Multi-level Programming Research Articles

A hierarchical multi-level model for compromise allocation in multivariate stratified sample surveys with non-response problem

Stratified sampling, a widely-applicable probabilistic technique, is especially suited for large and heterogeneously distributed populations. This paper studies optimal allocation of sampling units to minimize variances and cost. Given that not all strata hold equal importance in survey projects, we propose a hierarchical multi-level programming model for compromise allocation in stratified sampling. The model considers multiple objectives across hierarchical levels and addresses the issue of non-response by dividing strata into respondent and non-respondent groups. The survey budget restriction is considered as a constraint in our model. We employ a fuzzy concept-based solution methodology to solve the multi-level allocation problem. A literature-based numerical example describes the model’s applicability and efficiency. Comparative analysis shows our model’s superior efficiency over existing models due to its optimization of allocation across varied strata, non-response consideration, and budget constraint integration. The proposed model promotes flexibility, enhancing representativeness and cost-effectiveness of large-scale surveys, thereby improving decision-making in research and industry settings.

Three different optimization techniques for solving the fully rough interval multi-level linear programming problem

Due to the importance of the multi-level fully rough interval linear programming (MLFRILP) problem to address a wide range of management and optimization challenges in practical applications, such as policymaking, supply chain management, energy management, and so on, few researchers have specifically discussed this point. This paper presents an easy and systematic roadmap of studies of the currently available literature on rough multi-level programming problems and improvements related to group procedures in seven basic categories for future researchers and also introduces the concept of multi-level fully rough interval optimization. We start remodeling the problem into its sixteen crisp linear programming LP problems using the interval method and slice sum method. All crisp LPs can be reduced to four crisp LPs. In addition, three different optimization techniques were used to solve the complex multi-level linear programming issues. A numerical example is also provided to further clarify each strategy. Finally, we have a comparison of the methods used for solving the MLFRILP problem.

Fully intuitionistic fuzzy multi-level linear fractional programming problem

In many real situations, it is frequently difficult to accurately determine the membership and non-membership degrees related to an element of the set with complete satisfaction because of the ambiguity in the input data. In instances like these, intuitionistic fuzzy (IF) numbers are crucial. We present a simple approach in this paper to solve the fully intuitionistic fuzzy multi-level linear fractional programming (FIFMLLFP) problem. By applying the new suggested approach to the problem under consideration, each level of the FIFMLLFP problem is converted into five crisp linear (MLMOLFP) problems, where each crisp problem has an additional bounded variables constraint and the upper problems' optimization variables are treated as parameters. This is done by using an iterative technique for linearizing fractional objectives. We converted the MLMOLFP problem into a multilevel multiobjective linear programming (MLMOLP) problem, in addition to the ε-constraint method that is used to reduce MLMOLP problem to a single objective linear programming problem. The method is demonstrated step-by-step with a numerical example.

A latent profile analysis of at-risk students in a multilevel prevention program: Who chooses to participate and the impact on outcomes

The goal of the current study was to adopt a novel comprehensive approach to examine the efficacy of the targeted intervention component of a multilevel prevention program. We addressed four fundamental issues with this approach: (1) Distinct subpopulations within the sample; (2) Characteristics of those who chose to complete the intervention and those who did not by profile; (3) Changes in the experimental group by profile; and (4) Changes in the comparison group by profile? Latent Profile Analyses revealed that our initial sample of students identified as at-risk due to current symptoms of distress, clustered into three distinct profiles of risk (High Risk (HR), Average Risk (AR) and Low Risk (LR)). Regarding characteristics related to opting for active participation, we found that the higher the level of initial risk, the more likely students were to opt to participate in the program, and within the AR profile, we found that those participants with lower study skills opted more often for the intervention. Latent Growth Modeling, in the experimental group, showed that the HR profile benefited substantially from participation in the intervention with significant reductions in symptoms and risk factors, as well as significant increases in protective factors. Changes in the AR profile were in the expected direction, but this group remained notably anxious although not depressed anymore. The LR profile showed significant reductions in symptoms following the intervention. In the comparison group, the HR profile improved some, the AR and the LR did not change significantly, except for significant decreases in personal goal and values consolidation in the LR profile. The current study highlights the importance of adopting a more comprehensive evaluation of efficacy and how this must inform selection criteria for future studies.

