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Articles 1231 - 1260 of 3835
Full-Text Articles in Entire DC Network
Neutrosophic Statistical Interval Methods For Reliability Analysis: A Failure Censored Lifetest With Repetitive Group Sampling Plan, S. Jayalakshmi, S. Vijilamery
Neutrosophic Statistical Interval Methods For Reliability Analysis: A Failure Censored Lifetest With Repetitive Group Sampling Plan, S. Jayalakshmi, S. Vijilamery
Neutrosophic Sets and Systems
The Reliability Sampling Plans based on Failure-Censored data assume that all failure data is reli able, clear, and definitive, as noted in the literature.If the failure data measurements are unclear, indistinct, and unsure in a practical sense, we opt to adopt a new form of reliability theory known as Neutrosophic Reliability Theory. In this paper deals with Repetitive Group Sampling Plan based on failure-censored life tests using the Neutrosophic Statistical Interval Method. This plan assumes that failure times follow a Neutrosophic Gen eralized Exponential Distribution and also consider the Neutrosophic plan parameters for a given producer’s risk and a given …
Enhanced Mcdm Methodology Under Uncertainty: Applications To Energy Efficiency Evaluation Of Mechanical And Electrical Systems In Public Buildings, Daoming Wang
Neutrosophic Sets and Systems
Evaluation of Mechanical and Electrical systems in public Buildings is a multi- criteria decision-making problem that has various criteria. These criteria can affect energy efficiency. So, we aim to propose an MCDM method for rate the criteria importance and proposed a set of systems to select the best one in energy firms. This section can increase energy efficiency. We applied the ARAS methodology to rank the alternatives. The ARAS methodology is an MCDM method. It applied into criteria independent. The ARAS method is integrated under the plithogenic set to deal with the vague and uncertainty information. The plithogenic set is …
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
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
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 Integrated Plithogenic Mcdm Approach College English Blended Teaching Quality Evaluation, Yuan Huang, Jie Yu
An Integrated Plithogenic Mcdm Approach College English Blended Teaching Quality Evaluation, Yuan Huang, Jie Yu
Neutrosophic Sets and Systems
The Outcome-Based Education method has garnered increased attention due to its focus on curriculum creation based on learning outcomes and its concern for the abilities that society requires. This study proposed a multi-criteria decision making (MCDM) methodology for college English blended teaching quality evaluation. The MCDM method used to deal with different criteria. We proposed an uncertainty framework under the Plithogenic sets to deal with uncertainty and vague data. The Plithogenic sets integrated with the WASPAS method. We used the WASPAS method to rank the alternatives. Eight criteria and eleven colleges are used in this study. The results show the …
An Uncertainty Framework For Development Level Evaluation Of Preschool Education In Rural And Remote Communities, Jing Liu, Songlin Tang, Biqiong Luo
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 …
Plithogenic Sets-Based Mabac Framework For Evaluating The Quality Of Elderly Care Security Services For Left-Behind Elderly In Rural Areas Of Western China: A Healthcare Industry Perspective, Chenghua Wang, Xiaogang Liu, Jiyun Yao
Plithogenic Sets-Based Mabac Framework For Evaluating The Quality Of Elderly Care Security Services For Left-Behind Elderly In Rural Areas Of Western China: A Healthcare Industry Perspective, Chenghua Wang, Xiaogang Liu, Jiyun Yao
Neutrosophic Sets and Systems
This study proposed a multi-criteria decision-making (MCDM) methodology for evaluating the elderly care security services. These services consist various criteria, so the MCDM methodology is used. MABAC methodology is a MCDM method used to rank the alternatives. The MABAC methodology is integrated under the plithogenic sets to deal with vague and uncertainty data. The plithogenic sets are an extension of neutrosophic sets to deal with inconsistencies data. The criteria weights are computed in this study. Seven criteria and 13 alternatives are collected in this study. An application with opinions of three experts evaluate the criteria and alternatives. The results show …
Neutrosophic-Supported Machine Learning Models For Oral Disease Classification, Ibrahim M. Elezmazy, Doaa El-Shahat
