Digital Commons Network^™

Combined Plithogenic Hypersoft Sets In Decision Making On Supplier Selection With Different Mcdm Approaches., Sikkanan Sudha, Ravi Priya, Nivetha Martin, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Decision making methods integrated with Plithogenic sets are highly feasible and resilient in designing optimal solutions. This research work identifies the research gaps of limited applications of combined plithogenic hypersoft sets (CPHSS) and hence proposes a supplier selection decision problem with an integrated approach combining CPHSS with MCDM methods. A generalized form of Plithogenic accuracy function is used in determining the plithogenic accuracy matrix to which the prominent ranking methods of TOPSIS, ELECTRE, VIKOR and MAIRCA are applied. The proposed hybrid decision approach is illustrated using supplier selection decision problem as a case study. The ranking results are compared with …

Logical Pluralism And Neutrosophy: Reflections On The Nature Of Truth, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The article explores the shift from classical binary logic (true and false) to a more complex landscape of logical frameworks. It introduces logical pluralism, which suggests that no single, universally accepted system of logic exists. The paper connects this idea to neutrosophy, a framework that extends fuzzy logic by incorporating a third value: indeterminacy. This triadic approach, where every proposition has a degree of truth (T), falsity (F), and indeterminacy (I), is particularly useful for managing incomplete or contradictory information. The author argues that different logical systems, like different tools, are suited for different problems, and that the …

An Innovative Approach On Yao’S Three-Way Decision Model Using Intuitionistic Fuzzy Sets For Medical Diagnosis, Wajid Ali, Tanzeela Shaheen, Iftikhar Ul Haq, Florentin Smarandache, Hamza Ghazanfar Toor, Faiza Asif

Branch Mathematics and Statistics Faculty and Staff Publications

In the realm of medical diagnosis, intuitionistic fuzzy data serves as a valuable tool for representing information that is uncertain and imprecise. Nevertheless, decision-making based on this kind of knowledge can be quite challenging due to the inherent vagueness of the data. To address this issue, we employ power aggregation operators, which prove effective in combining several sources of data, such as expert thoughts and patient information. This allows for a more correct diagnosis; a particularly crucial aspect of medical practice where precise and timely diagnoses can significantly impact medication policy and patient results. In our research, we introduce a …

A New Mood’S Median Test For Imprecise Data, Abdulrahman Alaita, Muhammad Aslam, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The existing Mood’s median test is a non-parametric test used to compare two or more sample data sets whether they are from the same population or not. There can be no application of this test to uncertain and indeterminate data. Therefore, it is necessary to find a generalization of this test that will enable us to apply it in uncertain environments. This study will present a new approach that utilizes neutrosophic statistics to apply Mood’s median test. The approach involves defining hypotheses, determining a decision rule, and performing the test in an uncertain environment. An evaluation of the performance of …

A Neutrosophic Approach To Study Agnotology: A Case Study On Climate Change Beliefs, Florentin Smarandache, Maikel Leyva Vázquez

Branch Mathematics and Statistics Faculty and Staff Publications

Misinformation and biased information significantly impact public perception and political decisions, especially on critical issues such as climate change and environmental conservation. This study aims to understand how indeterminacy and contradiction influence public perception and policy formulation by applying neutrosophic theory to model the complexity and multi-dimensionality of ignorance. Using neutrosophic Likert scales, we capture a nuanced spectrum of opinions on the scientific certainty of human impact on climate change. The results are analyzed through a k-means clustering algorithm to identify patterns and segment participants into groups based on their levels of truth, indeterminacy, and falsehood. This approach reveals deeper …

A Refined Neutrosophic Components Into Subcomponents With Plausible Applications To Long Term Energy Planning Predominated By Renewable Energy, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

It is known that in the long-term planning of future energy supplies, in most countries, it is most likely that the energy mix will be predominated by renewable energy generation. While this feature of a predominating renewable energy mix appears too far fetched, such long term planning has been suggested, for instance, by Mark Jacobson from Stanford and also by John Blackburn. Here we consider two things, the first would be how to consider the long-term energy planning based on neutrosophic logic split into subcomponents.