Memristive Circuit Design of Quantized Convolutional Auto-Encoder

This work proposes a memristor-based quantized convolutional auto-encoder (MQCAE) and applies it in an image denoising application. The pulse width or amplitude is gradually tuned by incremental steps in current memristive programming methods, which can be extremely time-consuming. In this work, a multi-level programming method without incremental steps is proposed. MQCAE is composed of five kinds of network layers: convolution layers, deconvolution layers, activation function layers, batch normalization layers and max-pooling layers. We design a memristive circuit for realizing convolution and deconvolution with different kernel parameters. The proposed circuit generates one output feature row every cycle. Analog data buffers are designed to store the intermediate data among network layers. In addition, a reconfigurable analog circuit for realizing activation functions and batch normalization is presented. By using analog temp modules, convolution layers and max-pooling layers are able to compute simultaneously. We construct the MQCAE and introduce the pipeline technique among network layers based on the circuit modules. As a result, MQCAE is able to process one FashionMNIST image in 36 cycles with clock frequency 20 kHz. Finally, we verify the effectiveness of MQCAE in an image denoising task. The results show that the denoising performance of proposed scheme is close to software model while the processing speed is faster.

Suppressing Structural Relaxation in Nanoscale Antimony to Enable Ultralow-Drift Phase-Change Memory Applications.

Phase-change random-access memory (PCRAM) devices suffer from pronounced resistance drift originating from considerable structural relaxation of phase-change materials (PCMs), which hinders current developments of high-capacity memory and high-parallelism computing that both need reliable multibit programming. This work realizes that compositional simplification and geometrical miniaturization of traditional GeSbTe-like PCMs are feasible routes to suppress relaxation. While to date, the aging mechanisms of the simplest PCM, Sb, at nanoscale, have not yet been unveiled. Here, this work demonstrates that in an optimal thickness of only 4nm, the thin Sb film can enable a precise multilevel programming with ultralow resistance drift coefficients, in a regime of ≈10-4 -10-3 . This advancement is mainly owed to the slightly changed Peierls distortion in Sb and the less-distorted octahedral-like atomic configurations across the Sb/SiO2 interfaces. This work highlights a new indispensable approach, interfacial regulation of nanoscale PCMs, for pursuing ultimately reliable resistance control in aggressively-miniaturized PCRAM devices, to boost the storage and computing efficiencies substantially.

School-Based Sleep Education Program for Children: A Cluster Randomized Controlled Trial

Insufficient sleep contributes negatively to child developmental processes and neurocognitive abilities, which argues the need for implementing interventions to promote sleep health in children. In this study, we evaluated the effectiveness of a multimodal and multilevel school-based sleep education program in primary school children using a cluster randomized controlled design. Twelve schools were randomly assigned to either the sleep education or nonactive control groups. The sleep education group included a town hall seminar, small class teaching, leaflets, brochures, and a painting competition for children. Parents and teachers were invited to participate in a one-off sleep health workshop. Parental/caregiver-reported questionnaires were collected at baseline and 1-month follow-up. A total of 3769 children were included in the final analysis. There were no significant improvements observed in the sleep-wake patterns, daytime functioning, and insomnia symptoms between the two groups at follow-up, whereas the intervention group had significantly improved parental sleep knowledge than the controls (paternal: adjusted mean difference: 0.95 [95% confidence interval (CI): 0.18 to 1.71]; maternal: adjusted mean difference: 0.87 [95% CI: 0.17 to 1.57]). In addition, children receiving the intervention had a lower persistence rate of excessive beverage intake (adjusted odds ratio: 0.49 [95% CI: 0.33 to 0.73]), and experienced greater reductions in conduct problems (adjusted mean difference: 0.12 [95% CI: 0.01 to 0.24]) compared with the controls at 1-month of follow-up. Moreover, a marginally significant reduction for emotional problems in the intervention group was also observed (adjusted mean difference: 0.16 [95% CI: −0.00 to 0.32]). These findings demonstrated that school-based sleep education was effective in enhancing parental sleep knowledge and improving behavioral outcomes in children, but not sufficient in altering the children’s sleep-wake patterns and sleep problems.

Using Responsive Feedback in Scaling a Gender Norms-Shifting Adolescent Sexual and Reproductive Health Intervention in the Democratic Republic of Congo.