Neutrosophic-Supported Machine Learning Models For Oral Disease Classification, Ibrahim M. Elezmazy, Doaa El-Shahat
Neutrosophic Sets and Systems
This study is presented to investigate the influence of the neutrosophic (NS) domain on the performance of the most common machine learning (ML) models. Specifically, it evaluates the effectiveness of Random Forest (RF), Extra Trees (ET), K-Neighbors (KNN), Gaussian Naive Bayes (GaussianNB), and Decision Tree (DT) classifiers in detecting oral diseases. The NS domain divides any image into three membership components: falsity (��), indeterminacy (��) and truth (��), where T denotes the degree to which each pixel in an image is a member of a particular class or category, F denotes the degree to which the pixel is not a …
Mappings Of Plithogenic Cubic Sets, S.P. Priyadharshini, J. Ramkumar
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
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
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
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 …
A Hybrid Mcdm Approach For Evaluating Financial Performance Based On A Set Of Business Companies, Lei Sun, Hong Zheng
A Hybrid Mcdm Approach For Evaluating Financial Performance Based On A Set Of Business Companies, Lei Sun, Hong Zheng
Neutrosophic Sets and Systems
This paper uses multi-criteria decision making (MCDM) to evaluate the f inancial performance based on a set of business companies. This study proposed a decision-making methodology for computing the criteria weights and ranking the alternatives. The decision-making methodology is integrated with plithogenic sets to deal with uncertainty information. We collected seven criteria and eleven alternatives to be ranked. We used the WSM method under the plithogenic sets to rank the alternatives. The results show the Profitability criterion has the highest importance and the Market Valuation criterion has the lowest importance. In the ranking of alternatives, we show the alternative 11 …
Development Of Neutrosophic Gamma Distribution For Modeling Neonatal Mortality Data, Fuad S. Alduais, Zahid Khan
Development Of Neutrosophic Gamma Distribution For Modeling Neonatal Mortality Data, Fuad S. Alduais, Zahid Khan
Neutrosophic Sets and Systems
This study explores and investigates the key characteristics of the neutrosophic gamma model (NGM) to analyze neonatal mortality data. The proposed model has the ability to handle imprecision, vagueness and uncertainty in data which often exist in health statistics. The key characteristics of the proposed model such as the probability density function, cumulative distribution function, statistical moments and some basic shape coefficients are discussed to clarify its difference from the classical model. Air pollution mortality data are commonly encountered imprecise and incomplete information due to factors such as missing values, measurement errors, reporting inconsistencies. The proposed NGM has the inherent …
Neutrosophic Sets And Systems, Vol. 79,2025, Florentin Smarandache, Mohamed Abdel-Basset, Maikel. Leyva Vazquez
Neutrosophic Sets And Systems, Vol. 79,2025, Florentin Smarandache, Mohamed Abdel-Basset, Maikel. Leyva Vazquez
Neutrosophic Sets and Systems
the whole volume
, Cloud Computing And Neutrosophic Logic: Navigating Uncertainty In Educational Administration, Ibrahim Yasser, Aya A. Abd El-Khalek, Huda E. Khalid, A. A. Salama, Ahmed K. Essa
, Cloud Computing And Neutrosophic Logic: Navigating Uncertainty In Educational Administration, Ibrahim Yasser, Aya A. Abd El-Khalek, Huda E. Khalid, A. A. Salama, Ahmed K. Essa
Neutrosophic Sets and Systems
Educational institutions face inherent uncertainties in student performance, stakeholder priorities, and data analysis. This paper explores how cloud computing, with its data storage, analytics, and collaboration tools, can address these uncertainties in educational administration. We propose a neutrosophic framework utilizing "truth," "falsity," and "indeterminacy" values to represent these complexities within educational data. Real-world case studies analyze how cloud computing can reduce uncertainties and improve decision-making. Our findings reveal that cloud computing offers significant potential for navigating the "fog" of educational administration, but its effectiveness is enhanced by considering the "indeterminacy" inherent in educational data through the neutrosophic framework. This research …
A Comparative Analysis Of Data-Driven And Model-Based Neutrosophication Methods: Advancing True Neutrosophic Logic In Medical Data Transformation, Maikel Yelandi Leyva Vázquez, Lorenzo Cevallos-Torres, Omar Mar Cornelio, Florentin Smarandache
