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M 171.02: Calculus I, Christian J. Lopez Mercado Feb 2025

M 171.02: Calculus I, Christian J. Lopez Mercado

University of Montana Course Syllabi, 2021-2025

No abstract provided.


M 225.01: Introduction To Discrete Mathematics, Cory T. Palmer Feb 2025

M 225.01: Introduction To Discrete Mathematics, Cory T. Palmer

University of Montana Course Syllabi, 2021-2025

No abstract provided.


M 105.03: Contemporary Math With Corequisite Support, Bergen J. Dolan Feb 2025

M 105.03: Contemporary Math With Corequisite Support, Bergen J. Dolan

University of Montana Course Syllabi, 2021-2025

No abstract provided.


M 121.05: College Algebra With Co-Requisite Support, Ian Gonzales Feb 2025

M 121.05: College Algebra With Co-Requisite Support, Ian Gonzales

University of Montana Course Syllabi, 2021-2025

No abstract provided.


M 121.50: College Algebra, Lauren S. Fern Feb 2025

M 121.50: College Algebra, Lauren S. Fern

University of Montana Course Syllabi, 2021-2025

No abstract provided.


Stat 216.50: Introduction To Statistics, Scott Davis Feb 2025

Stat 216.50: Introduction To Statistics, Scott Davis

University of Montana Course Syllabi, 2021-2025

No abstract provided.


Stat 216.Vh1: Introduction To Statistics, Jamie C. Middleton Feb 2025

Stat 216.Vh1: Introduction To Statistics, Jamie C. Middleton

University of Montana Course Syllabi, 2021-2025

No abstract provided.


A Neutrosophic Approach To Robust Web Security: Mitigating Xss Attacks, A. A. Salama, El-Said F. Aboelfotoh, Hazem M. El-Bakry, Huda E. Khalid, Ahmed K. Essa, Ramiz Sabbagh, Doaa S. El-Morshedy Feb 2025

A Neutrosophic Approach To Robust Web Security: Mitigating Xss Attacks, A. A. Salama, El-Said F. Aboelfotoh, Hazem M. El-Bakry, Huda E. Khalid, Ahmed K. Essa, Ramiz Sabbagh, Doaa S. El-Morshedy

Neutrosophic Sets and Systems

Cross-Site Scripting (XSS) is one of the most grievous vulnerabilities-a pitfall through which web applications are affected. These types of attacks are complex, and the available threat landscape is always changing, making it hard for conventional security tools to effectively detect or prevent these types of attacks. We present here an approach that detects and prevents XSS attacks on Web pages. Since Neutrosophism works with different kinds of data, it aims at the validity degree of the attack. This way the system understands the different types of attacks and allows the system to act more effectively. Our system combines (1) …


A Neutrosophic Superiority And Inferiority Ranking-Based Model For Resource Allocation Efficiency In University Sports Management, Pute Lan, Jiaqi Guo, Changshun Bai Feb 2025

A Neutrosophic Superiority And Inferiority Ranking-Based Model For Resource Allocation Efficiency In University Sports Management, Pute Lan, Jiaqi Guo, Changshun Bai

Neutrosophic Sets and Systems

The evaluation of resource allocation efficiency in university recreational sports aims to analyze and assess the effectiveness of how universities allocate facilities, equipment, and personnel for recreational sports. By collecting relevant data and applying scientific methods, it evaluates the usage and impact of resources to optimize allocation and enhance student participation and satisfaction. This not only helps improve campus sports culture but also promotes students' physical and mental health and overall development. The resource allocation efficiency evaluation in university recreational sports is a MAGDM problem. Recently, the Superiority and Inferiority Ranking (SIR) method has been employed to cope with MAGDM …


A Neutrosophic Logic Ruled Based Machine Learning Approaches For Chronic Kidney Disease Risk Prediction, Bhabani S.Mohanty, Krishna Priya R, Liya Alias, R. Vijaya Kumar Reddy, Prasanta Kumar Raut, Samson Isaac, Manibharathi D, C. Saravanakumar, Nihar Ranjan Panda, Said Broumi Feb 2025

