Score Function Research Articles

The Perfect Score Function and Optimized Weighted Geometric Operator for Ranking Single‐Valued Neutrosophic Numbers in the Decision‐Making Process

The single‐valued neutrosophic set (SVNS) is a more common platform for representing the degree of truth, indeterminacy, and falsity memberships. Indeterminacy is an important aspect of SVNS, and the score function (SF) is important in ranking alternatives in decision‐making scenarios. When the score and accuracy values for different SVNNs were equal, existing SFs were unable to rank the alternatives. To address the limitations, this paper introduces the perfect score function (PSF) as a solution for ranking single‐valued neutrosophic numbers (SVNNs) without any errors and presents the concepts of strong and weak SVNSs. This article has emphasized the drawbacks of the existing SF in SVNNs. Additionally, we propose an optimized weighted geometric operator (OWGO) for SVNNs, and its properties such as idempotency, boundedness, monotonicity, and commutativity are explored. Furthermore, the decision‐making approach has been depicted based on the proposed score function and OWGO to select the finest faculty for a university.

Score Prior Guided Iterative Solver for Speckles Removal in Optical Coherent Tomography Images.

Optical coherence tomography (OCT) is a widely used non-invasive imaging modality for ophthalmic diagnosis. However, the inherent speckle noise becomes the leading cause of OCT image quality, and efficient speckle removal algorithms can improve image readability and benefit automated clinical analysis. As an ill-posed inverse problem, it is of utmost importance for speckle removal to learn suitable priors. In this work, we develop a score prior guided iterative solver (SPIS) with logarithmic space to remove speckles in OCT images. Specifically, we model the posterior distribution of raw OCT images as a data consistency term and transform the speckle removal from a nonlinear into a linear inverse problem in the logarithmic domain. Subsequently, the learned prior distribution through the score function from the diffusion model is utilized as a constraint for the data consistency term into the linear inverse optimization, resulting in an iterative speckle removal procedure that alternates between the score prior predictor and the subsequent non-expansive data consistency corrector. Experimental results on the private and public OCT datasets demonstrate that the proposed SPIS has an excellent performance in speckle removal and out-of-distribution (OOD) generalization. Further downstream automatic analysis on the OCT images verifies that the proposed SPIS can benefit clinical applications. The data and code are available at https://github.com/ lisanqian1212/SPIS.

Multi-criteria group decision making approach based on a new type of neutrosophic vague approach is used to select the shares of the companies for purchase

In this paper, we introduce the neutrosophic vague soft set, a combination of vague and neutrosophic soft sets. With the help of aggregated operations, we discuss neutrosophic vague soft sets. Multi-criteria group decision making can be evaluated effectively using the VIKOR approach. In this approach, the score function is generated by aggregating the VIKOR method to a neutrosophic vague soft approach. With the help of closeness values, alternative solutions are presented as optimal ones. To invest some money into the top five companies on the stock exchange, an investment company intends to purchase shares of the companies. Their investment strategy was to allocate some of their cash in percentages of 30 dollars, 25 dollars, 20 dollars, 15 dollars, and 10 dollars according to the top five ranked companies to minimize this effect.

A q-rung orthopair fuzzy decision-making framework considering experts trust relationships and psychological behavior: An application to green supplier selection