A Comparative Analysis Of Data-Driven And Model-Based Neutrosophication Methods: Advancing True Neutrosophic Logic In Medical Data Transformation, Maikel Yelandi Leyva Vázquez, Lorenzo Cevallos-Torres, Omar Mar Cornelio, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Neutrosophic logic extends fuzzy logic by explicitly modeling indeterminacy (I), offering a robust framework for uncertainty representation. The transformation of crisp data into neutrosophic triplets {T, I, F}—known as neutrosophication—is crucial for applying neutrosophic models in real-world analysis. However, comparative evaluations of existing neutrosophication methods remain limited. This study presents a systematic comparison of five approaches: three model-based methods (Parabolic, Threshold Distance, Fuzzy Membership), one density-based method (Kernel Density Estimation), and a proposed data-driven K-Means clustering method integrating sigmoid membership functions. Using a medical dataset of 299 patients and six continuous clinical variables, we assessed statistical behavior, consistency, and alignment …
Neutrosophic Perspectives On The Body-Mind-Soul-Spirit Fluidity, Florentin Smarandache
Neutrosophic Perspectives On The Body-Mind-Soul-Spirit Fluidity, Florentin Smarandache
Neutrosophic Sets and Systems
This paper examines the concepts of the ‘Body’, ‘Mind’, ‘Soul,’ and ‘Spirit’ through the lens of neutrosophy. Neutrosophy challenges traditional binary logic, positing that ‘truth’ is not a fixed entity. Through the lens of neutrosophy, which is a philosophical framework, one seeks to address and reconcile contradictions and uncertainties in various fields, including philosophy, mathematics and science in general, as well as logic. Any phenomenon or dynamic structure can exist in different degrees (of truth, indeterminacy, and falsity). By applying this triadic approach to these four components, we propose the notion of a Neutrosophic Body-Mind-Soul-Spirit as a Quadruple Fluidity, where …
Local-Neutrosophic Logic And Local-Neutrosophic Sets: Incorporating Locality With Applications, Florentin Smarandache, Takaaki Fujita
Local-Neutrosophic Logic And Local-Neutrosophic Sets: Incorporating Locality With Applications, Florentin Smarandache, Takaaki Fujita
Branch Mathematics and Statistics Faculty and Staff Publications
The study of uncertainty has been a significant area of research, with concepts such as fuzzy sets [87], fuzzy graphs [51], and neutrosophic sets [58] receiving extensive attention. In Neutrosophic Logic, indeterminacy often arises from real-world complexities. This paper explores the concept of locality as a key factor in determining indeterminacy, building upon the framework introduced by F. Smarandache in [73]. Locality refers to processes constrained within a specific region, where an object or system is directly influenced by its immediate surroundings. In contrast, nonlocality involves effects that transcend spatial or temporal boundaries, where changes in one location have direct …
Neutrosophic Twofold Superhyperalgebra And Anti Superhyperalgebra, Takaaki Fujita, Florentin Smarandache
Neutrosophic Twofold Superhyperalgebra And Anti Superhyperalgebra, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Neutrosophic Sets are conceptual frameworks designed to address uncertainty. A Neutrosophic TwoFold Algebra is a hybrid algebraic structure defined over a neutrosophic set, combining classical algebraic operations with neutrosophic components. Concepts such as Hyperalgebra and Superhyperalgebra extend classical Algebra using Power Sets and 𝑛-th powersets. Additionally, structures such as NeutroAlgebra and AntiAlgebra have been defined in recent y ears. This paper explores several related concepts, including TwoFold SuperhyperAlgebra and Anti SuperhyperAlgebra.
An Approach To Numerical Solutions For Refined Neutrosophic Differential Problems Of High-Orders, Ahmed Salem Heilat
An Approach To Numerical Solutions For Refined Neutrosophic Differential Problems Of High-Orders, Ahmed Salem Heilat
Neutrosophic Sets and Systems
The main goal of this paper is to studying a new numerical method for finding the refined neutrosophic numerical solutions to some refined neutrosophic differential problems of high orders. We use high-degrees refined neutrosophic polynomials to get the approximated solutions, where we apply our method on two different refined neutrosophic boundary value problems with numerical tables to compare the novel findings with classical ones.
