PID structures is demonstrated under various symmetry operating conditions as well as under different cyberattacks, leading to a denial of service (DoS) and delay in signal transmission.

Measurement of carbon effect in land consolidation projects and evaluation of low-carbon promotion paths: a case study of Wudi County, Shandong Province, China.

Against the backdrop of China's "double carbon" objective, the exploration of low-carbon land consolidation has become a prominent area of focus for enhancing the development of ecological civilization. In this study, three typical projects at different time points (2016, 2019, and 2022) in Wudi County were selected to measure the carbon effect of land consolidation from four perspectives: artificial and industrial materials, mechanical shift consumption, land use structure, and farmland ecosystem. Based on the calculation of carbon effect of land consolidation by using carbon emission coefficient method, the changes of land use structure and carbon storage of farmland ecosystem before and after land consolidation were corrected by using GIS tools and net ecosystem productivity (NEP) model based on remote sensing technology, and the carbon emission intensity of each land consolidation project was finally obtained. The study summarized the influencing factors of carbon emissions through the above analysis and uses the fuzzy interpretation structure (FISM) model to provide the hierarchy of influencing factors of carbon emissions, thus proposing a low-carbon promotion path for land consolidation. The findings of this study can serve as a useful reference for low-carbon land consolidation efforts. The results showed that (1) the first, second, and third projects emitted 6140.06 t, 1243.78 t, and 17,604.62 t of carbon, respectively. Among them, the largest contributors to these emissions were labor and industrial materials, followed by mechanical shift; land use structure and farmland ecosystem were the main sources of carbon sinks and have a positive impact on the carbon cycle. (2) The carbon emission intensity of project one, project two, and project three after standardization is 0.26, 0.49, and 0.25, respectively, which are all at a high level. (3) According to the FISM model categorized 15 low-carbon upgrading paths, it was recommended that the government take a leading role in Wudi County by developing a scientific and rational construction plan. Additionally, efforts were made to actively protect farmland and forest land from destruction, reduce energy and material consumption, increase carbon storage in the farmland ecosystem, and promote low carbonization of land consolidation to the fullest extent possible.

INTEGRATING NEURO-FUZZY SYSTEMS FOR ENHANCED CANCER DATA ANALYSIS AND PREDICTION

The abstract for Integrating Neuro-Fuzzy structures for more significant most cancers statistics analysis and Prediction describes research carried out to examine using a sort of artificial intelligence, known as a Neuro-Fuzzy device, to analyze and expect facts from most cancer sufferers. by leveraging the strengths of both Neural Networks and Fuzzy common sense structures, Neuro-Fuzzy systems provide a powerful answer for complicated statistics analysis. This research examines and tests the overall performance of Neuro-Fuzzy systems on hard and fast benchmark datasets from most cancers Toolbox Markup Language (TMX). Consequences showed that Neuro-Fuzzy yielded a higher accuracy charge when compared to different device learning algorithms in studying information from a diverse set of patients. Furthermore, the researchers also stated that Neural-Fuzzy systems were able to discern subtypes of cancer in an affected person population, which had not been formerly feasible with different techniques. The work defined in the abstract could have a long way to attaining implications for the remedy and prognosis of most cancer patients. With the promising results of this, have a look at showing that Neuro-Fuzzy structures are able to distinguish between particular forms of cancer correctly; a more precise treatment plan might be created for people living with cancer. Additionally, with the improved accuracy of Neuro-Fuzzy structures, more excellent dependable predictions will be made about the progression of most cancers in a selected patient, helping doctors to plan treatments. Ordinary, the findings of the research summarized in this summary are especially significant as the advanced accuracy and capacity to figure out subtle differences in most cancer types keep the promise of improved remedies and prognoses for people living with cancer.

Extracellular polymeric substances altered the physicochemical properties of molybdenum disulfide nanomaterials to mitigate its toxicity to Chlorella vulgaris

Although the toxic effects of two-dimensional nanomaterials (2D-NMs) have been widely reported, the influence of extracellular polymeric substances (EPS) on the environmental fate and risk of 2D-NMs in aquatic environments is largely unknown, and the processes and mechanisms involved remain to be revealed. Herein, we investigated the impact of EPS secreted by microalgae (Chlorella vulgaris (C. vulgaris)) on the environmental transformation and risk of molybdenum disulfide (MoS2). We found that the attachment of EPS increased the thickness of MoS2 (from 2 nm to 5 nm), changed it from a monolayer sheet to a fuzzy multilayer structure, and promoted the formation of defects on MoS2. The blue-shift of the peak associated with the plasmon resonances in the 1 T phase and the generation of electron-hole pairs suggested that EPS altered the surface electronic structure of MoS2. EPS interacted mainly with the S atoms on the 1 T phase, and the attachment of EPS promoted the oxidation of MoS2. The reduction in hydrodynamic diameter (Dh) and the decrease in zeta potential indicated that EPS inhibited the agglomeration behavior of MoS2 and enhanced its dispersion and stability in aqueous media. Notably, EPS reduced the generation of free radicals (superoxide anion (•O2−), singlet oxygen (1O2), and hydroxyl radicals (•OH−)). Furthermore, EPS mitigated the toxicity of MoS2 to C. vulgaris, such as attenuated reduction in biomass and chlorophyll content. Compared to pristine MoS2, MoS2 + BG11 + EPS exhibited weaker oxidative stress, membrane damage and lipid peroxidation. The adsorption of EPS on MoS2 surface reduced the attachment sites of MoS2, making MoS2 less likely to be enriched on the cell surface. The findings have significant contribution for understanding the interactions between EPS and MoS2 in aquatic ecosystems, providing scientific guidance for risk assessment of 2D-NMs.