Intuitionistic Fuzzy Relations Research Articles

ON THE CARTESIAN PRODUCT INTUITIONISTIC FUZZY RELATION

In this paper we study the intuitionistic fuzzy relation and the operations on the intuitionistic fuzzy relations. We first define theCartesian product of intuitionistic fuzzy sets, then introduce the projection and the cylindric extension of intuitionistic fuzzy relation and show the relation between them. The concept of a composition operator for the intuitionistic fuzzy relations, which represents a generalization for those of fuzzy sets is also discussed in this paper.

Ranking Method of Intuitionistic Fuzzy Numbers and Multiple Attribute Decision Making Based on the Probabilistic Dominance Relationship

The uncertainty of intuitionistic fuzzy numbers (IFNs) is further enhanced by the existence of the degree of hesitation (DH). The shortcomings of existing researches are mainly reflected in the following situations: when comparing IFNs, the comparison rules of IFNs are difficult to apply to the comparison of any two IFNs, or the relevant methods do not fully consider the uncertainty expressed by DH. Thus, the rationality of the decision results needs to be improved. On the other hand, multi-attribute decision making (DADM) based on IFNs is often not objective due to the need to determine the attribute weight. Moreover, the strict condition of attribute aggregation of classical dominance relation makes it a method that fails considering the practical application. Aiming at the comparison problem of IFNs, this paper takes probability conversion as the starting point and proposes an IFN comparison method based on the area method, which can better deal with the comparison problem of “either superior or inferior” IFNs. In addition, aiming at the MADM problem of an intuitionistic fuzzy information system, we propose an intuitionistic fuzzy probabilistic dominance relation model and construct the MADM method under the probabilistic dominance relation. The series properties of IFNs and probabilistic dominance relation were summarized and proved, which theoretically ensured the scientificity and rigor of the method. The results show that the comparison and ranking method of IFNs proposed in this paper can be applied to the comparison of any two IFNs, and the dominance degree of IFNs is presented in the form of probability, which is more flexible and practical than the classical method. The probabilistic dominance relation method based on IFNs avoids the problem of determining attribute weights subjectively or objectively, and the decision maker can reflect decision preference by adjusting decision parameters to better match the actual problem. The application of this model to a campus express site evaluation further verifies the feasibility of the proposed method and the rationality of the results. In addition, various extension problems of the model and method proposed in this paper are discussed, which pave the way for future related research. This paper constructs a complete decision-making framework through theoretical analysis and application from practical problems, which provides a reference for enriching and improving uncertain decision-making theory and the MADM method.

Deriving priority vector from pairwise comparisons matrix with fuzzy elements by solving optimization problem

Pairwise comparisons matrix with fuzzy elements (FPCM) are appropriate for the decision makers who are uncertain about the relative importance of elements. We can primarily find them in Fuzzy Analytic Hierarchy Process, PROMETHEE, TOPSIS methods, and many exact and heuristic algorithms. They are also useful in aggregating pairwise comparisons, particularly in consensus group decision making problems and they form the basis for many decision-making models as intuitionistic fuzzy relations, pythagorean, q-rung orthopair fuzzy preference relations, hesitant or interval fuzzy sets, and also stochastic judgments. Here, the decision model is formulated by investigating pairwise comparisons matrices (PCMs) with elements from abelian linearly ordered group (alo-group), which enables unifying multiplicative, additive and fuzzy PCMs. Then we define a novel concept of consistency, coherence and intensity of FPCMs, and propose a number of optimization methods for finding a consistent vector, coherent vector and intensity vector of a FPCM satisfying the desirable properties. Finally, two illustrating examples are discussed.

PN-GCN: Positive-negative graph convolution neural network in information system to classification

Graph convolution neural network (GCN) shows strong performance in non-Euclidean structure data. In recent years, many researchers have applied GCN to Euclidean structure data, such as images and languages, and obtained excellent results, which expanded the application range of GCN. Despite a large number of related methods, few studies deal with information systems from the perspective of graphs. In fact, the information system is also a non-Euclidean data structure, and there is serious information loss when using classical measurement methods to construct its data structure. Thus, the promotion of GCN is hindered in information systems. This paper applies GCN to the classification of information systems. Firstly, an intuitionistic fuzzy relation, called positive-negative relation, is established in the information system, and the physical meaning of this relationship is explained. Secondly, based on the positive-negative relation, a positive-negative relation graph convolution neural network model is constructed called PN-GCN. Finally, the effectiveness and robustness of PN-GCN are validated through experiments.

Some notes on intuitionistic fuzzy equivalence relations and their use on real data

The research presented in this paper is motivated by possibilities of using fuzzy equivalence relations to classify the data into the specific classes. We try to improve these results with the use of intuitionistic fuzzy equivalence relations. We define the basic structures and their properties, which are used in the paper. Then we present the data which we decided to classify and the methods of processing these data. At the end of the paper we discus obtained results and problems which occurred during the processing of the selected data.