The selection of an optimal supplier is a critical and open challenge in supply chain management. While experts' assessments significantly influence the supplier selection process, their subjective interactions can introduce unpredictable uncertainty. Existing methods have limitations in effectively representing and handling this uncertainty. The paper aims to address these challenges by proposing a novel approach that leverages q-rung orthopair fuzzy sets (q-ROFSs). The novelty of the proposed approach lies in its ability to accurately capture experts' preferences through the use of q-ROFSs, which offer membership and non-membership degrees, providing a broader expression space compared to conventional fuzzy sets. Additionally, it incorporates social network analysis (SNA) to effectively consider the trust relationships among experts. The proposed approach is divided into three stages. The first stage, presents a novel method to determine experts' weights by combining SNA, the Bayesian formula, and the maximum entropy principle. This approach allows for a more precise representation of varying levels of expertise and influence among experts, addressing the uncertainty arising from subjective interactions. The second stage introduces a hybrid weight determination method to determine criteria weights within the context of q-ROFSs. Entropy plays a crucial role in capturing fuzziness and uncertainty in q-ROFSs, while the projection measure simultaneously provides information about the distance and angle between alternatives. By employing both objective weights estimated using entropy and normalized projection measure and subjective weights derived using an aggregation operator and a score function, the presented approach achieves a comprehensive assessment of criteria importance. To incorporate both subjective and objective weights effectively, game theory is applied which allows us to align decision-making with both quantitative and qualitative aspects, making the method more versatile and applicable. The third stage redefines the traditional Combined Compromise Solution (CoCoSo) method using Bonferroni mean operators which captures interrelationships among arguments to be aggregated. Furthermore, in recognition of the importance of an expert risk preferences and psychological behaviors, we apply regret theory, ensuring that the chosen solutions align more effectively with their underlying preferences and aspirations. The applicability and effectiveness of the proposed approach are demonstrated through a numerical example of green supplier selection. The comparative analysis illustrates the practicality and real-world relevance while the sensitivity analysis, confirms the stability and robustness of the proposed approach.

CODAS method for Pythagorean 2-tuple linguistic multiple attribute group decision making

The evaluation of the financial performance of universities is conducive to the sustainable development of universities. Based on this, we extend the traditional CODAS (COmbinative Distance-based ASsessment) method to the Pythagorean 2-tuple linguistic fuzzy environment and propose a P2TL-CODAS model to evaluate the financial management performance of universities. Firstly, we briefly describe the definition, the score function, accuracy function, operational laws and the distance calculating method of P2TLSs. Next, two aggregation operators of P2TL including Pythagorean 2-tuple linguistic weighted averaging (P2TLWA) operator and Pythagorean 2-tuple linguistic weighted geometric (P2TLWG) operator are also introduced to fuse overall Pythagorean 2-tuple linguistic evaluation information. Then the steps of CODAS method are depicted briefly. Moreover, we use linguistic Pythagorean 2-tuple linguistic fuzzy numbers to extend the CODAS method. The P2TL-CODAS model is established and all computing steps are simply presented. Furthermore, we apply the proposed method to evaluate the financial management performance about five universities. Finally, a comparison between P2TL-CODAS method and P2TL-TODIM method is made to demonstrate the stability of the new method. The results show that the proposed method has unique advantages.

Complex interval-value intuitionistic fuzzy sets: Quaternion number representation, correlation coefficient and applications

<abstract><p>Complex interval-valued intuitionistic fuzzy sets not only consider uncertainty and periodicity semantics at the same time but also choose to express the information value with an interval value to give experts more freedom and make the solution to the problem more reasonable. In this study, we used the interval quaternion number space to generalize and extend the utility of complex interval-valued intuitionistic fuzzy sets, analyze their order relation, and offer new operations based on interval quaternion numbers. We proposed a new score function and correlation coefficient under interval quaternion representation. We applied the interval quaternion representation and correlation coefficient to a multi-criterion decision making model and applied the model to enterprise decision-making.</p></abstract>

DIFFUSION-MODEL-ASSISTED SUPERVISED LEARNING OF GENERATIVE MODELS FOR DENSITY ESTIMATION

We present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks (GANs), normalizing flows, and variational auto-encoders (VAEs), are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple, fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require the use of reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the University of California Irvine (UCI) repository.

Innovative approaches to solar cell selection under complex intuitionistic fuzzy dynamic settings

<abstract> <p>The need to meet current energy demands while protecting the interests of future generations has driven people to adopt regulatory frameworks that promote the careful use of limited resources. Among these resources, the sun is an everlasting source of energy. Solar energy stands out as a prime example of a renewable and environmentally friendly energy source. An imperative requirement exists for precise and dependable decision-making methods for the selection of the most efficacious solar cell. We aimed to address this particular issue. The theory of complex intuitionistic fuzzy sets (CIFS) adeptly tackles ambiguity, encompassing complex problem formulations characterized by both intuitionistic uncertainty and periodicity. We introduced two aggregation operators: The complex intuitionistic fuzzy dynamic ordered weighted averaging (CIFDOWA) operator and the complex intuitionistic fuzzy dynamic ordered weighted geometric (CIFDOWG) operator. Noteworthy features of these operators were stated, and significant special cases were meticulously outlined. An updated score function was devised to address the deficiencies, identified in the current score function within the context of CIF knowledge. In addition, we devised a methodical strategy for managing multiple attribute decision-making (MADM) problems that involve CIF data by implementing the proposed operators. To demonstrate the efficacy of the formulated algorithm, we presented a numerical example involving the selection of solar cells together with a comparative analysis with several well-established methodologies.</p> </abstract>

The STOP-BANG score and lung function in a general population.