Enhanced Madm Strategy With Heptapartitioned Neutrosophic Distance Metrics, Mohamed Eassa, M. Myvizhi, Mohamed Elkholy, Ahmed Abdelhafeez, Hussam Elbehiery
Enhanced Madm Strategy With Heptapartitioned Neutrosophic Distance Metrics, Mohamed Eassa, M. Myvizhi, Mohamed Elkholy, Ahmed Abdelhafeez, Hussam Elbehiery
Neutrosophic Sets and Systems
In this work, a novel methodological approach to multi-attribute decision-making problems is developed and the notion of Heptapartitioned Neutrosophic Set Distance Measures (HNSDM) is introduced. By averaging the Penta-Partitioned Neutrosophic Distance Measures under particular conditional criteria, the suggested technique ranks the options. Additionally, we explore the fundamental characteristics of HNSDM and provide several illustrative theorems. The Heptapartitioned Neutrosophic Set Distance Measures are formulated based on the Hepta Neutrosophic Set. Lastly, a practical numerical example is provided to illustrate the efficacy of the suggested methodology.
A Cross-Entropy-Based Framework Using Hypersoft Type-2 Neutrosophic Numbers For Innovation Capability Evaluation In Central Cities Of Emerging Economies, Xiangke Zhang, Shoukui He, Xu Chen
A Cross-Entropy-Based Framework Using Hypersoft Type-2 Neutrosophic Numbers For Innovation Capability Evaluation In Central Cities Of Emerging Economies, Xiangke Zhang, Shoukui He, Xu Chen
Neutrosophic Sets and Systems
The comprehensive evaluation of innovation capabilities in central cities of emerging countries is essential for promoting regional economic growth. This evaluation examines various factors, such as scientific activities, innovation infrastructure, talent resources, and policy environments, offering insights into the current innovation landscape and future potential. By guiding the allocation of resources and optimizing innovation policies, it fosters the transformation of technological achievements and accelerates urban economic transformation and sustainable development. Moreover, it helps cities attract investment and skilled talent, enhancing their competitiveness and influence. This evaluation is a multi-attribute decision-making (MADM) challenge, for which the cross-entropy method has been recently …
Utilizing Cocoso And Interval Neutrosophic Magdm With Superhypersoft For Competitiveness Assessment In Rural Tourism Of Surrounding Cities, Aiping Cui, Zhiyao Liu
Utilizing Cocoso And Interval Neutrosophic Magdm With Superhypersoft For Competitiveness Assessment In Rural Tourism Of Surrounding Cities, Aiping Cui, Zhiyao Liu
Neutrosophic Sets and Systems
With rising living standards, rural tourism near cities has rapidly developed, playing a key role in the sustainable development of urban economies and societies. Factors like ecological environment, historical and cultural resources, and landscape significantly influence the competitiveness of rural tourism. However, current research on this topic is still in its early stages, with a focus on tourism benefits to cities, often overlooking other impacts. Rural tourism boosts employment, promotes rural industries, and increases farmers' incomes, accelerating rural urbanization and economic growth. Therefore, evaluating the competitiveness of rural tourism near cities is essential for its development. The evaluation of rural …
Dvnn-Cocoso: A Hybrid Neutrosophic Model For Evaluating Social And Economic Impacts Of Sports Event, Changshun Bai, Pute Lan
Dvnn-Cocoso: A Hybrid Neutrosophic Model For Evaluating Social And Economic Impacts Of Sports Event, Changshun Bai, Pute Lan
Neutrosophic Sets and Systems
The evaluation of the social benefits of major sports events is a multifaceted process, focusing on assessing the positive impacts such events bring to a host city and society. These benefits include promoting public health, fostering national pride and social cohesion, boosting local economies, and improving infrastructure. This evaluation process can be viewed as a multiple-attribute decision making (MADM) problem. This study introduces a novel double-valued neutrosophic number CoCoSo (DVNN-CoCoSo) technique for MADM, incorporating DVNN Hamming distance (DVNNHD) and DVNN Logarithmic distance (DVNNLD). This method effectively handles the uncertainty inherent in evaluating social benefits. A numerical example of social benefits …
On A Novel Topological Space Based On Partially Ordered Ring Of Weak Fuzzy Complex Numbers And Its Relation With The Partially Ordered Neutrosophic Ring Of Real Numbers, Raed Hatamleh
Neutrosophic Sets and Systems
This work is dedicated to studying for the first time a novel topological space generated by weak fuzzy complex intervals based on the partial ordered ring structure of weak fuzzy complex numbers, where we build a topology structure over these intervals. Also, we present many novel results as mathematical theorems, mathematical proofs, and many related examples. On the other hand, we use the AH-isometry to determine the relationship between the weak fuzzy complex intervals, and neutrosophic intervals.