A novel intuitionistic fuzzy time series method based on bootstrapped combined pi-sigma artificial neural network

Intuitionistic fuzzy time series forecasting methods have been started to solve the forecasting problems in the literature. Intuitionistic fuzzy time series methods use both membership and non-membership values as auxiliary variables in their models. Because intuitionistic fuzzy sets take into consideration the hesitation margin and so the intuitionistic fuzzy time series models use more information than fuzzy time series models. The background of this study is about intuitionistic fuzzy time series forecasting methods. The study aims to propose a novel intuitionistic fuzzy time series method. It is expected that the proposed method will produce better forecasts than some selected benchmarks. The proposed method uses bootstrapped combined Pi-Sigma artificial neural network and intuitionistic fuzzy c-means. The combined Pi-Sigma artificial neural network is proposed for modelling the intuitionistic fuzzy relations. The proposed method is applied to different sets of SP&500 stock exchange time series. The proposed method can provide more accurate forecasts than established benchmarks for the SP&500 stock exchange time series. The most important contribution of the proposed method is that it creates statistical inference: probabilistic forecasting, confidence intervals and the empirical distribution of the forecasts. Moreover, the proposed method is better than the selected benchmarks for the SP&500 data set.

Analysis of evolutionary process in intuitionistic fuzzy set theory: A dynamic perspective

Since the intuitionistic fuzzy set theory was proposed, it has received widespread attention. To get a deeper understand of this field, this paper analyzes a total of 2913 papers downloaded from the Web of Science (WoS) from 1984 to 2019 from different perspectives. On the one hand, this research identifies important themes and their interrelationships, showing the thematic evolution of this field vividly. On the other hand, this research digs out the knowledge diffusion paths of this domain with the help of global and key-route main paths. From the perspective of the thematic evolution, five thematic area are detected including Intuitionistic fuzzy relation, IVIFS-Similarity, MCDM/MADM-GDM, Aggregation operator and Extensions of IFS. Among them, MCDM/MADM-GDM has evolved from an emerging theme to a motor theme being the most important topic and GDM integrating themes MADM、MCDM and Aggregation operator shows continuous growth. From the perspective of knowledge diffusion paths, research topic has gradually translated from theorical construction to practical application, and several factors such as self-citation, indirect citation, hierarchy and references that may influence the result of the main path are discussed. In general, this research systematically provides scholars with the development process in this domain, which is conductive to them to fully grasp the state-of-the-art research.

Generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systems

The fuzzy set theory enables us to represent our knowledge under multiple interpretations and axiomatic foundations from linguistic to computational representations. While the intuitionistic fuzzy set, as a generalization of the fuzzy set, cannot only represent the tolerance levels, but also the intolerance levels which a decision maker can tolerate and cannot tolerate in the accomplishment of a linguistic interpretation, in this paper, we introduce the generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations. It is shown that such problems can be transformed into the classical (nonfuzzy) generalized variational inequalities by means of level sets of the intuitionistic fuzzy relation. Furthermore, the equivalence between the generalized variational inequalities with intuitionistic fuzzy relations and the fuzzy fixed point problems is established. Finally, based on the projection method, we propose an iterative algorithm and a projected neural network model for the generalized variational inequalities with intuitionistic fuzzy relations, and the stability of the proposed projected dynamical system is also investigated.

A New Approach to Model Machine Learning by Using Complex Bipolar Intuitionistic Fuzzy Information

Many industries are developing robust models, capable of analyzing huge and complex data by using machine learning (ML) while delivering faster and more accurate results on vast scales. ML is a subfield of artificial intelligence, which is broadly defined as the capability of a machine to imitate intelligent human behavior. ML tools enable organizations to swiftly identify profitable opportunities and potential risks. Besides these uses, ML also has a wide range of applications in our daily lives. So, the development in ML is most important in this age of digital system to solve more complex problems. In order to further develop ML and diminish the uncertainties to improve accuracy, an innovative concept of complex bipolar intuitionistic fuzzy sets (CBIFSs) is introduced in this article. Further, the Cartesian product of two CBIFSs is defined. Moreover, the complex bipolar intuitionistic fuzzy relations (CBIFRs) and their types with suitable examples are defined. In addition, some important results and properties are also presented. The proposed modeling techniques are used to study different ML factors and their interrelationship, so that the functionality of ML might be enhanced. Furthermore, the advantages and benefits of proposed methods are described by their side to side comparison with preexisting frameworks in the literature.