Growing Up GREAT! (GUG) is a sexual and reproductive health (SRH) program for adolescents aged 10-14 years in Kinshasa, Democratic Republic of the Congo (DRC). The multilevel program takes an ecological approach to foster community examination of gender inequitable norms and to increase adolescents' SRH knowledge, skills, and gender-equitable attitudes. GUG design, piloting, and scale-up were informed by a theory of change and responsive feedback mechanisms (RFMs) during piloting and scale-up. The program engaged stakeholders via quarterly learning meetings to review monitoring data, evaluation results, and practice-based knowledge and to subsequently identify challenges and develop solutions. The program commissioned rapid research on specific intervention elements to improve implementation and documented scale-up learnings using the World Health Organization/ExpandNet framework. RFMs used in the pilot period allowed the program to address community concerns by intensifying orientation activities with parents and schools, shifting the calendar of activities to increase male engagement, and increasing facilitator training length to improve facilitation quality. Using RFMs during scale-up prompted further adaptations for program sustainability, including recommendations for task-shifting from NGO facilitators to community health workers. GUG used RFMs from pilot through scale-up to foster a learning culture among local partners, implementers at headquarters, and global research partners. Using responsive feedback (RF) enabled timely response to the evolving implementation context, resulting in strategic program adaptations that fostered increased community support of the project. Other successes due, at least in part, to this RF approach include incorporation of the program into DRC's national adolescent health strategy, and rapid response to the COVID-19 pandemic in educational strategies for program beneficiaries.

Reaching Populations to Address Disparities in Cancer Care Delivery: Results From a Six-Site Initiative.

Large segments of the US population do not receive quality cancer care due to pervasive and systemic inequities, which can increase morbidity and mortality. Multicomponent, multilevel interventions can address inequities and improve care, but only if they reach communities with suboptimal access. Intervention studies often underenroll individuals from historically excluded groups. The Alliance to Advance Patient-Centered Cancer Care includes 6 grantees across the United States who implemented unique multicomponent, multilevel intervention programs with common goals of reducing disparities, increasing engagement, and improving the quality of care for targeted populations. The Reach, Effectiveness, Adoption, Implementation, and Maintenance (RE-AIM) framework informed the evaluation efforts across sites. Each Alliance site identified their intended populations, which included underrepresented minorities (eg, Black and Latinx persons), individuals who prefer a language other than English, and rural residents. We evaluated the demographic characteristics of participants to determine program reach. Between 2018 and 2020, a total of 2,390 of 5,309 potentially eligible participants were enrolled across the 6 sites. The proportion of enrolled individuals with selected characteristics included 38% (n=908) Black adults, 24% (n=574) Latinx adults, 19% (n=454) preferring a language other than English, and 30% (n=717) rural residents. The proportion of those enrolled who were the intended population was commensurate to the proportion with desired characteristics in those identified as potentially eligible. The grantees met or exceeded enrollments from their intended populations who have been underserved by quality cancer care into patient-centered intervention programs. Intentional application of recruitment/engagement strategies is needed to reach individuals from historically underserved communities.

Matters of Gender and Social Disparities Regarding Postnatal Care Use Among Nepalese Women: A Cross-Sectional Study in Morang District.

The study compares the uses of postnatal care (PNC) and women's autonomy gradients across social caste and used intersectionality concepts to estimate odds ratio of women's autonomy and social caste on complete PNC. A community-based cross-sectional study among 600 women aged 15-49 years who had at least one child younger than the age of 2 years in Morang District, Nepal, was conducted from April to July 2019. PNC, women's autonomy (decision-making power, freedom of movement, and control over finances) and social caste were collected by both methods. Multivariable logistic regressions were used to determine associations between women's autonomy, social caste, and complete PNC. Complete PNC totaled 13.5% of respondents. About one-fourth of respondents reported poor overall autonomy; however, non-Dalit demonstrated higher autonomy than Dalit. Non-Dalit exhibited greater odds of complete PNC by four times. Women exhibited high women's autonomy in decision-making power, control over finance, and freedom of movement and have greater odds of complete PNC than low autonomy by 17, 3, and 7 times, respectively. The study raises awareness of intersectionality (gender and social caste), relating to maternal health in caste-based system countries. To improve maternal health outcomes, health care personnel should identify and systematically address barriers that women of lower-caste membership face and offer these women appropriate advice or resources to obtain care. A multilevel change program that involves different actors like husbands and community leaders is needed for improving women's autonomy and lessening stigmatized perceptions, attitudes, or practices toward non-Dalit caste-members.

Investigation of key domains associated with worker well-being and burnout and turnover in the early care and education workforce.

