Search Results (10)

Intuitionistic fuzzy (IF) $\beta$-minimal description operators can deal with noise data in the IF covering-based rough set theory. That is to say, they can be used to find data that we need in IF environments. For an IF $\beta$-covering approximation space (i.e., an IF environment) with a high cardinality, it would be tedious and complicated to use IF set representations to calculate them. Therefore, it is necessary to find a quick method to obtain them. In this paper, we present the notion of IF $\beta$-maximal description based on the definition of IF $\beta$-minimal description, along with the concepts of IF granular matrix and IF reduction. Moreover, we propose matrix calculation methods for IF covering-based rough sets, such as IF $\beta$-minimal descriptions, IF $\beta$-maximal descriptions, and IF reductions. Firstly, the notion of an IF granular matrix is presented, which is used to calculate IF $\beta$-minimal description. Secondly, inspired by IF $\beta$-minimal description, we give the notion of IF $\beta$-maximal description. Furthermore, the matrix representations of IF $\beta$-maximal descriptions are presented. Next, two types of reductions for IF $\beta$-covering approximation spaces via IF $\beta$-minimal and fuzzy $\beta$-minimal descriptions are presented, along with their matrix representations. Finally, the new calculation methods are compared with corresponding set representations by carrying out several experiments. Full article

In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy $\beta$-neighborhoods (IHF $\beta$-neighborhoods) and intuitionistic hesitant fuzzy complementary $\beta$-neighborhoods (IHFC $\beta$-neighborhoods. Through theoretical analysis of covering-based IHFRS models, we propose the intuitionistic hesitant fuzzy TOPSIS (IHF-TOPSIS) technique for order of preference by similarity to an ideal solution, addressing multicriteria decision-making (MCDM) challenges concerning the assessment of IHF data. A compelling example aptly showcases the suggested approach. Furthermore, we address MCDM problems regarding the assessment of IHF information based on CIHFRS models. Through comparison and analysis, it is evident that addressing MCDM problems by assessing IHF data using CIHFRS models proves more effective than utilizing intuitionistic fuzzy data with CIFRS models or hesitant fuzzy information with CHFRS models. IHFS emerges as a unique and superior tool for addressing real-world challenges. Additionally, covering-based rough sets (CRSs) have been successfully applied to decision problems due to their robust capability in handling unclear data. In this study, by combining CRSs with IHFS, four classes of CIFRS versions are established using IHF $\beta$-neighborhoods and IHFC $\beta$-neighborhoods. A corresponding approximation axiomatic system is developed for each. The roughness and precision degrees of CBIHFRS models are specifically talked about. The relationship among these four types of IHFRS versions and existing related versions is presented based on theoretical investigations. A method for MCDM problems through IHF information, namely, IHF-TOPSIS, is introduced to further demonstrate its effectiveness and applicability. By conducting a comparative study, the effectiveness of the suggested approach is evaluated. Full article

A fuzzy graph G is stated to have a set of trees as its tree cover if all the vertices of G are in their union. The maximum weight tree in the tree cover is assumed to be the cost of a tree cover for a fuzzy graph. For an integer $\beta >0$, finding a set of trees to cover all the vertices of a graph with minimum cost and at most $\beta$ number of spanning trees is known as the $\beta$-tree cover problem. Combining the tree-covering concept and facility location problem in a fuzzy environment for solving critical real-life problems in the recent era is a more fruitful approach. This issue strongly inspires us to develop a model with a practical algorithm. This paper provides an algorithm and complexity analysis to determine the number of rooted trees s covering the given fuzzy graph. In addition, a model is constructed with three optimization programming problems in the facility location problem and a tree covering fuzzy graphs. The model includes two types of the facility location problem, simultaneously addressing a variable covering radius and a fixed covering radius. A numerical example is provided to further describe the model, then, in the application part of the paper, the proposed model is applied to solve the real-life problem of maximizing demand saturation by minimizing the number of small denominations in the Indian banking system. This problem involves the data input of different indicators in the banking system along with details of the denominations of banknotes. Full article

As nonassociative fuzzy logic connectives, it is important to study fuzzy rough set models using overlap functions that replace the role of t-norms. Overlap functions and t-norms are logical operators with symmetry. Recently, intuitionistic fuzzy rough set and multi-granulation fuzzy rough set models have been proposed based on overlap functions. However, some results (that contain five propositions, two definitions, six examples and a proof) must be improved. In this work, we improved the existing results. Moreover, to extend the existing fuzzy rough sets, a new fuzzy covering rough set model was constructed by using the generalized overlap function, and it was applied to the diagnosis of medical diseases. First, we improve some existing results. Then, in order to overcome the limitations of the fuzzy covering rough set model based on overlap functions, a fuzzy $\beta$-covering rough set model based on generalized overlap functions was established. Third, some properties of the fuzzy $\beta$-covering rough set model based on generalized overlap functions are discussed. Finally, a multi-criteria decision-making (MCDM) method of the fuzzy $\beta$-covering rough set based on generalized overlap functions was proposed. Taking medical disease diagnosis as an example, the comparison with other methods shows that the proposed method is feasible and effective. Full article