Residual Attention Augmentation Graph Neural Network For Improved Node Classification Residual Attention Augmentation Graph Neural Network For Improved Node Classification, Muhammad Affan Abbas, Waqar Ali, Florentin Smarandache, Sultan S. Alshamrani, Muhammad Ahsan Raza, Abdullah Alshehri, Mubashir Ali

Branch Mathematics and Statistics Faculty and Staff Publications

Graph Neural Networks (GNNs) have emerged as a powerful tool for node representation learning within graph structures. However, designing a robust GNN architecture for node classification remains a challenge. This study introduces an efficient and straightforward Residual Attention Augmentation GNN (RAA-GNN) model, which incorporates an attention mechanism with skip connections to discerningly weigh node features and overcome the over-smoothing problem of GNNs. Additionally, a novel MixUp data augmentation method was developed to improve model training. The proposed approach was rigorously evaluated on various node classification benchmarks, encompassing both social and citation networks. The proposed method outperformed state-of-the-art techniques by achieving …

Bv2trs Appraiser Model: Enforcing Bharat Version2 In Tree Soft Modelling For Appraising E-Mobility Hurdles, Mona Mohamed, Florentin Smarandache, Michael Gr. Voskoglou

Branch Mathematics and Statistics Faculty and Staff Publications

Electric vehicles (EVs) are being introduced to lessen greenhouse gas (GHG) emissions, air pollution, and reliance on fossil fuels. As a result of the government's aggressive promotion of EVs and rising environmental consciousness, EVs are quickly rising to the top of the low-carbon transportation market. Several viewpoints suggested that shifting to electric vehicles has been seen as a potential way to achieve sustainable mobility. Nevertheless, many studies discussed the obstacles and hurdles that obstruct the embracing of various electric-mobility (E-mobility) as EVs and electric-scooters (E-scooters) as eco-friendly means. Herein, we discussed these hurdles and determined them through surveys for prior …

Automated Livestock Practices: Incorporation Emerging Contemporary Technologies Toward Sustainable Livestock In Era Of Smart Cities, Asmaa Elsayed, Mona Mohamed, Florentin Smarandache, Michael Gr. Voskoglou

Branch Mathematics and Statistics Faculty and Staff Publications

Currently, numerous spheres now face a wider range of needs due to the increasingly competitive and globalized global market. Moreover, digital technologies are necessary for analysis and comprehension in many sectors of contemporary society. For instance, Internet of Things (IoT) has the potential to revolutionize livestock management, including the dairy cattle industry, by providing real-time data and enabling data-driven decisions to improve animal welfare, increase productivity, and promote sustainable farming practices. The main components of IoT-enabled livestock management include sensors, communication systems, data storage, and analysis systems. These components of IoT-enabled livestock management improve animal welfare, increase productivity, and reduce …

Distinctions Between Various Types Of Fuzzy-Extension Hypersoft Sets, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We define the universes of discourses for all fuzzy and fuzzy-extension sets. Then present many types of Plithogenic Universes of discourse and their connections to HyperSoft Sets. Afterward, we make distinctions between various hybrid forms of HyperSoft Sets.

Neutrosophical Plant Hybridization In Decision-Making Problems, M. Arockia Dasan, E. Bementa, Florentin Smarandache, X. Tubax

Branch Mathematics and Statistics Faculty and Staff Publications

Florentin Smarandache developed the neutrosophic set theory to study inconsistency, incomplete, and uncertainty information by using truth-membership, indeterminacy-membership, and falsity-membership functions. One of the main objectives of this chapter is to develop a new methodological approach of neutrosophic sets in multi-criteria decision-making problems. This method considers neutrosophic sets with their unions in the direct direction and the complements of given neutrosophic sets with their intersections are also considered in the reverse direction. Using these collections, single-valued neutrosophic score functions are computed in both directions. After this process, all the alternatives are ranked in the ascending order arrangement to find the …

Evaluating Blockchain Cybersecurity Based On Tree Soft And Opinion Weight Criteria Method Under Uncertainty Climate, Florentin Smarandache, Mona Mohamed, Michael Gr. Voskoglou

Branch Mathematics and Statistics Faculty and Staff Publications

In the era of digital transformation (DT), many digital technologies have emerged and have had a positive impact on society. Nevertheless, because of certain issues with existing technologies, innovative technology has developed to eradicate them. Fog computing (FC) plays a vital role as an intermediate between edge layer and cloud computing (CC) to resolve limited resources and capabilities. In the same vein, blockchain technology (BCT) is responsible for resolving privacy and security issues that IoT suffers from. Due to using cryptography rules and hashing which is utilized in BCT to prevent any trickery. Hence, BC shows promise as a possible …

A Compact Exploration Of Turiyam Neutrosophic Competition Graphs, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Graph theory, a branch of mathematics, examines relationships between entities using vertices and edges. Within this field, Uncertain Graph Theory has emerged to model uncertainties in real-world networks. A notable concept in this area is the competition graph, which captures interactions by connecting vertices that “compete” for the same neighbor, represented by directed edges indicating common neighbors in a digraph. This brief paper introduces the concept of the Generalized Turiyam Neutrosophic Competition Graph and explores its relationships with other graph classes.