Obstructive sleep apnea (OSA) commonly coexists with lung disease. However, the association between OSA components and lung function remains unclear. This study estimated STOP-BANG scores according to lung function using nationwide Korean data. Three thousand and two hundred eighty adults with available STOP-BANG scores and spirometry data were analyzed. Multivariate regression models were applied to estimate STOP-BANG scores according to lung function. Approximately 28% of participants had abnormal lung function, and the characteristics were diverse. The significant factors associated with abnormal lung function included the STOP-BANG score. In multivariate regression analyses, individuals with abnormal lung function had significantly higher STOP-BANG scores than those with normal lung function (odds ratio: 1.19; 95% confidence interval: 1.10- 1.29; P < 0.001), and this difference was remarkable in men. Our results suggest that screening and management of OSA components are warranted to prevent impaired lung function.

Pythagorean hesitant fuzzy rough multi-attribute decision-making method with application to wearable health technology devices

&lt;p&gt;Identifying the most optimal wearable health technology devices for hospitals is a crucial step in emergency decision-making. The multi-attribute group decision-making method is a widely used and practical approach for selecting wearable health technology devices. However, because of the various factors that must be considered when selecting devices in emergencies, decision-makers often struggle to create a comprehensive assessment method. This study introduced a novel decision-making method that took into account various factors of decision-makers and has the potential to be applied in various other areas of research. First, we introduced a list of aggregation operators based on Pythagorean hesitant fuzzy rough sets, and a detailed description of the desired characteristics of the operators under investigation were provided. The proposed operators were validated by a newly defined score and accuracy function. Second, this paper used the proposed approach to demonstrate the Pythagorean hesitant fuzzy rough technique for order of preference by similarity to ideal solution (TOPSIS) model for multiple attribute decision-making and its stepwise algorithm. We developed a numerical example based on suggested operators for the evaluation framework to tackle the multiple-attribute decision-making problems while evaluating the performance of wearable health technology devices. In the end, the sensitivity analysis has confirmed the performance and reliability of the proposed framework. The findings indicated that the models being examined demonstrated greater reliability and efficacy compared to existing methodologies.&lt;/p&gt;

Assessment of Mild Cognitive Impairment Using CogEvo: A Computerized Cognitive Function Assessment Tool.

To assess the utility of the computerized cognitive function assessment tool, CogEvo, as a screening tool for mild cognitive impairment in primary care, we explored the relationship between CogEvo performance, age, and the severity of cognitive dysfunction evaluated by the Mini-Mental State Examination (MMSE). The observational cross-sectional study included 209 individuals' data (mean age 79.4 ± 8.9 years). We conducted a correlation analysis between CogEvo and MMSE scores, compared the performance among the 3 cognitive function groups (MMSE ≥ 28 group; MMSE24-27 group; MMSE ≤ 23 group) using the MMSE cut-off, and evaluated CogEvo's predictive accuracy for cognitive dysfunction through ROC analysis. Both total CogEvo and MMSE scores significantly decreased with age. A significant positive correlation was observed between total CogEvo and MMSE scores, but a ceiling effect was detected in MMSE performance. Significant differences were observed in the total CogEvo score, including orientation and spatial cognitive function scores, among the 3 groups. CogEvo showed no educational bias. ROC analyses indicated moderate discrimination between the MMSE ≥ 28 group and the MMSE24-27 and MMSE ≤ 23 groups. The computer-administered CogEvo has the advantage of not exhibiting ceiling effects or educational bias like the MMSE, and was found to be able to detect age-related cognitive decline and impairment.

Dietary Inflammatory Index and Cognitive Function: Findings from a Cross-Sectional Study in Obese Chinese Township Population from 45 to 75 Years.