Through a combination of overlap functions (which have symmetry and continuity) and a fuzzy $\beta$-covering fuzzy rough set (FCFRS), a new class of FCFRS models is established, and the basic properties of the new fuzzy $\beta$-neighborhood lower and upper approximate operators are analyzed and studied. Then the model is extended to the case of multi-granulation, and the properties of a multi-granulation optimistic fuzzy rough set are mainly investigated. By theoretical analysis for the fuzzy covering (multi-granulation) fuzzy rough sets, the solutions to problems in multi-criteria decision-making (MCDM) and multi-criteria group decision-making (MCGDM) problem methods are built, respectively. To fully illustrate these methodologies, effective examples are developed. By comparing the method proposed in this paper with the existing methods, we find that the method proposed is more suitable for solving decision making problems than the traditional methods, while the results obtained are more helpful to decision makers. Full article

This paper presents a comprehensive survey about the fundamental components of the artificial pancreas (AP) system including insulin administration and delivery, glucose measurement (GM), and control strategies/algorithms used for type 1 diabetes mellitus (T1DM) treatment and control. Our main focus is on the T1DM that emerges due to pancreas’s failure to produce sufficient insulin due to the loss of beta cells (β-cells). We discuss various insulin administration and delivery methods including physiological methods, open-loop, and closed-loop schemes. Furthermore, we report several factors such as hyperglycemia, hypoglycemia, and many other physical factors that need to be considered while infusing insulin in human body via AP systems. We discuss three prominent control algorithms including proportional-integral- derivative (PID), fuzzy logic, and model predictive, which have been clinically evaluated and have all shown promising results. In addition, linear and non-linear insulin infusion control schemes have been formally discussed. To the best of our knowledge, this is the first work which systematically covers recent developments in the AP components with a solid foundation for future studies in the T1DM field. Full article

On the basis of decision-theoretical rough sets (DTRSs), the three-way decisions give new model of decision approach for deal with the problem of decision. This proposed model of decision method is based on the loss function of DTRSs. First, the concept of fractional orthotriple fuzzy $\beta$ -covering (FOF $\beta$ -covering) and fractional orthotriple fuzzy $\beta$ -neighborhood (FOF $\beta$ -neighborhood) was introduced. We combined loss feature of DTRSs with covering-based fractional orthotriple fuzzy rough sets (CFOFSs) under the fractional orthotriple fuzzy condition. Secondly, we proposed a new FOF-covering decision-theoretical rough sets model (FOFCDTRSs) and developed related properties. Then, based on the grade of positive, neutral and negative membership of fractional orthotriple fuzzy numbers (FOFNs), five methods are established for addressing the expected loss expressed in the form of FOFNs and the corresponding three-way decisions are also derived. Based on this, we presented a FOFCDTRS-based algorithm for multi-criteria decision making (MCDM). Then, an example verifies the feasibility of the five methods for solving the MCDM problem. Finally, by comparing the results of the decisions of five methods with different loss functions. Full article

Since fuzzy $\beta$ -covering was proposed, few papers have focused on how to calculate the reduct in fuzzy $\beta$ -covering and how to update the reduct while adding and deleting some objects of the universe. Here, we propose a matrix-based approach for computing the reduct in a fuzzy $\beta$ -covering and updating it dynamically using a matrix. First, matrix forms for computing the reduct in a fuzzy $\beta$ -covering are proposed. Second, properties of the matrix-based approaches are studied while adding and deleting objects. Then, matrix-based algorithms for updating the reduct in a fuzzy $\beta$ -covering are proposed. Finally, the efficiency and validity of the designed algorithms are verified by experiments. Full article

In real life, human opinion cannot be limited to yes or no situations as shown in an ordinary fuzzy sets and intuitionistic fuzzy sets but it may be yes, abstain, no, and refusal as treated in Picture fuzzy sets or in Spherical fuzzy (SF) sets. In this article, we developed a comprehensive model to tackle decision-making problems, where strong points of view are in the favour; neutral; and against some projects, entities, or plans. Therefore, a new approach of covering-based spherical fuzzy rough set (CSFRS) models by means of spherical fuzzy $\beta$ -neighborhoods (SF $\beta$ -neighborhoods) is adopted to hybrid spherical fuzzy sets with notions of covering the rough set. Then, by using the principle of TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) to present the spherical fuzzy, the TOPSIS approach is presented through CSFRS models by means of SF $\beta$ -neighborhoods. Via the SF-TOPSIS methodology, a multi-attribute decision-making problem is developed in an SF environment. This model has stronger capabilities than intuitionistic fuzzy sets and picture fuzzy sets to manage the vague and uncertainty. Finally, the proposed method is demonstrated through an example of how the proposed method helps us in decision-making problems. Full article

Intuitionistic fuzzy rough sets are constructed by combining intuitionistic fuzzy sets with rough sets. Recently, Huang et al. proposed the definition of an intuitionistic fuzzy (IF) $\beta$ -covering and an IF covering rough set model. In this paper, some properties of IF $\beta$ -covering approximation spaces and the IF covering rough set model are investigated further. Moreover, we present a novel methodology to the problem of multiple criteria group decision making. Firstly, some new notions and properties of IF $\beta$ -covering approximation spaces are proposed. Secondly, we study the characterizations of Huang et al.’s IF covering rough set model and present a new IF covering rough set model for crisp sets in an IF environment. The relationships between these two IF covering rough set models and some other rough set models are investigated. Finally, based on the IF covering rough set model, Huang et al. also defined an optimistic multi-granulation IF rough set model. We present a novel method to multiple criteria group decision making problems under the optimistic multi-granulation IF rough set model. Full article