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The mixed metric dimension of a graph is an important parameter in characterizing its structural complexity, specifically in nanoscale networks where precision is paramount. In this article, we calculate the mixed metric dimension of hexagonal nano-network, a modal with significant applications in nanotechnology and material science. Through rigorous analysis, we set up that the mixed metric dimension of the hexagonal nano-network is exactly three, highlighting its minimal but enough resolving set that uniquely identifies all vertices. Furthermore, we check out the exchange property within this context, demonstrating the robust adaptability of the hexagonal network's resolving sets. Our findings display that the alternate assets aren't the handiest preserved but stronger in these nano-networks, allowing for flexible adjustments in resolving sets without compromising the network's integrity. This examination offers critical insights into the fundamental properties of hexagonal nano-networks, offering a theoretical foundation for future research in nanomaterial design and optimization. The results underscore the potential of leveraging mixed metric dimensions and exchange properties to achieve efficient and scalable solutions in nano-network applications., (© 2024. The Author(s).) more...

As a useful tool for managing ambiguous and inconsistent data, the Single Value Neutrosophic Set (SVNSs) is an extension of both Fuzzy Sets (FSs) and Intuitionistic Fuzzy Sets (IFSs). In the field of information theory, metrics like similarity, entropy, and distance are important. Although a number of entropy measures for SVNSs have been put forth and used in real-world situations, both academic research and real-world applications have pointed out certain drawbacks. Additionally, the Similarity Measures (SMs) is a useful instrument for determining how similar any two fuzzy values are to one another. The distance between the values allows the current SMs to evaluate the similarity. However, due to a few characteristics and intricate value operations, there are irrational and nonsensical cases. To deal with these preposterous cases, this paper proposed a parametric similarity measure in view of three parameters m 1 , m 2 , m 3 in which decision makers can obtain the appropriate SMs by changing parameters with different decision styles. Furthermore, we analyze some existing SMs from a mathematical perspective and demonstrate the success of the proposed SMs using mathematical models. Ultimately, we apply the suggested SMs to resolve the Multi-Attribute Decision-Making (MADM) problems. We learn from the correlation and analysis that the suggested SM outperforms certain other SMs that are based on the SVNSs., Competing Interests: Authors declare no conflict of interest., (© 2024 The Authors.) more...

This article proposes a new multiattribute group decision-making (MAGDM) method with probabilistic linguistic information that considers the following three aspects: an allocation of ignorance information, a realization of group consensus, and an aggregation of assessments. To allocate ignorance information, an optimization model based on minimizing the distances among experts is developed. To measure the consensus degree, a consensus index that considers the information granules of linguistic terms (LTs) is defined. On this basis, a suitable optimization model is established to realize the group consensus adaptively by optimizing the allocation of information granules of LTs with the particle swarm optimization (PSO) algorithm. With an objective to reduce the information loss during aggregation phases, the process of generating comprehensive assessments of alternatives with the evidential reasoning (ER) algorithm is presented. Therefore, a new method is developed based on the adaptive consensus reaching (ACR) model and the ER algorithm. Finally, the applicability of the proposed method is demonstrated by solving a selection problem of a financial technology company. Comparative analyses are conducted to show the advantages of the proposed method. more...

Automatic retinal blood vessel segmentation is a key link in the diagnosis of ophthalmic diseases. Recent deep learning methods have achieved high accuracy in vessel segmentation but still face challenges in maintaining vascular structural connectivity. Therefore, this paper proposes a novel retinal blood vessel segmentation strategy that includes three stages: vessel structure detection, vessel branch extraction and broken vessel segment reconnection. First, we propose a multiscale linear structure detection network (MS-LSDNet), which improves the detection ability of fine blood vessels by learning the types of rich hierarchical features. In addition, to maintain the connectivity of the vascular structure in the process of binarization of the vascular probability map, an adaptive hysteresis threshold method for vascular extraction is proposed. Finally, we propose a vascular tree structure reconstruction algorithm based on a geometric skeleton to connect the broken vessel segments. Experimental results on three publicly available datasets show that compared with current state-of-the-art algorithms, our strategy effectively maintains the connectivity of retinal vascular tree structure., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Ltd. All rights reserved.) more...