Cognitive dysfunction is highly prevalent in obese people, and food is a key factor in obesity, and dietary inflammatory index (DII) can reflect whether diet has anti-inflammatory or pro-inflammatory potential. In addition, dietary fatty acid consumption is linked to inflammation, obesity, and cognitive impairment. Erythrocyte membrane fatty acids can reflect dietary fatty acid intake. Our hypothesis was that erythrocyte membrane fatty acids might have a significant impact on the relationship between DII and cognition in obese individuals, and we designed experiments to test the hypothesis. In three villages in Beijing, we collected 579 respondents from individuals 45 to 75 years old and categorized them by body mass index. The Montreal Cognitive Assessment (MoCA) score and DII score was calculated and gas chromatography was used to measure the proportion of erythrocyte membrane fatty acids. The relationship between the DII score and cognition was examined using multiple linear regression and binary logistic regression. Mediation analysis can help to understand the causal chain between variables, deeply explore the internal relationship and mechanism of action between variables. So a multiple chain mediation model was developed to investigate the mediating factors between the DII score and cognitive association. According to adjusted linear regression, higher DII scores were linked to lower MoCA scores in the obese group. The negative correlation between DII score and cognitive function score remains in binary linear regression. We discovered through mediation analysis that erythrocyte membrane fatty acids mediate the detrimental link between DII and cognitive function in obese individuals. We propose that higher DII scores in obese people are associated with a decline in cognitive function. In addition, this effect might be mediated via the fatty acids in the erythrocyte membrane.

Upper-limb interval versus constant-load exercise in patients with COPD: a physiological crossover study.

Upper-limb exercise is recommended for patients with COPD, albeit there are limited data concerning the optimal modality to implement. We compared interval (INT-EX) to continuous (CONT-EX) upper-limb exercise in terms of exercise tolerance, ventilatory and metabolic responses when both conditions were sustained at an equivalent work rate. 26 stable COPD patients undertook three upper-limb exercise sessions to initially establish peak work rate (PWR) via an incremental exercise test and subsequently two equivalent work rate tests to the limit tolerance in balanced order: 1) INT-EX consisting of 30-s work at 100% PWR interspersed with 30-s work at 40% of PWR; and 2) CONT-EX at 70% PWR. 20 patients (76.9%) had longer tolerance during INT-EX, while six out of 26 (23.1%) exhibited longer tolerance during CONT-EX. The average endurance time was 434.1±184.7 and 315.7±128.7 s for INT-EX and CONT-EX, respectively. During INT-EX at isotime (i.e. when work completed was the same between INT-EX and CONT-EX), the majority of patients manifested lower oxygen uptake, minute ventilation, pulmonary hyperinflation, heart rate, symptoms and higher CO2 blood concentration. Patients with longer INT-EX had a lower comorbidity score (Cumulative Illness Rating Scale: 1.58±0.30 versus 1.88±0.29, p=0.0395) and better-preserved lung function (forced vital capacity 84.7±15.31% versus 67.67±20.56%, p=0.0367; forced expiratory volume in 1 s 57.15±14.59 versus 44.67±12.99% predicted, p=0.0725) compared to patients with longer CONT-EX. INT-EX is more sustainable than CONT-EX for the majority of COPD patients with moderate obstruction, leading to lower dynamic hyperinflation and symptoms at isotime. Further studies need to define the benefits of its application during pulmonary rehabilitation.

Associations between cardiovascular health and low thyroid function among US adults: a population-based study.

