Physical Sciences and Mathematics Commons^™

New Similarity And Entropy Measures Of Temporal Complex Neutrosophic Set And Its Application In Multi-Criteria Decision Making, Luong Thi Hong Lan, Nguyen Tho Thong, Nguyen Long Giang, Florentin Smarandache, Vo Si Nam, Dinh Van Dzung

Branch Mathematics and Statistics Faculty and Staff Publications

The Temporal complex neutrosophic set (TCNS) is an effective structure for resolving information that has uncertain, indeterminate, and timerelated factors in decision-making problems. In the last decade, many researchers focused on estimating the vagueness and ambiguity in knowledge using the theory of neutrosophic sets or extensions of neutrosophic sets. Similarity and entropy measures are valuable tools to measure information with the aim of dealing with real-life multi-criteria decisionmaking (MCDM) problems. However, the existing method did not care or interest in the information measures of TCNS. This paper proposes several new similarity and entropy measures under the TCNS environment. The suggested …

The Encyclopedia Of Neutrosophic Researchers, Vol. 6, Florentin Smarandache, Maikel Yelandi Leyva Vázquez, Jesús Estupiñán Ricardo

Branch Mathematics and Statistics Faculty and Staff Publications

Este es el Sexto 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 sus impacto en latinoamérica junto con enlaces a los principales artículos y libros. Conjunto neutrosófico, lógica neutrosófica, probabilidad neutrosófica, estadística neutrosófica, medida neutrosófica, precálculo neutrosófico, cálculo neutrosófico, psicología neutrosófica, sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión, vaguedad, incompletitud, inconsistencia e indeterminación. En …

New Types Of Topologies And Neutrosophic Topologies, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we recall the six new types of topologies that we introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology.

Applications Of Neutrosophic Soft Open Sets In Decision Making Via Operation App, J. J. Mershia Rabuni, N. Balamani, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Enterprise resource planning (ERP) has a significant impact on modern businesses by enhancing productivity, automation, and streamlining of business processes, even accounting. Manufacturers can assure proper functioning and timely client demand using ERP software. Coordination, procurement control, inventory control, and dispatch of commodities are all features of supply chain management. Manufacturers may design better logistics plans with this capability, which will substantially aid them in lowering operational and administrative expenses. In this article, we instigate the idea of neutrosophic soft γ- open sets (NSγ-open sets) by employing the operation γ on the family of neutrosophic soft open sets written symbolically …

Professor Cai Wen’S Extenics ( A Letter To The Editor-In-Chief), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

I had the chance and honor to meet Prof. Dr. Cai Wen (1941 - 2021), the founder of Extenics, in the summer of 2012, at the Guangdong University of Technology (GDUT), Institute of Extenics and Innovative Methods, in Guangzhou, P. R. China, where I was invited by Dr. Xingsen Li to do research on Extenics about solving contradictory problems in science.

I have passed a wonderful time in China (17 May – 15 August, 2012) presenting and listening to many scientific presentations on Extenics and their applications in various fields of knowledge, and studying new papers and book provided to …

Special Subset Linguistic Topological Spaces, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, authors, for the first time, introduce the new notion of special subset linguistic topological spaces using linguistic square matrices. This book is organized into three chapters. Chapter One supplies the reader with the concept of ling set, ling variable, ling continuum, etc. Specific basic linguistic algebraic structures, like linguistic semigroup linguistic monoid, are introduced. Also, algebraic structures to linguistic square matrices are defined and described with examples. For the first time, non-commutative linguistic topological spaces are introduced. The notion of a linguistic special subset of doubly non-commutative topological spaces of linguistic topological spaces is introduced in this …

Neutrosophic Transport And Assignment Issues (Arabic Version), Florentin Smarandache, Maissam Ahmad Jdid

