Fuzzy Soft Relations Research Articles

A novel approach towards web browser using the concept of a complex spherical fuzzy soft information

The modern technology is the practical application of scientific knowledge, whether in industry or daily life, for goals or purposes. More quickly than any other technological advancement in human history, digital technologies have advanced. The technology sector is expanding and provides both new educational opportunities and innovative, exciting products. Right now, one of the most widely used and fascinating technologies is the web browser. This article introduced the novel concepts of complex spherical fuzzy soft relations (CSFSRs) by using the Cartesian Product (CP) of two complex spherical fuzzy soft sets (CSFSSs). Additionally, examples are used to clarify various types of relations. Because it discusses all levels of membership, abstinence, and non-membership with multidimensional variables, the CSFSRs have a detailed structure. The CSFSR-based modelling tools developed in this research, which primarily rely on the score function, can be used to choose the best Web browser. The transaction could be as easy as users sharing records via a functional web browser. Finally, the advantages of this suggested structure are illustrated by contrasting it with alternative structures.

Mathematical analysis of big data analytics under bipolar complex fuzzy soft information

The aim of this study is to develop new and efficient theories for handling complex and unreliable data in real-world scenarios. The proposed approach integrates two distinct theories: the Bipolar Complex Fuzzy Set (BCFS) and the Soft Set (SS), resulting in a novel and superior method compared to existing solutions. Furthermore, the value of big data analytics cannot be overstated as it provides businesses with the opportunity to use their data to find areas for development and progress. To gain insights from raw data, it must first be collected and organized. Data modeling represents these large, complex data sets in a visual format, such as a chart or diagram. However, the visualization process often results in uncertainties and inaccuracies, highlighting the need for a more robust approach to data analysis. To address this issue, this paper introduces the concept of Bipolar Complex Fuzzy Soft Relations (BCFSRs), a fuzzy decision-making method within a complex bipolar fuzzy environment that can have the advantages of both a Bipolar Complex fuzzy relation and a soft relation at the same time. In BCFSRs, an element can have degrees of membership in both the positive and negative directions, reflecting a more nuanced and versatile representation of uncertainty or ambiguity. These mathematical ideas are explained through the Cartesian product of two Bipolar Complex Fuzzy Soft Sets (BCFSSs) and serve to simplify the decision-making process by presenting the BCFSSs in a clear and concise manner. The inventive notion of the BCFSRs elucidates the combined positive and negative effects of anything with parameterization. To support organizations in making data-driven choices and obtain insights for strategic planning and inventiveness, the analysis of big data is essential in several industries, including financial services, marketing, and medical treatment, among others. To choose the optimal big data analytics for efficient operation, this research presents modeling methodologies based on BCFSRs, including the formulation and analysis of scoring functions. The validity of the proposed work is demonstrated through a comparison study with existing methods, providing valuable insights for effective data analysis.

An integrated complex T-spherical fuzzy set and soft set model for quantum computing and energy resource planning

This study introduces the Complex T-Spherical Fuzzy Soft Set (CTSFSS), a novel and practical model for representing two-dimensional ambiguous information. This is achieved by integrating the Complex T-Spherical Fuzzy Set (CTSFS) with the Soft Set (SS). The development of the CTSFSS theory is motivated by the absence of neutral membership in complex q-rung orthopair fuzzy soft sets and the limitations of Traditional Spherical Fuzzy Soft Sets (TSFSS) in capturing two-dimensional data. Data storage and processing in the modern technological landscape necessitate sophisticated algorithmic computations and robust representation of information. To this end, computational systems predominantly rely on a binary system structured on two fundamental states: 0 (off) and 1 (on). Moreover, the significance of energy resources and computer-aided tools is underscored in this domain, especially considering the potential impact of quantum computing and advances in energy resources on the evolution of digital technology. In addressing these complexities, we propose Complex T-Spherical Fuzzy Soft Relations (CTSFSRs), formulated through the Cartesian product of two CTSFSSs. These relations are adept at handling complex and uncertain data in real-world scenarios. We define and categorize various types of CTSFSRs, followed by an in-depth analysis of their outcomes. Additionally, this paper introduces innovative visualization techniques based on CTSFSRs, tailored for decision-making processes involving energy resources and quantum computing applications. The efficacy and applicability of these proposed methodologies are substantiated through comparative analysis with existing models.