Symbolic Hyperplithogenic Set, Takaaki Fujita, Florentin Smarandache
Symbolic Hyperplithogenic Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets have been widely investigated for tackling uncertainty, with numerous applications explored across various domains. As extensions of the Plithogenic Set, the HyperPlithogenic Set and the SuperHyperPlithogenic Set are also recognized. A Symbolic Plithogenic Set (SPS) is a structured set defined by symbolic components 𝑃𝑖 and coefficients 𝑎𝑖 , enabling flexible algebraic operations under a specified prevalence order. In this paper, we examine concepts including the Symbolic HyperPlithogenic Set and the Symbolic 𝑛-SuperhyperPlithogenic Set.
Some Types Of Hyperneutrosophic Set (4): Cubic, Trapozoidal, Q-Rung Orthopair, Overset, Underset, And Offset, Florentin Smarandache, Takaaki Fujita
Some Types Of Hyperneutrosophic Set (4): Cubic, Trapozoidal, Q-Rung Orthopair, Overset, Underset, And Offset, Florentin Smarandache, Takaaki Fujita
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds upon the foundational work presented in [38–40]. The Neutrosophic Set provides a comprehensive mathematical framework for managing uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set, which are specifically designed to address increasingly complex and multidimensional problems. The formal definitions of these sets are available in [30]. In this paper, we extend the Neutrosophic Cubic Set, Trapezoidal Neutrosophic Set, q-Rung Orthopair Neutrosophic Set, Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset using the frameworks of the Hyperneutrosophic Set and the SuperHyperneutrosophic Set. Furthermore, …
Some Types Of Hyperneutrosophic Set (3): Dynamic, Quadripartitioned, Pentapartitioned, Heptapartitioned, M-Polar, Takaaki Fujita, Florentin Smarandache
Some Types Of Hyperneutrosophic Set (3): Dynamic, Quadripartitioned, Pentapartitioned, Heptapartitioned, M-Polar, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds upon the foundation established in [50, 51]. The Neutrosophic Set provides a robust mathematical framework for handling uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent developments have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to tackle increasingly complex and multidimensional problems. In this study, we explore further extensions, including the Dynamic Neutrosophic Set, Quadripartitioned Neutrosophic Set, Pentapartitioned Neutrosophic Set, Heptapartitioned Neutrosophic Set, and m-Polar Neutrosophic Set, to address advanced challenges and applications.
Plithogenic Duplets And Plithogenic Triplets, Takaaki Fujita, Florentin Smarandache
Plithogenic Duplets And Plithogenic Triplets, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
A Neutrosophic Set is a mathematical framework that represents degrees of truth, indeterminacy, and falsehood to address uncertainty in membership values [41, 42]. In contrast, a Plithogenic Set extends this concept by incorporating attributes, their possible values, and the corresponding degrees of appurtenance and contradiction [50]. Among the related concepts of Neutrosophic Sets, Neutrosophic Duplets and Neutrosophic Triplets are well-known. This paper defines Plithogenic Duplets and Plithogenic Triplets as extensions of these concepts using the Plithogenic Set framework and briefly examines their relationship with existing concepts.