A Neutrosophic Logic Ruled Based Machine Learning Approaches For Chronic Kidney Disease Risk Prediction, Bhabani S.Mohanty, Krishna Priya R, Liya Alias, R. Vijaya Kumar Reddy, Prasanta Kumar Raut, Samson Isaac, Manibharathi D, C. Saravanakumar, Nihar Ranjan Panda, Said Broumi

Neutrosophic Sets and Systems

Chronic kidney disease (CKD) represents a significant global health challenge in society, and early detection of risk is essential for on-time treatment and intervention. This research suggests a novel machine-learning technique to create a reliable and accurate CKD risk prediction model by combining neutrosophic logic with various classification algorithms. We use neutrosophic logic to address the inherent imprecision and uncertainty in medical data, resulting in a more realistic portrayal of real-world scenarios. We measure the effectiveness of the proposed neutrosophic logic-based models using various metrics, including precision, specificity, and sensitivity. The results show that the neutrosophic logic method is better …


Neutrosophic Dus Exponential Distribution, Megha. C.M, Divya. P.R, Sajesh.T. A Feb 2025

Neutrosophic Dus Exponential Distribution, Megha. C.M, Divya. P.R, Sajesh.T. A

Neutrosophic Sets and Systems

The exponential distribution is a widely used lifetime model with applications spanning numerous disciplines. The DUS transformation extends the applicability of the exponential distribution by improving its flexibility for diverse real-world scenarios. This study proposes the Neutrosophic DUS Exponential Distribution (NDUS-ED), an extension of the DUS Exponential Distribution, designed to effectively address and quantify uncertainty, inconsistency, and indeterminacy in data. Key statistical properties of NDUS-ED, including quantiles, moments, moment-generating functions, and order statistics, are derived under neutrosophic conditions. The performance of estimated parameters is evaluated through simulation, revealing superior results with larger sample sizes, particularly in managing imprecise and indeterminate …


Neutrosophic Dynamic Network Dea: Efficient Allocation Of Carryover Variables In Organizational Processes, Maryam Heydar, Hadi Bagherzadeh Valami Feb 2025

Neutrosophic Dynamic Network Dea: Efficient Allocation Of Carryover Variables In Organizational Processes, Maryam Heydar, Hadi Bagherzadeh Valami

Neutrosophic Sets and Systems

Carryover activities in dynamic DEA refer to the persistence of resources, inputs, or outputs across periods in organizational processes, reflecting the impact of past decisions on current and future performance. In practical applications, some carryover variables can extend beyond the immediate next period, and their allocation is discretionary, controlled by the Decision-Maker (DM). This paper introduces a novel dynamic network DEA (DNDEA) model aimed at optimizing the allocation of these carryovers and identifying inefficiencies within a network system across multiple evaluation periods. Recognizing the uncertainties present in real-world data, we incorporate neutrosophic sets to effectively process uncertain information, which adds …


Numerical And Semi Analytical Scheme For Developing A Solution To Falkner Skan Equation In Neutrosophic Environments, B. Amudha, M. Shanmugapriya, R. Sundareswaran, Said Broumi Feb 2025

Numerical And Semi Analytical Scheme For Developing A Solution To Falkner Skan Equation In Neutrosophic Environments, B. Amudha, M. Shanmugapriya, R. Sundareswaran, Said Broumi

Neutrosophic Sets and Systems

This study presents a detailed analysis of the Falkner-Skan equation under uncertainty by employing neutrosophic numbers to represent the uncertainty in no slip conditions and the parameter ��̃. By applying appropriate similarity transformation, partial differential equation (PDE) are converted into ordinary differential equation (ODE). Both the Shooting Method and the Homotopy Perturbation Method (HPM) are utilized to solve ODE’s. These ODE’s are then transmuted into neutrosophic differential equation (NDE) by employing (Α ̃,Β, ̃ Γ ̃)������ approach. The parameter ��̃ and no slip conditions are taken as triangular and trapezoidal neutrosophic numbers. The results are presented graphically to illustrate the …


The Pamssem Approach For Multi-Attribute Group Decision-Making Using Single-Valued Neutrosophic Sets: Applications To Evaluating The Effectiveness Of College Students' Psychological Education, Xiaolan Liang Feb 2025