Branch Mathematics and Statistics Faculty and Staff Publications

We all know that problems of transportation and allocation appear frequently in practical life. We need to transfer materials from production centers to consumption centers to secure the areas’ need for the transported material or allocate machines or people to do a specific job at the lowest cost, or in the shortest time. We know that the cost factors Time is one of the most important factors that decision-makers care about because it plays an “important” role in many of the practical and scientific issues that we face in our daily lives, and we need careful study to enable us …

Neutrosophic Transport And Assignment Issues, Florentin Smarandache, Maissam Ahmad Jdid

Branch Mathematics and Statistics Faculty and Staff Publications

We all know that problems of transportation and allocation appear frequently in practical life. We need to transfer materials from production centers to consumption centers to secure the areas’ need for the transported material or allocate machines or people to do a specific job at the lowest cost, or in the shortest time. We know that the cost factors Time is one of the most important factors that decision-makers care about because it plays an “important” role in many of the practical and scientific issues that we face in our daily lives, and we need careful study to enable us …

Development Of Some New Hybrid Structures Of Hypersoft Set With Possibility-Degree Settings, Atiqe Ur Ur Rahman, Florentin Smarandache, Muhammad Saeed, Khuram Ali Khan

Branch Mathematics and Statistics Faculty and Staff Publications

The concept of a hypersoft membership function is introduced in the extension of a soft set known as a hypersoft set, permitting it to handle complicated and uncertain information in a more powerful and flexible manner. Many academics have already become fascinated with this new area of study, leading to the development of a number of hybrid structures. This chapter develops some new hybrid hypersoft set structures by taking into account multiple fuzzy set-like settings and possibility degree-based settings collectively. Additionally, numerical examples are included to clarify the concept of these structures. Researchers can utilize this work to better understand …

Nidus Idearum. Scilogs, Xi: In-Turns And Out-Turns, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this eleventh book of scilogs – called in-turns and out-turns –, one may find new and old questions and solutions, referring mostly to topics on Neutrosophy, but also Multispace, with miscellaneous addition of topics on Physics, Mathematics, or Sociology – email messages to research colleagues, or replies, notes about authors, articles, or books, spontaneous ideas, and so on.

A Neutrosophic Decision-Making Model For Determining Young People’S Active Engagement, Mihaela Colhon, Monica Tilea, Ana Gonzalez-Marcos, Alina Resceanu, Florentin Smarandache, Fermin Navaridas-Naida

Branch Mathematics and Statistics Faculty and Staff Publications

Young people’s skills and attitudes must be observed, studied and evaluated in order to create appropriate models that would serve an educational purpose. In this paper, we propose a decision-making model with the aim to detect certain attitudinal and behavioural patterns of actively engaged young people. The data used in this research resulted from a questionnaire drawn up by a group of researchers from 6 European countries with the aim to investigate the youth’s awareness about the Sustainable Development Goals and their engagement as active agents of development and change at regional level. For the purpose of this study, we …

Inspection Assignment Form For Product Quality Control Using Neutrosophic Logic, Maissam Jdid, Florentin Smarandache, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

During the production process, production companies need to monitor the finished products and ensure their quality, which imposes on them the appointment of inspectors for auditing, and this appointment costs the company amounts that affect the general profit, so it strives to make this cost as low as possible and that the audit process is carried out with high accuracy because in case that the finished products do not conform to the basic specifications of the product, the company is required to pay a fine. In this research, we will formulate the text of the problem appropriately for such a …

On Single-Valued Neutrosophic Soft Uniform Spaces, Yaser Saber, Hanan Alohali, Tawfik Elmasry, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduce the notion of single-valued neutrosophic soft uniform spaces as a view point of the entourage approach. We investigate the relationship among single-valued neutrosophic soft uniformities, single-valued neutrosophic soft topologies and single-valued neutrosophic soft interior operators. Also, we study several single-valued neutrosophic soft topologies induced by a single-valued neutrosophic soft uniform space.

Several New Types Of Neutrosophic Set, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the literature, new types of neutrosophic sets have been introduced in the meantime by the growing neutrosophic community. We present a few: Pythagorean Neutrosophic Set, Fermatean Neutrosophic Set, Generalized Fermatean Neutrosophic Set, n-power Neutrosophic Set, Cubic Spherical Neutrosophic Set, Spherical Neutrosophic Set, n-HyperSpherical Neutrosophic Set, Refined n-HyperSpherical Neutrosophic Set.