Analysis of Networks and Digital Systems by Using the Novel Technique Based on Complex Fuzzy Soft Information

In the last few years, intelligent industrial systems and consumer electronics are being developed extensively and broadly. Fuzzy logic and fuzzy techniques that integrate these approaches are recognized as effective ways to realize such intelligent functions. These intelligent systems rely on fuzzy control techniques i.e., common sense rules to describe system behavior instead of complex mathematical models. This work provides solutions to such uncertainties and aids in the relative decision-making processes. To this end, an innovative concept of complex fuzzy soft relation (CFSR) is defined based on the Cartesian product (CP) between two complex fuzzy soft sets (CFSSs). The main goal of this analysis is to develop some new and valuable concepts which will be suitable for managing awkward and unreliable information in real-life problems. The proposed idea is more dominant and superior to the prevailing ideas, where the presented idea is the modified technique of two different theories, called fuzzy set (FS) and soft set (SS). In addition, some reliable results have also been proved. Moreover, an application of the proposed techniques is proposed which demonstrates the process of choosing a good network. Finally, the advantages of the proposed framework are explained by the comparison with pre-existing frameworks.

Investigation of Robotics Technology Based on Bipolar Complex Intuitionistic Fuzzy Soft Relation

Investigation of Robotics Technology Based on Bipolar Complex Intuitionistic Fuzzy Soft Relation

Prediction Model of a Generative Adversarial Network Using the Concept of Complex Picture Fuzzy Soft Information

A computer vision model known as a generative adversarial network (GAN) creates all the visuals, including images, movies, and sounds. One of the most well-known subfields of deep learning and machine learning is generative adversarial networks. It is employed for text-to-image translations, as well as image-to-image and conceptual image-to-image translations. Different techniques are used in the processing and generation of visual data, which can lead to confusion and uncertainty. With this in mind, we define some solid mathematical concepts to model and solve the aforementioned problem. Complex picture fuzzy soft relations are defined in this study by taking the Cartesian product of two complex picture fuzzy soft sets. Furthermore, the types of complex picture fuzzy soft relations are explained, and their results are also discussed. The complex picture fuzzy soft relation has an extensive structure comprising membership, abstinence, and non-membership degrees with multidimensional variables. Therefore, this paper provides modeling methodologies based on complex picture fuzzy soft relations, which are used for the analysis of generative adversarial networks. In the process, the score functions are also formulated. Finally, a comparative analysis of existing techniques was performed to show the validity of the proposed work.

Mathematical analysis of generative adversarial networks based on complex picture fuzzy soft information

Generative Adversarial Networks (GANs) are the models that generate data samples from the statistical distribution of the data. It is one of the most well-known branches of machine learning and deep learning. Different techniques are involved in the processing and production of visual data, which sometimes gives rise to misperception uncertainties. Bearing this issue in mind, we define some solid mathematical concepts to model and resolve the stated problem named complex picture fuzzy soft relations (CPFSRs) which is defined by the Cartesian product (CP) of two complex picture fuzzy soft sets (CPFSSs). The major objective of this study is to develop some innovative and useful notions that may be used to handle difficult and inconsistent information in practical situations. The proposed notion is foremost and superior to the prevailing ideas, where the presented idea is the improved technique of two different theories, named picture fuzzy set (PFS) and soft set (SS). Additionally, it presents the picture fuzzy soft set (PFSS) in professional decision-making by reducing complexions. The evaluated CPFSRs are the improved versions of soft relations, fuzzy relations, complex soft relations, and complex fuzzy relations. Therefore, this paper provides modeling methodologies based on CPFSRs which are used for the analysis of electing the best GAN for effective working. In the process, the score functions are also formulated and analyzed. Finally, a comparative study of existing techniques has been done to show the validity of the proposed work.