The early care and education (ECE) workforce provides care for children aged zero to five. This critical segment of the workforce experiences significant burnout and turnover rates resulting from extensive demands, including job stress and poor overall well-being. Factors associated with well-being in these settings and the resulting impacts on burnout and turnover are understudied. The purpose of this study was to investigate associations between five well-being domains and burnout and turnover outcomes among a large sample of Head Start ECE staff in the United States. An 89-item survey based off the National Institutes of Occupational Safety and Health Worker Wellbeing Questionnaire (NIOSH WellBQ) was administered to ECE staff employed in five large urban and rural Head Start agencies. The WellBQ is made up of five domains intended to measure worker well-being as a holistic construct. We utilized linear mixed-effect modeling with random intercepts to investigate associations between sociodemographic characteristics, well-being domain sum scores and burnout and turnover. After controlling for sociodemographic variables, the well-being Domain 1 (Work Evaluation and Experience) (β = -.73, p < .05) and Domain 4 (Health Status) (β = -.30, p < .05) were significantly and negatively associated with burnout; the well-being Domain 1 (Work Evaluation and Experience) (β = -.21, p < .01) was significantly and negatively associated with turnover intent. These findings suggest that multi-level well-being promotion programs could be critical to mitigate ECE teacher stress and address individual-, interpersonal-, and organizational-level predictors of overall ECE workforce well-being.

Memristor-Based Cryogenic Programmable DC Sources for Scalable In Situ Quantum-Dot Control

Current quantum systems based on spin qubits are controlled by classical electronics located outside the cryostat. This approach creates a major wiring bottleneck, which is one of the main roadblocks toward scalable quantum computers. Thus, we propose a scalable memristor-based programmable dc source that can perform biasing of quantum dots (QDs) inside the cryostat. This novel cryogenic approach would enable to control the applied voltage on the electrostatic gates by programming the resistance of the memristors, thus storing in the latter the appropriate conditions to form the QDs. In this study, we first demonstrate multilevel resistance programming of TiO2 memristors at 4.2 K, an essential feature to achieve voltage tunability of the memristor-based dc source. We then report hardware-based simulations of the electrical performance of the proposed dc source. A cryogenic TiO2 memristor model fit on our experimental data at 4.2 K was used to show a 1 V voltage range and 100 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{V}$ </tex-math></inline-formula> resolution in situ memristor-based dc source. Finally, we simulate the biasing of double QDs (DQDs), enabling 120 s stability diagrams. This demonstration is a first step toward advanced cryogenic applications for resistive memories, such as cryogenic control electronics for quantum computers.

"Climate Change and Health?": Knowledge and Perceptions among Key Stakeholders in Puducherry, India.

Climate change has far-reaching impacts on human health, with low- and middle-income countries, including India, being particularly vulnerable. While there have been several advances in the policy space with the development of adaptation plans, little remains known about how stakeholders who are central to the strengthening and implementation of these plans perceive this topic. We conducted a qualitative study employing key interviews with 16 medical doctors, researchers, environmentalists and government officials working on the climate change agenda from Puducherry, India. The findings were analysed using the framework method, with data-driven thematic analysis. We elucidated that despite elaborating the direct and indirect impacts of climate change on health, there remains a perceived gap in education and knowledge about the topic among participants. Knowledge of the public health burden and vulnerabilities influenced the perceived health risks from climate change, with some level of scepticism on the impacts on non-communicable diseases, such as cardiovascular diseases. There was also a felt need for multi-level awareness and intervention programmes targeting all societal levels along with stakeholder recommendations to fill these gaps. The findings of this study should be taken into consideration for strengthening the region's climate change and health adaptation policy. In light of limited research on this topic, our study provides an improved understanding of how key stakeholders perceive the impacts of climate change on health in India.

Suicide and Violence against Women in Azerbaijan: Risk Factors and Barriers for Seeking Mental Healthcare