A Reconsideration Of Advanced Concepts In Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, And Chemical Graphs, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

One of the most powerful tools in graph theory is the classification of graphs into distinct classes based on shared properties or structural features. Over time, many graph classes have been introduced, each aimed at capturing specific behaviors or characteristics of a graph. Neutrosophic Set Theory, a method for handling uncertainty, extends fuzzy logic by incorporating degrees of truth, indeterminacy, and falsity. Building on this framework, Neutrosophic Graphs [9,84,135] have emerged as significant generalizations of fuzzy graphs. In this paper, we extend several classes of fuzzy graphs to Neutrosophic graphs and analyze their properties.

Soft Sets Extensions Used In Bioinformatics, Florentin Smarandache, Daniela Gifu

Branch Mathematics and Statistics Faculty and Staff Publications

This comprehensive review delves into the intricate realm of Soft Sets and their extensions, including HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set, within the context of biomedical data analysis. Soft Sets serve as a foundational framework for managing the inherent uncertainty and imprecision inherent in biological data, thereby facilitating informed decision-making and knowledge discovery. The exploration of Soft Set Products, particularly in the context of multiple soft sets, underscores their pivotal role in advancing biomedical research. By extending these concepts to HyperSoft Sets, researchers can unlock deeper insights into complex biological phenomena, enabling more accurate predictions and classification.

Neutrosophic Adaptive Lsb And Deep Learning Hybrid Framework For Ecg Signal Classification, Abdallah Rezk, Ahmed S. Sakr, H. M. Abdulkader

Applied Mathematics & Information Sciences

This paper proposes a novel hybrid framework for ECG signal classification and privacy preservation. The framework includes two phases: the first phase uses LSTM+CNN with attention gate for ECG classification, while the second phase utilizes adaptive least signal bit with neutrosophic for hiding important data during transmission. The proposed framework converts data into three sets of degrees (true, false, and intermediate) using neutrosophic and passes them to an embedding layer. In the sender part, the framework hides important data in ECG signal as true and false degrees, using the intermediate set as a shared dynamic key between sender and receiver. …

Generalization Of Renyi’S Entropy And Its Application In Source Coding, Ashiq Hussain Bhat, Niyamat Ali Siddiqui, Ismail A Mageed, Shawkat Alkhazaleh, Vidyanand Rabi Das, M. A. K Baig

Applied Mathematics & Information Sciences

In this paper, we introduce a new generalization of Renyis entropy β(P) and the most important feature of this generalized entropy Rαβ (P) is that it derives most important entropies that are well known and influence information theory and applied mathematics. Some significant properties of Rαβ (P) has been undertaken in this article. In addition, we introduce a new generalized exponentiated mean codeword length Lβα (P) in this article then determine how Rβα (P) and Lβα (P) are related in terms of source coding theorem.

Optimal Agricultural Land Use: An Efficient Neutrosophic Linear Programming Method, Maisam Jdid, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The increase in the size of the problems facing humans, their overlap, the division of labor, the multiplicity of departments, as well as the diversity of products and commodities, led to the complexity of business and the emergence of many administrative and production problems. It was necessary to search for appropriate methods to confront these problems. The science of operations research, with its diverse methods, provided the optimal solutions. It addresses many problems and helps in making scientific and thoughtful decisions to carry out the work in the best way within the available capabilities. Operations research is one of the …

Medical Diagnosis Via Refined Neutrosophic Fuzzy Logic: Detection Of Illness Using Neutrosophic Sets, K. Hemabala, B. Srinivasa Kumar, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures in refined neutrosophic fuzzy sets.

On Refined Neutrosophic Finite P-Group, Sunday Adesina Adebisi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The neutrosophic automorphisms of a neutrosophic groups G (I) , denoted by Aut(G (I)) is a neu-trosophic group under the usual mapping composition. It is a permutation of G (I) which is also a neutrosophic homomorphism. Moreover, suppose that X1 = X(G (I)) is the neutrosophic group of inner neutrosophic auto-morphisms of a neutrosophic group G (I) and Xn the neutrosophic group of inner neutrosophic automorphisms of Xn-1. In this paper, we show that if any neutrosophic group of the sequence G (I), X1, X2, … is the identity, then G (I) is nilpotent.