Energy utilization area under Complex q-rung orthopair fuzzy soft information

<abstract> <p>The utilization of energy (EU) encompasses technologies aimed at discovering more effective methods for using electricity across various sectors, including residential, commercial, industrial, and transportation. Energy is an integral aspect of modern society and a driving force behind many processes in the universe. This paper aims to introduce a new concept, the Complex q-rung Orthopair Fuzzy Soft Relation (CqROFSRs), achieved through the Cartesian product of two Complex q-rung Orthopair Fuzzy Soft Sets (CqROFSSs). The proposed model has the capability to effectively capture and model graded imprecision and vagueness, which are commonly encountered in human interpretations. It provides a parameterized mathematical framework for ranking-based fuzzy modeling of two-dimensional paradoxical data. The theory integrates the CqROFS with the parametric structure of soft sets to achieve this purpose. Moreover, the utilization of complex numbers imbues these structures with the ability to effectively address phase-related and multidimensional challenges, thus conferring them with unparalleled power in managing ambiguity. Furthermore, we delved into various types of relationships, providing corresponding examples, which led to the establishment of accurate outcomes. The CqROFSRs framework is inclusive, encompassing both membership and non-membership degrees with regard to time duration. Additionally, the use of CqROFSRs techniques in selecting the optimal EU area for a daily living has been demonstrated, empowering individuals to make informed decisions and obtain verified results through the score function. To clarify the distinction, a comprehensive comparative analysis was conducted between the proposed concept and previous concepts.</p> </abstract>

Investigation of Blockchain Technology by Using the Innovative Concepts of Complex Pythagorean Fuzzy Soft Information

A blockchain is a valuable and proficient type of digital ledger technology that involves of expanding list of records, called blocks, that are strongly connected simultaneously using cryptography. Further, complex Pythagorean fuzzy sets (CPFSs) are the generalized form of the intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PyFSs), and complex intuitionistic fuzzy sets (CIFSs), used for evaluating the awkward and unreliable information in genuine life problems. In this analysis, we aim to diagnose the innovative idea of complex Pythagorean fuzzy soft relations (CPyFSRs) by using the Cartesian product (CP) of two complex Pythagorean fuzzy soft sets (CPyFSSs), which are computed with the help of two different ideas, called complex Pythagorean fuzzy relation and soft sets. Additionally, using the presented approaches, we examined different kinds of relations and also justified them with the help of some suitable examples. The CPyFSRs has a comprehensive structure because it is discussing both degrees of membership and non‐membership with multidimensional variable. Further, includes the CPyFSR‐based modeling techniques that use the score function to choose the best blockchain technology (BCT) to enhance the worth of the evaluated information. Using a good BCT, the transaction may be simply transferred record between users. Finally, the benefit of this proposed framework is demonstrated by comparing it to other frameworks to show the supremacy and feasibility of the diagnosed approaches.

Novel multi-criteria decision-making methods with soft rough q-rung orthopair fuzzy sets and q-rung orthopair fuzzy soft rough sets

The aim of this paper is to introduce the concepts of soft rough q-rung orthopair fuzzy set (SRqROFS) and q-rung orthopair fuzzy soft rough set (qROPFSRS) based on soft rough set and fuzzy soft relation, respectively. We define some fundamental operations on both SRqROFS and qROPFSRS and discuss some key properties of these models by using upper and lower approximation operators. The suggested models are superior than existing soft rough sets, intuitionistic fuzzy soft rough sets and Pythagorean fuzzy soft rough sets. These models are more efficient to deal with vagueness in multi-criteria decision-making (MCDM) problems. We develop Algorithm i (i = 1, 2, 3, 4, 5) for the construction of SRqROFS, construction of qROFSRS, selection of a smart phone, ranking of beautiful public parks, and ranking of government challenges, respectively. The notions of upper reduct and lower reduct based on the upper approximations and lower approximations by variation of the decision attributes are also proposed. The applications of the proposed MCDM methods are demonstrated by respective numerical examples. The idea of core is used to find a unanimous optimal decision which is obtained by taking the intersection of all lower reducts and upper reducts.