Higher thyroid-stimulating hormone (TSH) amidst normal thyroid hormone (TH) levels may contribute to a negative impact on cardiovascular health (CVH). We sought to probe the associations between Life's Essential 8 (LE8), a newly revised CVH evaluation, and low thyroid function among US adults. The datasets from the 2007-2012 National Health and Nutrition Examination Survey (NHANES) were applied to the study. Low-normal thyroid function and subclinical hypothyroidism (SCH) were both regarded to be low thyroid function. Multivariable logistic regressions were utilized to inquire about the relationship between LE8 and low thyroid function. Among the 6,315 participants (age ≥20 years), 1,375 (21.77%) were ascertained to be low thyroid function. After adjusting possible confounders, a higher LE8 score was linked to a lower probability of experiencing low thyroid function (Odds ratio [OR] for each 10-point increase: 0.923 [95% CI, 0.884-0.964]). A similar correlation was found between the health factors score and low thyroid function (OR for each 10-point increase: 0.905 [95% CI, 0.876-0.935]). Also, scoring better on physical activity (PA), body mass index (BMI), blood lipid, blood glucose (BG), and blood pressure (BP) may be conducive to reducing the rates of low thyroid function. Furthermore, subgroup and sensitivity analyses indicated that the negative correlations were generally robust. The LE8 score and health factors score were nonlinearly and negatively related to the prevalence concerning low thyroid function. Promoting the regulation of optimum CVH levels could work on mitigating the load of low thyroid function and cardiovascular diseases (CVDs).

Midterm Outcomes after Operative Management of Hawkins Type III Talar Neck Fractures.

This study aims to report the midterm outcomes after surgical treatment of Hawkins Classification III Talar neck fractures. From March 2010 to April 2022, among a total of 155 patients who visited our hospital with talus fractures, 31 patients underwent surgical treatment for Hawkins classification III talar neck fractures. The inclusion criteria comprised patients with a symptom duration of over 1 year who were available for outpatient follow-up and underwent magnetic resonance imaging (MRI) follow-up 2 months after surgery. Exclusion criteria included patients without preoperative ankle periarticular arthritis, and a total of 27 patients were enrolled. Traffic accidents and falls accounted for 86% of 23 cases, open fractures were 8 cases, and the mean follow-up period was 34.10 months (range, 12-80 months). Clinical outcomes were measured by American Orthopaedic Foot and Ankle Society (AOFAS) score and Foot function index (FFI), and radiological results were obtained using simple radiographs before and after surgery and MRI at 2 months postoperatively to confirm bone union and complications. Complete bone union was achieved in all cases, and the mean duration of union was 4.9 months (range, 4-6 months) and there were no nonunion and varus malunion. At the final follow-up, the mean AOFAS score was 80.18 points (range, 36-90 points) and the mean FFI score was 31.43 points (range, 10-68 points), showing relatively good clinical outcomes. There were 15 cases of avascular necrosis, 6 cases of traumatic arthritis of the ankle joint, 6 cases of irritation of the posterior tibial nerve, and 4 cases of wound problems. Hawkins classification III talar neck fractures are mostly caused by high-energy injuries and have a relatively poor prognosis due to the high incidence of complications such as avascular necrosis or posttraumatic arthritis. However, if correct anatomical reduction and rigid internal fixation are performed within a short time after the injury, good results can be expected.

Derivation and validation of the BIMAST score for predicting the presence of fibrosis due to Metabolic dysfunction-associated steatotic liver disease among diabetic patients in the community.

Current screening pathways, developed from tertiary care cohorts, underestimate the presence of Metabolic-dysfunction associated steatotic liver disease (MASLD) in patients with type 2 diabetes mellitus (T2DM) in the community. We developed, validated, and assessed cost-effectiveness of a new score for screening the presence of fibrosis due to MASLD in primary care. Consecutive T2DM patients underwent screening for liver diseases with transient elastography (TE). Based on predictors of significant/advanced fibrosis, we generated the BIMAST score (based on aspartate aminotransferase (AST) and body mass index (BMI)) and validated it internally and externally (Royal Free Hospital, London and Palermo Hospital). For cost-effectiveness analysis, 6 screening strategies were compared against standard of care: BIMAST score, ultrasound plus abnormal liver function tests, FIB-4, NAFLD fibrosis score, ELF and transient elastography (TE). A Markov model was built based on fibrosis status. Cost per quality-adjusted life year (QALY) gained and the incremental cost-effectiveness ratio (ICER) were estimated over a lifetime. Among 300 patients enrolled, 64% (186) had MASLD and 10% (28) other causes of liver disease. In the whole population, patients with significant fibrosis, advanced fibrosis, and cirrhosis due to MASLD were 17% (50/287), 11% (31/287), and 3% (8/287), respectively. In primary care, BIMAST performed better than other non-invasive markers at predicting significant and advanced fibrosis. Moreover, BIMAST reduced false negatives from 54% (ELF) and 38% (FIB-4) to 10%. In both validation cohorts, BIMAST performance was as good as FIB-4. In the cost-utility analysis, ICER was £2,337.92/QALY for BIMAST. The BIMAST predicts the presence of significant fibrosis in the community, reduces false negatives and is cost-effective. The BIMAST score should be included in the holistic assessment of diabetic patients.

Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems

The goal of this research is to investigate fuzzy multiobjective dynamic programming issues with fuzzy parameters in the objective functions and single valued trapezoidal neutrosophic numbers in the left hand side of the constraints. Piecewise quadratic fuzzy numbers characterize these fuzzy parameters. In addition, applying the score function of the neutrosophic numbers to convert the constraints parameters into its crisp . Some basic notions in the problem under the pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique is presented for obtaining a subset of the parametric space that has the same pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

Robust PAC m : Training Ensemble Models Under Misspecification and Outliers.

Standard Bayesian learning is known to have suboptimal generalization capabilities under misspecification and in the presence of outliers. Probably approximately correct (PAC)-Bayes theory demonstrates that the free energy criterion minimized by Bayesian learning is a bound on the generalization error for Gibbs predictors (i.e., for single models drawn at random from the posterior) under the assumption of sampling distributions uncontaminated by outliers. This viewpoint provides a justification for the limitations of Bayesian learning when the model is misspecified, requiring ensembling, and when data are affected by outliers. In recent work, PAC-Bayes bounds-referred to as PAC m -were derived to introduce free energy metrics that account for the performance of ensemble predictors, obtaining enhanced performance under misspecification. This work presents a novel robust free energy criterion that combines the generalized logarithm score function with PAC m ensemble bounds. The proposed free energy training criterion produces predictive distributions that are able to concurrently counteract the detrimental effects of misspecification-with respect to both likelihood and prior distribution-and outliers.

Gradient-Based Local Causal Structure Learning.

Finding the causal structure from a set of variables given observational data is a crucial task in many scientific areas. Most algorithms focus on discovering the global causal graph but few efforts have been made toward the local causal structure (LCS), which is of wide practical significance and easier to obtain. LCS learning faces the challenges of neighborhood determination and edge orientation. Available LCS algorithms build on conditional independence (CI) tests, they suffer the poor accuracy due to noises, various data generation mechanisms, and small-size samples of real-world applications, where CI tests do not work. In addition, they can only find the Markov equivalence class, leaving some edges undirected. In this article, we propose a GradieNt-based LCS learning approach (GraN-LCS) to determine neighbors and orient edges simultaneously in a gradient-descent way, and, thus, to explore LCS more accurately. GraN-LCS formulates the causal graph search as minimizing an acyclicity regularized score function, which can be optimized by efficient gradient-based solvers. GraN-LCS constructs a multilayer perceptron (MLP) to simultaneously fit all other variables with respect to a target variable and defines an acyclicity-constrained local recovery loss to promote the exploration of local graphs and to find out direct causes and effects of the target variable. To improve the efficacy, it applies preliminary neighborhood selection (PNS) to sketch the raw causal structure and further incorporates an l1 -norm-based feature selection on the first layer of MLP to reduce the scale of candidate variables and to pursue sparse weight matrix. GraN-LCS finally outputs LCS based on the sparse weighted adjacency matrix learned from MLPs. We conduct experiments on both synthetic and real-world datasets and verify its efficacy by comparing against state-of-the-art baselines. A detailed ablation study investigates the impact of key components of GraN-LCS and the results prove their contribution.

Nano Fuzzy Z - Open Sets and its Application in Nano Fuzzy Topological Space

This research aims to define and investigate the properties of Nano fuzzy Z-open explicitly sets defined in Nano fuzzy topological spaces. Also, there is an attempt to define Nano fuzzy Z-closure Nano fuzzy Z-interior in Nano fuzzy topological spaces. The work has grown by incorporating Nano fuzzy δ open sets, Nano fuzzy δ semi-open sets, Nano fuzzy δ semi-open sets, and Nano fuzzy δ pre-open sets. Also, the work has been concluded with a numerical application of the Nano fuzzy score function in the medical field (to check the proper diagnosis of disease and drug combinations given to the patient).