The Pamssem Approach For Multi-Attribute Group Decision-Making Using Single-Valued Neutrosophic Sets: Applications To Evaluating The Effectiveness Of College Students' Psychological Education, Xiaolan Liang

Neutrosophic Sets and Systems

The evaluation of the effectiveness of college students' psychological education involves using scientific approaches and tools to assess the actual impact of psychological education on improving students' mental health, fostering personality development, and enhancing psychological adjustment abilities. The evaluation covers aspects such as students' mental health status, the achievement of educational goals, the effectiveness of interventions, and student satisfaction. Through such evaluations, psychological education programs can be optimized to improve quality, help students better cope with psychological challenges in academics, life, and relationships, and promote their holistic development and healthy growth. The results also provide a scientific basis for continuous …


Statistical Analysis Of Foreign Investment Using Neutrosophic Interval Based Approach, Jamil Afzal, Naim Mathlouthi, Mohamed Saer Rahal, Chen Yongmei, Aftab Haider, Muhammad Adeel Afzal Feb 2025

Statistical Analysis Of Foreign Investment Using Neutrosophic Interval Based Approach, Jamil Afzal, Naim Mathlouthi, Mohamed Saer Rahal, Chen Yongmei, Aftab Haider, Muhammad Adeel Afzal

Neutrosophic Sets and Systems

Pakistan, a nation at the crossroads of South Asia, has been actively striving to attract foreign investment to boost its economic growth and development. As a country rich in natural resources, with a young and vibrant workforce, and a strategic geographic location, Pakistan offers significant opportunities for foreign investors seeking to explore new markets and tap into its potential. The foreign investment policies in Pakistan have undergone substantial reforms over the years to create a more investor-friendly environment. These policies are designed to facilitate and incentivize foreign direct investment while ensuring the protection of investors' rights and contributing to the …


The First Resolution Of The Travelling Salesman Problem Under Neutrosophic Octagonal Fuzzy Environment, Mariem Miledia, Taicir Loukilb, Souhail Dhouiba Feb 2025

The First Resolution Of The Travelling Salesman Problem Under Neutrosophic Octagonal Fuzzy Environment, Mariem Miledia, Taicir Loukilb, Souhail Dhouiba

Neutrosophic Sets and Systems

The Travelling Salesman Problem (TSP) is a challenging combinatorial optimization problem classified as NP-hard. Its objective is to identify the shortest cycle that visits every city precisely once before returning to the initial city. To the best of our knowledge there is no one in the literature who solved the TSP under the neutrosophic octagonal fuzzy environment. That’s why, in this paper the novel heuristic namely Dhouib-Matrix-TSP1 (DM-TSP1) is exploited to optimize the TSP under the neutrosophic octagonal fuzzy domain. So, this research work represents the first application of DM-TSP1 on this mentioned environment. A defuzzification function is used to …


Neutrosophic Soft Sets In One And Two-Dimensions Using Iteration Method, M.N. Bharathi, G. Jayalalitha Feb 2025

Neutrosophic Soft Sets In One And Two-Dimensions Using Iteration Method, M.N. Bharathi, G. Jayalalitha

Neutrosophic Sets and Systems

This paper introduces a different perspective of Neutrosophic Fractals and Neutrosophic Soft Fractals, merging the principles of Neutrosophic Logic, Soft set theory, and Fractal Geometry to address indeterminacy in complex, self-similar structures specifically the Von Koch curve and the Sierpinski triangle. It sightsees the complex qualities of Neutrosophic soft sets by incorporating attributes of falsification, indefiniteness, and truth into union and intersection operations. The research elucidates the interplay between Neutrosophic Logic and fractal geometry, leading to more precise modeling of complex systems. Proving theorems and providing examples examine the intricate interactions between membership characteristics in these fractal structures, demonstrating self-similarity. …


Some Harmonic Aggregation Operators For N-Valued Neutrosophic Trapezoidal Numbers And Their Application To Multi-Criteria Decision-Making, İrfan Deli̇, Vakkas Uluçay Feb 2025