IntroductionAzerbaijan ranks among the top 3 countries with the highest rates of suicide in the Muslim world. Yet, research indicates an underestimate of risk due to cultural stigma related to suicidal behavior that may influence reporting and given that many Muslim-majority countries, where populations exceed 100 million, do not report any data on suicide rates. Violence against women also occurs at alarming rates in Azerbaijan and is a significant risk factor for suicide.ObjectivesWe examine perspectives towards suicide and violence against women and barriers to care among key stakeholders.MethodsThirty qualitative interviews and 4 semi-structured focus groups were held with female survivors of suicide and mental health professionals working with individuals at risk of suicide to assess for perspectives on suicide and violence against women, factors influencing help-seeking, and the nature of existing resources.ResultsMost participants viewed suicide (83%) and violence against women (73%) as problems. Nevertheless, 33% reported negative stereotypes regarding suicide and 50% reported psychological treatment as unaccepted in Azerbaijan. Findings highlight that domestic violence is the strongly identified as risk factor for suicide among women in Azerbaijan. Stigma and related cultural values regarding gender norms are significant contributors to violence against women and suicide. Existing services are underrecognized and perceived of as unavailable or insufficient.ConclusionsEmploying a social determinants of health lens, multi-level programming is needed that spans micro (individual level supports), mezzo (family level supports), and macro (advocacy and outreach) levels to support a comprehensive strategy that beings with prevention and extends to address intervention, management, and capacity building to halt the increasing rates of suicide and deter violence against women.Disclosure of InterestNone Declared

PECULIARITIES OF IMPROVING STUDENTS' HEALTH BY MEANS OF SWIMMING

The article analyzes the use of modern methods in the process of swimming classes to improve the physical condition of students of higher education. The effectiveness of systematic swimming lessons on improving health indicators of students was studied. A low level of health among students who lead a sedentary lifestyle was determined. The motivational aspects of the involvement of student youth in active swimming lessons have been determined. It was found that when teaching proper breathing in an unfamiliar environment for initial swimming lessons, it is recommended to spend up to 40% of the class time on breathing exercises, thus, students who are just learning to swim will more easily overcome the barrier of fear in the water environment. Thus, swimming lessons are shown with various health conditions for students of special medical groups. In addition- in the above recommendations, you can add add the following when mastering the skill of breathing in an unusual environment for initial swimming training. Early multi-level swimming programs are recommended for all children to help them overcome their fear of water, improve pool performance and improve swimming performance. This will eventually increase the percentage of adults who can swim. It is necessary to create a favorable environment for the classes of students with mild and severe disabilities. For this, it is necessary to adapt run swimming programs. The variety of aspects of physical training, the specifics and features of swimming represent the best pedagogical conditions for the development of emotional and volitional stability during classes in this type of pedagogical activity.

EFECTOS DE UN PROYECTO INTERDISCIPLINAR DE PROMOCIÓN DE COMPORTAMIENTOS SALUDABLES EN ESTUDIANTES DE EDUCACIÓN PRIMARIA DE UN COLEGIO RURAL

Although the benefits associated with a healthy lifestyle are known, a large percentage of young people do not comply with the established recommendations for the different healthy behaviors, especially during Covid-19. Thus, the aim of this study was to design, implement, and evaluate the effects of a multicomponent and multilevel school-based program on multiple health-related behaviors in Primary Education students. For this, 12 students (M=10.33±1.07), from a multilevel Primary Education classroom of a rural school in Teruel, participated. This five-week program aimed to raise awareness about the importance of adopting a healthy lifestyle. The results showed an increase in daily physical activity and perceived health status after participating in the intervention program. Likewise, recreational screen time also showed a significant decrease. However, the students did not report significant differences in sleep duration, adherence to the Mediterranean diet, and quality of life. Thus, it seems convenient to develop multicomponent, multibehavioral, and multilevel school programs, involving different subjects and areas of action, as well as the entire educational community, to improve these healthy behaviors in young people from rural schools.

Blockchain technology empowers the crowdfunding decision-making of marine ranching

Marine ranching, as a new commercial form, the lack of construction and development funds has become its development constraint. Crowdfunding provides a new way to break through the financing bottleneck of marine ranching, and blockchain technology (BT) can effectively solve the problem of information asymmetry in crowdfunding progress. However, the choice of enterprise crowdfunding methods and the influence of consumer crowdfunding and pre-sale crowdfunding on supply chain value co-creation have not been deeply studied. Based on the theory of value co-creation, this paper uses multi-level programming and backward induction method to construct and solve the supply chain models of consumer crowdfunding and pre-sale crowdfunding under the traditional mode and BT mode, and obtains balanced results. Analyze the influence of the product green attributes, the degree of the enterprise’s attention to crowdfunding consumer value and ordinary consumer value, consumer recognition of product attributes (quality attributes, green attributes) and other parameters on supply chain operation; Through the comparative analysis of different models and numerical simulation, the optimal decision results are further discussed. The research shows that: (1) The overall value of the supply chain is higher when the marine ranching leading enterprise adopts the consumer crowdfunding method than when the pre-sale crowdfunding method. Moreover, the introduction of BT can improve the value of each subject in the supply chain system. (2) The marine ranching leading enterprise pays attention to the value of crowdfunding consumers and ordinary consumers, which will reduce their own value and increase the value of other subjects in the supply chain. The improvement of crowdfunding consumers' recognition of product attributes will improve their consumer value. (3) When the green attributes of products increase, the values of the leading enterprise, the retailer, the crowdfunding platform and consumers all increase, and the overall value of supply chain is improved. (4) Increasing product sales is the unified goal of all subjects in crowdfunding supply chain system, thus promoting the economic value and environmental value of enterprises.