The economic implications from the COVID-19 crisis are not like anything people have ever experienced. As predictions indicated, it is not until the year 2025 may the global economy recover to the ideal situation as it was in 2020. Regions lacked of developing category is among the mostly affected regions, because the category includes weakly and averagely potential power. For supporting the decision of economic system recovery scientifically and accurately under the stress of COVID-19, one feasible solution is to assess the regional economic restorability by taking into account a variety of indicators, such as development foundation, industrial structure, labor forces, financial support and government's ability. This is a typical multi-criteria decision-making (MCDM) problem with quantitative and qualitative criteria/indicator. To solve this problem, in this paper, an investigation is conducted to obtain 14 indicators affecting regional economic restorability, which form an indicator system. The interval type-2 fuzzy set (IT2FS) is an effective tool to express experts' subjective preference values (PVs) in the process of decision-making. First, some formulas are developed to convert quantitative PVs to IT2FSs. Second, an improved interval type-2 fuzzy ORESTE (IT2F-ORESTE) method based on distance and likelihood are developed to assess the regional economic restorability. Third, a case study is given to illustrate the method. Then, robust ranking results are acquired by performing a sensitivity analysis. Finally, some comparative analyses with other methods are conducted to demonstrate that the developed IT2F-ORESTE method can supporting the decision of economic system recovery scientifically and accurately., Competing Interests: Conflict of interestThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© The Author(s) 2022.) more...

Background and Objective: Accurate extraction of the coronary artery centerline is crucial in the processes of coronary artery reconstruction, coronary artery stenosis or lesion detection, and surgical navigation. Furthermore, in clinical medicine, the complex background of angiography, low signal-to-noise ratio, and complex vascular structure make coronary artery centerline extraction challenging. In this study, a direct centerline extraction method is proposed that automatically and accurately extracts vascular centerlines from X-ray coronary angiography images based on deep learning and conventional methods., Methods: In this study, a coronary artery centerline extraction method is proposed that comprises two parts: the preliminary centerline extraction network based on U-Net with a residual network, called C-UNet, and the multifactor centerline reconnection algorithm based on the geometric characteristics of blood vessels., Results: The qualitative and quantitative results demonstrate the effectiveness of the presented method. In this study, three widely used evaluation indices were adopted to evaluate the performance of the method: precision, recall, and F1_Score. The experimental results show that this method can accurately extract coronary artery centerlines., Conclusions: The proposed centerline extraction method accurately extracts centerlines from X-ray coronary angiography images and improves both the accuracy and continuity of centerline extraction., Competing Interests: Declaration of Competing Interest Authors declare that they have no conflict of interest., (Copyright © 2022 Elsevier B.V. All rights reserved.) more...

In this paper, we first introduce a new type of rough sets called α -upward fuzzified preference rodownward fuzzy preferenceugh sets using upward fuzy preference relation. Thereafter on the basis of α -upward fuzzified preference rough sets, we propose approximate precision, rough degree, approximate quality and their mutual relationships. Furthermore, we presented the idea of new types of fuzzy upward β -coverings, fuzzy upward β -neighborhoods and fuzzy upward complement β -neighborhoods and some relavent properties are discussed. Hereby, we formulate a new type of upward lower and upward upper approximations by applying an upward β -neighborhoods. After employing the upward β -neighborhoods based upward rough set approach to it any times, we can only get the six different sets at most. That is to say, every rough set in a universe can be approximated by only six sets, where the lower and upper approximations of each set in the six sets are still lying among these six sets. The relationships among these six sets are established. Subsequently, we presented the idea to combine the fuzzy implicator and t -norm to introduce multigranulation ( ℐ , T ) -fuzzy upward rough set applying fuzzy upward β -covering and some relative properties are discussed. Finally we presented a new technique for the selection of medicine for treatment of coronavirus disease (COVID-19) using multigranulation ( ℐ , T ) -fuzzy upward rough sets., (© 2021 Wiley Periodicals LLC.) more...

In regard to multicriteria decision making (MCDM) problems where the values of the criteria are expressed by 2-D uncertain linguistic variables (2DULVs), where the criteria are interactive and the criteria weights are incompletely known, two novel MCDM methods are proposed in this paper. First, we offer some novel operational laws of 2DULVs, which can avoid the operational results exceeding the boundary of linguistic term sets. Then, we propose four operators to capture the interactions over the criteria, namely, the 2-D uncertain linguistic Choquet averaging (2DULCA) operator, the 2-D uncertain linguistic Choquet geometric (2DULCG) operator, the Shapley 2DULCA (S2DULCA) operator, and the Shapley 2DULCG (S2DULCG) operator. In addition, we establish the models based on the maximization deviation approach and the Shapley function to get the criteria weights. Finally, we propose two novel MCDM methods under 2-D uncertain linguistic environments, where four examples are used to explain the created MCDM methods. Comparative experimental results are presented to highlight the superiorities of the created approaches. more...