Latent fingerprint enhancement and matching using intuitionistic type-2 fuzzy

Latent fingerprints are obtained from crime places by law enforcement and forensic agencies to identify the suspect. The latent fingerprints have vague ridge structures and various overlapping valley-based structures that result in low image quality. Furthermore, background noise, low contrast, and low information content make feature extraction difficult. To address these challenges, we propose a novel intuitionistic type-2 fuzzy relation for enhancing image quality. And to improve the matching score, a crossing number method is applied to extract minutiae points. The matching score is calculated using four different distance algorithms: Manhattan distance, Euclidean distance, Earth mover's distance, and chi-square distance. The proposed methodology is evaluated using three datasets IIITD, FVC-2004-1, and FVC-2004-2. The experimental results show that the proposed method yields satisfactory results, with the chi-square distance achieving the highest accuracy. The proposed method can be used by law enforcement and forensic agencies to reduce the workload.

Interval-valued intuitionistic fuzzy linear transformation

In this paper we introduce the concept of interval-valued intuitionistic fuzzy relations(in biefly IVIFR) and composition of IVIFR-equations. Then we continued it to interval-valued intuitionistic fuzzy linear transformation(in brief IVIFL-transformation) and discussed its properties. Also introduced the concept of composition of IVIFL-transformations.

A Novel Intuitionistic Fuzzy Time Series Method Based on Bootstrapped Combined Pi-Sigma Artificial Neural Network

Background: Intuitionistic fuzzy time series forecasting methods have been started to solve the forecasting problems in the literature. Intuitionistic fuzzy time series methods use both membership and non-membership values as auxiliary variables in their models. Because intuitionistic fuzzy sets take into consideration the hesitation margin and so the intuitionistic fuzzy time series models use more information than fuzzy time series models. The background of this study is about intuitionistic fuzzy time series forecasting methods. Objective: The study aims to propose a novel intuitionistic fuzzy time series method. It is expected that the proposed method will produce better forecasts than some selected benchmarks. Method: The proposed method uses bootstrapped combined Pi-Sigma artificial neural network and intuitionistic fuzzy c-means. The combined Pi-Sigma artificial neural network is proposed to model the intuitionistic fuzzy relations. Results and Conclusion: The proposed method is applied to different sets of SP&500 stock exchange time series. The proposed method can provide more accurate forecasts than established benchmarks for the SP&500 stock exchange time series. The most important contribution of the proposed method is that it creates statistical inference: probabilistic forecasting, confidence intervals and the empirical distribution of the forecasts. Moreover, the proposed method is better than the selected benchmarks for the SP&500 data set.

Norms over intuitionistic fuzzy congruence relations on rings

In this paper, by using norms, we define the concept of intuitionistic fuzzy equivalence relations and intuitionistic fuzzy congruence relations on ring R and we investigate some assertions. Also we define intuitionistic fuzzy ideals of ring R under norms and compare this with fuzzy equivalence relation and fuzzy congruence relation on ring R such that we define new introduced ring.

Evaluating Blockchain requirements for effective digital supply chain management

Collapsing traditional supply chain (SC) nodes into digitally interconnected networks creates several opportunities for efficiency, cost savings, and SC traceability. Blockchain is one of the pioneering transformative 4.0 technologies and is seen as the backbone of digital SCs (DSCs). Several attempts have been made to create explorative designs or models, however, forming a strategic Blockchain vision remains a challenge. This paper specifies those customer needs and design requirements that should be prioritized with a systematic approach for effective Blockchain integration into SCs. The proposed functional methodology provides a practical roadmap for practitioners. It is based on the House of Quality (HoQ) method, with its customer-focused design aspect, utilizing a group decision making (GDM) approach with an incomplete intuitionistic fuzzy relation (IIFR) extension. The GDM approach is employed to overcome the biases of decision making, while IIFRs deal with different or complementary focus centers in qualitative data. The usefulness of this methodology is tested with an application, and the results are validated by experts in the field. The results indicate that a Blockchain-based DSC (BC-DSC) is expected to deliver continuing financial benefit, efficient use of time, and the ability to support. Automation, effective coordination, and conformity are identified as highly critical design requirements. GDM and IIFR are combined for the first time in the literature. The originality of this paper comes from its generation of critical factors geared to obtaining an effective BC-DSC structure and the implementation of HoQ as an efficient tool for design.

Investigation of Cyber-Security and Cyber-Crimes in Oil and Gas Sectors Using the Innovative Structures of Complex Intuitionistic Fuzzy Relations.

Recently, there has been enormous development due to advancements in technology. Industries and enterprises are moving towards a digital system, and the oil and gas industries are no exception. There are several threats and risks in digital systems, which are controlled through cyber-security. For the first time in the theory of fuzzy sets, this research analyzes the relationships between cyber-security and cyber-crimes in the oil and gas sectors. The novel concepts of complex intuitionistic fuzzy relations (CIFRs) are introduced. Moreover, the types of CIFRs are defined and their properties are discussed. In addition, an application is presented that uses the Hasse diagram to make a decision regarding the most suitable cyber-security techniques to implement in an industry. Furthermore, the omnipotence of the proposed methods is explained by a comparative study.