Some Harmonic Aggregation Operators For N-Valued Neutrosophic Trapezoidal Numbers And Their Application To Multi-Criteria Decision-Making, İrfan Deli̇, Vakkas Uluçay

Neutrosophic Sets and Systems

As an extension of the both trapezoidal fuzzy numbers and neutrosophic trapezoidal numbers, the N-valued neutrosophic trapezoidal numbers, which are special neutrosophic multi-sets on subset of real numbers. Harmonic mean is a conservative average, which is widely used to aggregate central tendency data. In the existing literature, the harmonic mean is generally considered as a fusion technique of numerical data information. In this paper, we investigate a method for the situations in which the input data are expressed in neutrosophic values. Therefore, we propose two aggregations are called harmonic aggregation operators and weighted harmonic mean operators on N-valued neutrosophic trapezoidal …


Innovative Assessment Of Dance Teaching Effectiveness Using The Electre Approach And Neutrosophic Hypersoft Sets For Comprehensive Performance Analysis, Pei Yao Feb 2025

Innovative Assessment Of Dance Teaching Effectiveness Using The Electre Approach And Neutrosophic Hypersoft Sets For Comprehensive Performance Analysis, Pei Yao

Neutrosophic Sets and Systems

The evaluation of dance teaching quality in universities is a process of assessing the effectiveness of dance courses through multiple dimensions. The focus is on examining students' improvement in dance skills, artistic expression, mastery of theoretical knowledge, teaching methods, and the learning environment. By using scientific evaluation methods, such as multi attribute decision-making models, the quality of teaching is quantified and optimized, promoting students' overall development and the improvement of teaching practices. The evaluation of dance teaching quality is often considered a multiple attribute group decision-making (MAGDM) problem. In this paper, the ELECTRE method is proposed to address MAGDM using …


A Neutrosophic Approach To Solving First-Order Differential Equations: Applications To Heat Convection With Uncertain Initial Conditions, Said Broumi, M. Shanmugapriya, R. Sundareswaran Feb 2025

A Neutrosophic Approach To Solving First-Order Differential Equations: Applications To Heat Convection With Uncertain Initial Conditions, Said Broumi, M. Shanmugapriya, R. Sundareswaran

Neutrosophic Sets and Systems

This study explores the solution of first-order differential equations (����) using trapezoidal neutrosophic numbers (����������������������) as initial conditions. It examines various forms of ���������������������� based on the dependencies of truth (��), indeterminacy (��), and falsity (��). The application first order DE is illustrated through heat conduction problems in fluids. The temperature distribution ��1(��,��), � �2(��,��), ��1′(��, ��), ��1′′(��, ��), ��2 ′(��, ��) and ��2 ′′(��, ��) are analyzed through tables and graphs. A solution procedure for the system of first-order ODEs is developed and demonstrated with numerical examples.


The “Mitssp” Strategy And Its Impact On The Development Of Critical Thinking: A Study Based On Neutrosophic Statistics, Flor De María Ureta-Chávez, Nélida Angela Beraun-Sánchez, Yris Yolanda Bedoya-Campos, Wilber Huamanyauri-Cornelio, Edgar Augusto Salinas-Loarte, Beker Maraza-Vilcanqui, Rosaluz Victoria Bardales-Gonzales, Arcadio Aguirre-Rojas Feb 2025

The “Mitssp” Strategy And Its Impact On The Development Of Critical Thinking: A Study Based On Neutrosophic Statistics, Flor De María Ureta-Chávez, Nélida Angela Beraun-Sánchez, Yris Yolanda Bedoya-Campos, Wilber Huamanyauri-Cornelio, Edgar Augusto Salinas-Loarte, Beker Maraza-Vilcanqui, Rosaluz Victoria Bardales-Gonzales, Arcadio Aguirre-Rojas

Neutrosophic Sets and Systems

Nowadays, with the massive use of Information and Communication Technologies and social networks, it is more necessary than ever for citizens to develop critical thinking. Information media such as the Internet are flooded with false ideas, totally or partially. That is why it is necessary to provide young people with critical thinking that allows them to differentiate what is true from what is false, or even to identify dubious information. Based on the scientific method and under the protection of the educational research methodology, this article aims to demonstrate the effectiveness of the MITSSP strategy for the de velopment of …