Approximations of fuzzy soft sets by fuzzy soft relations with image processing application

Fuzzy soft sets represent a generalization of fuzzy sets with considerable application potential in decision-making problems, optimization, and computer science. In the paper, we use the fact that the fuzzy soft sets powerset theory is defined by the monad and, using this theory, we introduce the concept of fuzzy soft relations defined by the monad. Using that general method, we can also introduce the fuzzy soft approximation of fuzzy soft sets defined by fuzzy soft relations. We show that fuzzy soft sets and fuzzy soft approximations can be naturally used in selective color segmentation problem, where reliable and fully automated methods do not yet exist.

ON SOFT AND FUZZY SOFT RELATIONS WITH THEIR APPLICATIONS

In our day to day life we face many problems which are abstract or vague in nature. These problems cannot be solved only by using simple mathematical tools. To deal with such kind of problems a new technique popularly known as Fuzzy Set Theory was discovered. Fuzzy set is the generalization of crisp set and is used in almost every field of life including Medical Sciences, Business, Administration, Social Science and Operation Research. Later on, a new concept of parameterization of power set of the universal set was introduced. Consequently, Fuzzy Soft Set Theory was defined by embedding Fuzzy Set and Soft Set. In the present communication fuzzy binary relation is described and its applications are studied. The concepts of soft and fuzzy soft relations are also defined with their applications in decision making problems.

Algorithm to compute transitive closure of fuzzy soft relation

Fuzzy soft set is a mapping from a parameter set to the collection of fuzzy subset of universal set. In this paper fuzzy soft relation is presented based on the cartesian product of fuzzy soft sets and the notion of fuzzy soft equivalence relation is introduced. The basic properties of these relations are studied to explain the concept of transitive closure of a fuzzy soft relation. Existence and uniqueness of transitive closure of a fuzzy soft relation is established and an algorithm to compute the transitive closure of a fuzzy soft relation is also given.

Q-Neutrosophic Soft Relation and Its Application in Decision Making.

Q-neutrosophic soft sets are essentially neutrosophic soft sets characterized by three independent two-dimensional membership functions which stand for uncertainty, indeterminacy and falsity. Thus, it can be applied to two-dimensional imprecise, indeterminate and inconsistent data which appear in most real life problems. Relations are a suitable tool for describing correspondences between objects. In this study we introduce and discuss Q-neutrosophic soft relations, which can be discussed as a generalization of fuzzy soft relations, intuitionistic fuzzy soft relations, and neutrosophic soft relations. Q-neutrosophic soft relation is a sub Q-neutrosophic soft set of the Cartesian product of the Q-neutrosophic soft sets, in other words Q-neutrosophic soft relation is Q-neutrosophic soft sets in a Cartesian product of universes. We also present the notions of inverse, composition of Q-neutrosophic soft relations and functions along with some related theorems and properties. Reflexivity, symmetry, transitivity as well as equivalence relations and equivalence classes of Q-neutrosophic soft relations are also defined. Some properties of these concepts are presented and supported by real life examples. Finally, an algorithm to solve decision making problems using Q-neutrosophic soft relations is developed and verified by an example to show the efficiency of this method.

Bipolar Fuzzy Soft Relations and Applications in Decision Making Problems

Bipolar Fuzzy Soft Relations and Applications in Decision Making Problems

Generalized intuitionistic fuzzy soft sets with applications in decision-making

The concept of intuitionistic fuzzy soft set (IFSS) arising from intuitionistic fuzzy set (IFS) is generalized by including a parameter reflecting a moderator's opinion about the validity of the information provided. The resulting generalized intuitionistic fuzzy soft set (GIFSS) finds a special role in the decision making applications. It can evaluate the given criteria along with the moderator's assessment of the furnished data. The properties of GIFSS are investigated and the associated relations called generalized intuitionistic fuzzy soft relations (GIFSR) are given. A similarity measure is given to compare two GIFSSs. As this is not applicable to fuzzy numbers, a new score function is devised to compare two intuitionistic fuzzy numbers (IFNs), the components of IFS. The effectiveness of the proposed GIFSS in decision making is demonstrated on four case studies.