This Letter presents an ultrahigh resolution optic fiber strain sensor. A random distributed feedback fiber laser (RDFL) is locked by the proposed frequency-shift Pound-Drever-Hall technique, which tracks the resonant frequency change of a π-phase-shifted fiber Bragg grating. The random distributed feedback for the RDFL gives a Lorentzian envelope over the original laser frequency noise, which can suppress the thermally induced frequency noise. The frequency noise of the laser is reduced from about 100 to 20 Hz/√Hz at 1 kHz. An ultrahigh dynamic strain resolution of 140  fε/√Hz at 1  kHz is achieved. more...

Linguistic neutrosophic numbers (LNNs) can easily describe the incomplete and indeterminate information by the truth, indeterminacy, and falsity linguistic variables (LVs), and the Hamy mean (HM) operator is a good tool to deal with multiple attribute group decision making (MAGDM) problems because it can capture the interrelationship among the multi-input arguments. Motivated by these ideas, we develop linguistic neutrosophic HM (LNHM) operator and weighted linguistic neutrosophic HM (WLNHM) operator. Some desirable properties and special cases of two operators are discussed in detail. Furthermore, considering the situation in which the decision makers (DMs) can't give the suitable weight of each attribute directly from various reasons, we propose the concept of entropy for linguistic neutrosophic set (LNS) to obtain the attribute weight vector objectively, and then the method for MAGDM problems with LNNs is proposed, and some examples are used to illustrate the effectiveness and superiority of the proposed method by comparing with the existing methods. more...

Archimedean t -conorm and t -norm provide the general operational rules for intuitionistic fuzzy numbers (IFNs). The aggregation operators based on them can generalize most of the existing aggregation operators. At the same time, the Heronian mean (HM) has a significant advantage of considering interrelationships between the attributes. Therefore, it is very necessary to extend the HM based on IFNs and to construct intuitionistic fuzzy HM operators based on the Archimedean t -conorm and t -norm. In this paper, we first discuss intuitionistic fuzzy operational rules based on the Archimedean t -conorm and t -norm. Then, we propose the intuitionistic fuzzy Archimedean Heronian aggregation (IFAHA) operator and the intuitionistic fuzzy weight Archimedean Heronian aggregation (IFWAHA) operator. We also further discuss some properties and some special cases of these new operators. Moreover, we also propose a new multiple attribute group decision making (MAGDM) method based on the proposed IFAHA operator and the proposed IFWAHA operator. Finally, we use an illustrative example to show the MAGDM processes and to illustrate the effectiveness of the developed method. more...

Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. Besides, it is a universal operator since it can contain other general operators by assigning some special parameter values. However, the MM can only process the crisp numbers. Inspired by the MM' advantages, the aim of this paper is to extend MM to process the intuitionistic fuzzy numbers (IFNs) and then to solve the multi-attribute group decision making (MAGDM) problems. Firstly, we develop some intuitionistic fuzzy Muirhead mean (IFMM) operators by extending MM to intuitionistic fuzzy information. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present two new methods to deal with MAGDM problems with the intuitionistic fuzzy information based on the proposed MM operators. Finally, we verify the validity and reliability of our methods by using an application example, and analyze the advantages of our methods by comparing with other existing methods., Competing Interests: The authors have declared that no competing interests exist. more...

The intuitionistic linguistic variables are easier to describe the fuzzy information which widely exists in the real world, and Bonferroni mean can capture the interrelationship of the individual arguments. However, the traditional Bonferroni mean can only process the crisp number. In this paper, we will extend Bonferroni mean to the intuitionistic linguistic environment and propose a multiple attribute decision making method with intuitionistic linguistic information based on the extended Bonferroni mean which can consider the interrelationship of the attributes. Firstly, score function and accuracy function of intuitionistic linguistic numbers are introduced. Then, an intuitionistic linguistic Bonferroni mean (ILBM) operator and an intuitionistic linguistic weighted Bonferroni mean (ILWBM) operator are developed, and some desirable characteristics of them are studied. At the same time, some special cases with respect to the parameters p and q in Bonferroni are analyzed. Based on the ILWBM operator, the approach to multiple attribute decision making with intuitionistic linguistic information is proposed. Finally, an illustrative example is given to verify the developed approach and to demonstrate its effectiveness. more...