Energy Of A Neutrosophic Soft Set And Its Applications To Multi-Criteria Decision-Making Problems, Zeynep Baser, Vakkas Ulucay Feb 2025

Energy Of A Neutrosophic Soft Set And Its Applications To Multi-Criteria Decision-Making Problems, Zeynep Baser, Vakkas Ulucay

Neutrosophic Sets and Systems

In our paper, we continue the study of the theory of neutrosophic soft sets and their properties. Based on the singular values of the corresponding matrix, we de ne the energy of a neutrosophic soft set, as well as the lower energy of a neutrosophic soft set and the upper energy of a neutrosophic soft set, allowing us to introduce an e ective method for decision-making. To do this, we rst write a neutrosophic soft set as a matrix and multiply it by its transpose with respect to the given product and the given norm t, s. Then, we consider …


Operators For Uncertain Over/Under/Off-Sets/-Logics/-Probabilities/-Statistics, Florentin Smarandache Feb 2025

Operators For Uncertain Over/Under/Off-Sets/-Logics/-Probabilities/-Statistics, Florentin Smarandache

Neutrosophic Sets and Systems

In this paper we propose for the first time the operators (intersection/conjunction and union/disjunction) for the Uncertain Over/Under/Off-Sets/-Logics/-Probabilities-Statistics. Practical applications of Fuzzy Over/Under/Off-Sets/-Logics/-Probabilities-Statistics are presented. Similar applications can be designed for any fuzzy-extensions Over/Under/Off-Sets/-Logics/-Probabilities Statistics.


Analytical Solutions Of Heat Transfer Model In Two-Dimensional Case Of Neutrosophic Fredholm Integro-Di Erential Equations, Amer Darweesh, Kamel Al- Khaled, Marwan Alquran, Adel Almalki, Sohad Al-Omari Feb 2025

Analytical Solutions Of Heat Transfer Model In Two-Dimensional Case Of Neutrosophic Fredholm Integro-Di Erential Equations, Amer Darweesh, Kamel Al- Khaled, Marwan Alquran, Adel Almalki, Sohad Al-Omari

Neutrosophic Sets and Systems

This article uses the fractional residual power series (FRPS) method to solve a linear neutrosophic fractional integro-di erential equation in two dimensions. In what context does the term fractional derivative appeared, we presented the modi ed fractional power series method, a new technique that uses fractional power series expansion to approximate neutrosophic fractional integro-di erential equations. A modi ed new method has been formulated, which is an improvement on the RPS, named as Modi ed Fractional Power Series Method (MFPSM), to solve the same problem under investigation. Novel results associated with the rate of convergent and error order of the …


On Consistent And Weak Transitive Neutrosophic Fuzzy Matrices, K. Radhika, M. Kavitha, K. Thirumalai, R. Geethanjaliyadav, N. Buvaneswari, V. Kamalakannan Feb 2025

On Consistent And Weak Transitive Neutrosophic Fuzzy Matrices, K. Radhika, M. Kavitha, K. Thirumalai, R. Geethanjaliyadav, N. Buvaneswari, V. Kamalakannan

Neutrosophic Sets and Systems

This paper delves into the properties of two specific types of Neutrosophic Fuzzy Matrices (NFM) namely consistent and weakly transitive NFM. A significant focus is placed on nilpotent and transitive NFM, highlighting their critical role in the analysis. It is demonstrated that these two types of matrices are controllable, and a formula is derived for determining the canonical form of a weakly transitive NFM. To support and clarify the findings, counterexamples are provided throughout the discussion. We introduce an operation on NFM, referred to as the Gödel implication operator. Utilizing this operator, we establish several significant results for NFM, with …


An Uncertainty Framework For Development Level Evaluation Of Preschool Education In Rural And Remote Communities, Jing Liu, Songlin Tang, Biqiong Luo Feb 2025

An Uncertainty Framework For Development Level Evaluation Of Preschool Education In Rural And Remote Communities, Jing Liu, Songlin Tang, Biqiong Luo