Cybersecurity against the Loopholes in Industrial Control Systems Using Interval-Valued Complex Intuitionistic Fuzzy Relations

Technology is rapidly advancing and every aspect of life is being digitalized. Since technology has made life much better and easier, so organizations, such as businesses, industries, companies and educational institutes, etc., are using it. Despite the many benefits of technology, several risks and serious threats, called cyberattacks, are associated with it. The method of neutralizing these cyberattacks is known as cybersecurity. Sometimes, there are uncertainties in recognizing a cyberattack and nullifying its effects using righteous cybersecurity. For that reason, this article introduces interval-valued complex intuitionistic fuzzy relations (IVCIFRs). For the first time in the theory of fuzzy sets, we investigated the relationships among different types of cybersecurity and the sources of cyberattacks. Moreover, the Hasse diagram for the interval-valued complex intuitionistic partial order set and relation is defined. The concepts of the Hasse diagram are used to inspect different cybersecurity techniques and practices. Then, using the properties of Hasse diagrams, the most beneficial technique is identified. Furthermore, the best possible selection of types of cybersecurity is made after putting some restrictions on the selection. Lastly, the advantages of the proposed methods are illuminated through comparison tests.

Linear Diophantine Fuzzy Relations and Their Algebraic Properties with Decision Making

Binary relations are most important in various fields of pure and applied sciences. The concept of linear Diophantine fuzzy sets (LDFSs) proposed by Riaz and Hashmi is a novel mathematical approach to model vagueness and uncertainty in decision-making problems. In LDFS theory, the use of reference or control parameters corresponding to membership and non-membership grades makes it most accommodating towards modeling uncertainties in real-life problems. The main purpose of this paper is to establish a robust fusion of binary relations and LDFSs, and to introduce the concept of linear Diophantine fuzzy relation (LDF-relation) by making the use of reference parameters corresponding to the membership and non-membership fuzzy relations. The novel concept of LDF-relation is more flexible to discuss the symmetry between two or more objects that is superior to the prevailing notion of intuitionistic fuzzy relation (IF-relation). Certain basic operations are defined to investigate some significant results which are very useful in solving real-life problems. Based on these operations and their related results, it is analyzed that the collection of all LDF-relations gives rise to some algebraic structures such as semi-group, semi-ring and hemi-ring. Furthermore, the notion of score function of LDF-relations is introduced to analyze the symmetry of the optimal decision and ranking of feasible alternatives. Additionally, a new algorithm for modeling uncertainty in decision-making problems is proposed based on LDFSs and LDF-relations. A practical application of proposed decision-making approach is illustrated by a numerical example. Proposed LDF-relations, their operations, and related results may serve as a foundation for computational intelligence and modeling uncertainties in decision-making problems.

Isomorphism Theorems on Intuitionistic Fuzzy Abstract Algebras

The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems were proved by authors in 2017. In this study, homomorphism between intuitionistic fuzzy abstract algebras is defined, intuitionistic fuzzy function is examined and then intuitionistic fuzzy congruence relations are defined on intuitionistic fuzzy abstract algebra. First and third isomorphism theorems on intuitionistic abstract algebras are introduced.

Intuitionistic fuzzy congruences on product lattices under norms

The aim of this paper is to further develop intuitionistic fuzzy congruences on product lattices under norms. Firstly, the notions of intuitionistic fuzzy equivalence relation on product lattices under norms and intuitionistic fuzzy congruences on product lattices under norms are introduced. Secondly, the characterizations of them are investigated. Tirdly, the direct product of them is studied. Finally, it is considered that the factor lattice corresponding of them is isomorphic to the product of the factor lattices of the component lattices.

A novel intuitionistic fuzzy preference relations for multiobjective goal programming problems

This paper investigates novel intuitionistic fuzzy preferences relations to determine the imprecise linguistic terms with fuzzy goals. The proposed intuitionistic fuzzy goal programming (IFGP) considers the degree of vagueness and hesitations simultaneously. Different sorts of membership functions such as linear, exponential, parabolic, and hyperbolic have been introduced to depict the linguistic importance term. The overall satisfaction level is achieved by maximizing the convex combination of each fuzzy goals and the preference relations simultaneously. To verify and validate the proposed IFGP model, a numerical example is presented with the comparative study. Further, it is also applied to a banking financial statement management system problem. The proposed IFGP approach outperforms over others. At last, the conclusion and future research direction are suggested based on the performed study.