Neutrosophic Treatment Of The Modified Simplex Algorithm To Find The Optimal Solution For Linear Models, Florentin Smarandache, Maissam Ahmad Jdid

Branch Mathematics and Statistics Faculty and Staff Publications

Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and …

(R1976) A Novel Approach To Solve Fuzzy Rough Matrix Game With Two Players, Vinod Jangid, Ganesh Kumar, Gaurav Sharama, Vishnu Narayan Mishra

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes a new method for solving a two-person zero-sum fuzzy matrix game with goals, payoffs, and decision variables represented as triangular fuzzy rough numbers. We created a pair of fully fuzzy rough linear programming problems for players. Triangular fuzzy rough numbers can be used to formulate two fuzzy linear programming problems for the first player in the form of upper approximation intervals and lower approximation intervals. Two problems for the second player can be created in the same way. These problems have been split into five sub-crisp problems for the player first and five sub-crisp problems for the …

New Development Of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, And Neutrosophic Plithogenic Optimizations, Florentin Smarandache, Yanhui Guo

Branch Mathematics and Statistics Faculty and Staff Publications

This collective book presents state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, and neutrosophic symmetry, as well as their applications in the real world.

Nidus Idearum. Scilogs, Ix: Neutrosophia Perennis, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this ninth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, – in email messages to research colleagues, or replies, and personal notes, some handwritten on the planes to, and from international conferences, about topics on Neutrosophy and its applications, such as: Neutrosophic Bipolar Set, Linguistic Neutrosophic Set, Neutrosophic Resonance Frequency, n-ary HyperAlgebra, n-ary NeutroHyperAlgebra, n-ary AntiHyperAlgebra, Plithogenic Crisp Graph, Plithogenic Fuzzy Graph, Plithogenic Intuitionistic Fuzzy Graph, Plithogenic Neutrosophic Graph, Plithogenic Real Number Graph, Plithogenic Complex Number Graph, Plithogenic Neutrosophic Number Graph, and many more.

Exchanging ideas with: Tareq Al-Shami, …

The Encyclopedia Of Neutrosophic Researchers - 4th Volume (2021), Florentin Smarandache, Maykel Leyva-Vazquez

Branch Mathematics and Statistics Faculty and Staff Publications

Este es el cuarto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial se su impacto en Latinoamérica junto con enlaces a los principales artículos y libros. Los conjuntos neutrosóficos, la lógica neutrosófica, la probabilidad neutrosófica, la estadística neutrosófica, el precálculo neutrosófico, el cálculo neutrosófico, la psicología neutrosófica, la sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión, …

Theory And Application Of Hypersoft Set, Florentin Smarandache, Muhammad Saeed, Muhammad Saqlain, Mohamed Abdel-Baset

Branch Mathematics and Statistics Faculty and Staff Publications

Aims and Scope Florentin Smarandache generalize the soft set to the hypersoft set by transforming the function �� into a multi-argument function. This extension reveals that the hypersoft set with neutrosophic, intuitionistic, and fuzzy set theory will be very helpful to construct a connection between alternatives and attributes. Also, the hypersoft set will reduce the complexity of the case study. The Book “Theory and Application of Hypersoft Set” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic, intuitionistic, and fuzzy information. Our goal is to develop a strong relationship with the MCDM solving techniques and to …

Solving Neutrosophic Linear Equations Systems Using Symbolic Computation (Resolucion De Sistemas De Ecuaciones Lineales Neutrosóficas Mediante Computación Simbólica), Maykel Leyva-Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we apply the concept of neutrosophic numbers to solve a systems of neutrophic linear equations using symbolic computation. Also, we utilize Jupyter, which is supported in Google Colaboratory for performing symbolic computation. The sympy library of Python is used to perform the process of neutrosophic computation. Systems of neutrosophic linear equations are solved through symbolic computation in Python. A case study was developed for the determination of vehicular traffic with indeterminacy. This king of computation opens new ways to deal with indeterminacy in real-world problems.

Structure, Neutrostructure, And Antistructure In Science, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false. Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that are totally true. The NeutroTheorem and AntiTheorem are generalizations and alternatives of …

Combination Of The Single-Valued Neutrosophic Fuzzy Set And The Soft Set With Applications In Decision-Making, Florentin Smarandache, Ahmed Mostafa Khalil, Dunqian Chao, A. A. Azzam, W. Alharby

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making …

Variants Of Meir-Keeler Fixed Point Theorem And Applications Of Soft Set-Valued Maps, Akbar Azam, Mohammed Shehu Shagari

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we prove a Meir-Keeler type common fixed point theorem for two mappings for which the range set of the first one is a family of soft sets, called soft set-valued map and the second is a point-to-point mapping. In addition, it is also shown that under some suitable conditions, a soft set-valued map admits a selection having a unique fixed point. In support of the obtained result, nontrivial examples are provided. The novelty of the presented idea herein is that it extends the Meir-Keeler fixed point theorem and the theory of selections for multivalued mappings from the …