Evaluation of the 9th-grade 2018 Physics Curriculum With Multilevel Rasch Analysis

&lt;p style="text-align:justify"&gt;This study aims to examine the 9th-grade 2018 physics curriculum according to various criteria. A cross-sectional survey model was used. The sample consists of 36 physics teachers working in various high schools in 12 regions of Turkey in the 2022-2023 academic year. The data of the study were collected via the “9th-grade 2018 physics curriculum Evaluation Form”. The data collected via the evaluation form were determined with the multilevel Rasch analysis program. The results of the research revealed that the criteria determined in the evaluation of the 9th-grade physics curriculum differed in terms of strictness and generosity. In addition, the quantitative data analysis revealed that the physics teachers mostly comply with the criteria set in the program while they disapprove of some criteria. The physics teachers reported some deficiencies in the objectives, content, and educational status of the elements included in the program. In this context, it is recommended that the achievements of the 9th-grade 2018 physics curriculum be reviewed in line with the evaluations of the stakeholders related to the subject.&lt;/p&gt;

Development and Evaluation of Neighborhood Care Volunteer Training Programs—Preparing for Older Adult Community Care in Taiwan

The prevalence of chronic diseases and functional disorders is projected to escalate as the older adult population increases. Thus, the demand for and burdens of long-term care are increasing. Training middle-aged and older volunteers at the community level will enhance health promotion and disease prevention in communities. In this study, multilevel volunteer training programs and related implementation methods were designed for neighborhood caregivers. This study was divided into two phases. In Phase 1, an expert review was conducted using the modified Delphi method to congregate expert opinions into an interdisciplinary consensus and establish the content and methods of implementation of the multilevel training program. In Phase 2, the training programs were implemented and evaluated. In Phase 1, 17 experts in geriatric and long-term care were enrolled in the Delphi surveys. Consensus was defined as at least 80% agreement. These experts devised volunteer training programs for neighborhood caregivers at three levels: basic caregiver training, advanced caregiver training, and volunteer caregiver instructor training. The curriculum focused on fulfilling the health demands of neighborhood care; adopted disability-prevention and disability-delaying healthcare as the basic framework; and referred to the attention, relevance, confidence, and satisfaction model of motivational design. This model of motivational design drew on the attributes of volunteers and the current state of care programs, including interest, program difficulty, and feasibility of future services. In Phase 2, 50 community middle-aged and older volunteers enrolled in the training programs and, after completing the program, were asked to evaluate their satisfaction with the program content and program effectiveness. A high level of satisfaction was reported across all three levels. The training programs achieved satisfactory consistency and convergence and were well received by the volunteer trainees. These programs may be referenced in the development of future training programs and the creation of a model of community healthcare services. The curriculum was designed from the learners' perspective with direct healthcare applications. A progressive multilevel set of neighborhood care volunteer training programs was offered to cultivate community volunteers.

On neutrosophic multi-level multi-objective linear programming problem with application in transportation problem

In this research, we use the harmonic mean technique to present an interactive strategy for addressing neutrosophic multi-level multi-objective linear programming (NMMLP) problems. The coefficients of the objective functions of level decision makers and constraints are represented by neutrosophic numbers. By using the interval programming technique, the NMMLP problem is transformed into two crisp MMLP problems, one of these problems is an MMLP problem with all of its coefficients being upper approximations of neutrosophic numbers, while the other is an MMLP problem with all of its coefficients being lower approximations of neutrosophic numbers. The harmonic mean method is then used to combine the many objectives of each crisp problem into a single objective. Then, a preferred solution for NMMLP problems is obtained by solving the single-objective linear programming problem. An application of our research problem is how to determine the optimality the cost of multi-objective transportation problem with neutrosophic environment. To demonstrate the proposed strategies, numerical examples are solved.