Neutrosophic Sets and Systems

This study proposed an uncertainty framework for evaluation of Integrated Preschool with School in Rural and Remote Communities. This evaluation has various criteria so, we used the concept of multi-criteria decision making (MCDM). There are various MCDM methods to deal with decision making problems. We used the COPRAS method to rank the alternatives. COPRAS is a MCDM method dealing with various criteria and alternatives. This study used the Plithogenic sets to deal with uncertainty and vague information. Three experts are invited to evaluate the criteria and alternatives. Case study with an empirical example with nine criteria and nine alternatives is …


Mappings Of Plithogenic Cubic Sets, S.P. Priyadharshini, J. Ramkumar Feb 2025

Mappings Of Plithogenic Cubic Sets, S.P. Priyadharshini, J. Ramkumar

Neutrosophic Sets and Systems

Objectives: To introduce novel mappings for plithogenic fuzzy cubic structures and derive core properties of stable and almost stable plithogenic neutrosophic cubic mappings. Methods: This study employs a theoretical approach to develop mappings for plithogenic cubic sets. We conducted a comprehensive analysis of stable and almost stable mappings, utilizing comparative techniques to assess their properties. Unique modifications include the introduction of specific stability criteria and a detailed examination of their implications in decision-making contexts. Findings: Our findings reveal that the newly introduced mappings exhibit distinct stability characteristics, enhancing the theoretical framework of Plithogenic cubic mapping. These mappings not only align …


Weighted Statistical Convergence In Neutrosophic Normed Linear Spaces, P. Jenifer, M. Jeyaraman, M. Mursaleen Feb 2025

Weighted Statistical Convergence In Neutrosophic Normed Linear Spaces, P. Jenifer, M. Jeyaraman, M. Mursaleen

Neutrosophic Sets and Systems

In this research, the authors provide a de nition among the Neutrosophic norm(NN)( terms of the summability property ( Nqn). We generalize the idea among Statistical Convergence (SC) in terms of NN by introducing the notion of ( Nqn)-summability with respect to NN( ... ) in ). Here, the novel strategy is referred to by the term neutrosophic weighted statistical convergence. We also investigated its dependence on the NN( ... ) in terms of statistical convergence and ( Nqn)-summability.


Multiple-Criteria Decision-Making And Plithogenic Sets-Based Topsis Framework For 'Dual-Qualified' Teachers Quality Evaluation In The Context Of High-Quality Development Of Vocational Education, Wenjing Liu, Yuemin Gao, Qiongyao Liu, Wenqiang Dai Feb 2025

Multiple-Criteria Decision-Making And Plithogenic Sets-Based Topsis Framework For 'Dual-Qualified' Teachers Quality Evaluation In The Context Of High-Quality Development Of Vocational Education, Wenjing Liu, Yuemin Gao, Qiongyao Liu, Wenqiang Dai

Neutrosophic Sets and Systems

This study proposed a multi-criteria decision making (MCDM) methodology for evaluating the Dual-Qualified" Teachers Quality. This evaluation has various criteria and factors. So, the MCDM can deal with these factors. This study combines the MCDM methodology with the plithogenic set to deal with uncertainty and vague information. Three experts are invited to evaluate the criteria and alternatives. Then we replace their opinions by using plithogenic numbers. We used plithogenic operators to combine these numbers. Eight criteria and eleven alternatives are used in this study. We used the TOPSIS method under the plithogenic numbers to rank the alternatives. the results show …


Enhanced Approach For Japanese Teaching Quality Evaluation In Higher Education Under Plithogenic Sets, Yifan Liang Feb 2025

Enhanced Approach For Japanese Teaching Quality Evaluation In Higher Education Under Plithogenic Sets, Yifan Liang

Neutrosophic Sets and Systems

Japanese language instruction has drawn more attention in the twenty-first century, a time of frequent international interactions and the rapid advancement of knowledge. Colleges and universities are now concentrating on raising the standard of Japanese education going forward as a result. To improve teaching quality, we must strengthen the entire management of teaching quality, particularly the evaluation of instructors' instruction. However, it is challenging to translate the evaluation results into a mathematical analytical formula because there are several elements that affect the quality of instruction, and the weight of each factor changes. We proposed a multi-criteria decision making (MCDM) methodology …