Solar Power Plant Location Selection Problem By Using Electre-Iii Method In Pythagorean Neutrosophic Programming Approach (A Case Study On Green Energy In India), Florentin Smarandache, Rajesh Kumar Saini, Ashik Ahirwar Ahirwa

Branch Mathematics and Statistics Faculty and Staff Publications

India dropped its target of generating 500 GW of renewable energy capacity from non responsibilities to ations Framework Convention on reducing carbon Abstract: India dropped its target of 500 GW of renewable energy capacity fossil fuel sources by 2030. Its responsibilities the United Nations Framework Conven Climate Change [UNFCCC],and reducing radiations by one billion tonnes by the end of the decade at the COP26 conference, held in Glasgow in November 2022.Researchers are continually searching for inexhaustible and reasonable energy sources. Solar energy is one of the greenest sources of energy and is also one of the cleanest. The most important …

Chi-Square Test For Imprecise Data In Consistency Table, Muhammad Aslam, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we propose the introduction of a neutrosophic chi-square-test for consistency, incorporating neutrosophic statistics. Our aim is to modify the existing chi-square -test for consistency in order to analyze imprecise data. We present a novel test statistic for the neutrosophic chi-square -test for consistency, which accounts for the uncertainties inherent in the data. To evaluate the performance of the proposed test, we compare it with the traditional chi-square -test for consistency based on classical statistics. By conducting a comparative analysis, we assess the efficiency and effectiveness of our proposed neutrosophic chi-square-test for consistency. Furthermore, we illustrate the application …

Complete Study Of An Original Power-Exponential Transformation Approach For Generalizing Probability Distributions, Mustafa S. Shama, Farid El Ktaibi, Jamal N. Al Abbasi, Christophe Chesneau, Ahmed Z. Afify

All Works

In this paper, we propose a flexible and general family of distributions based on an original power-exponential transformation approach. We call it the modified generalized-G (MGG) family. The elegance and significance of this family lie in the ability to modify the standard distributions by changing their functional forms without adding new parameters, by compounding two distributions, or by adding one or two shape parameters. The aim of this modification is to provide flexible shapes for the corresponding probability functions. In particular, the distributions of the MGG family can possess increasing, constant, decreasing, “unimodal”, or “bathtub-shaped“ hazard rate functions, which are …

The Set Chromatic Numbers Of The Middle Graph Of Tree Families, Mark Anthony C. Tolentino, Gerone Russel J. Eugenio

Mathematics Faculty Publications

The neighborhood color set of each vertex v in a vertex-colored graph G is defined as the collection of the colors of all the neighbors of v. If there are no two adjacent vertices that have equal neighborhood color sets, then the coloring is called a set coloring of G. The set coloring problem on G refers to the problem of determining its set chromatic number, which refers to the fewest colors using which a set coloring of G may be constructed. In this work, we consider the set coloring problem on graphs obtained from applying middle graph, a unary …

New Types Of Soft Sets: Hypersoft Set, Indetermsoft Set, Indetermhypersoft Set, And Treesoft Set, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This is a review paper, where we recall the definitions together with practical applications of the Soft Set and its extensions to HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set.

Perceptual Anthropomorphic Walking Robot Platform For Navigation In Unstructured And Undifferentiated Environments, Luige Vladareanu, Mihai Rădulescu, Marius Pandelea, Hongbo Wang, Florentin Smarandache, Yongfei Feng, Ionel-Alexandru Gal, Alexandra C. Ciocîrlan

Branch Mathematics and Statistics Faculty and Staff Publications

This scientific presentation studies the VIPRO Platform for control of Anthropomorphic Walking Robots (AWR), the architecture control system of the SiMeLA MP robot motion, and shows several experimental results.

New Types Of Soft Sets: Hypersoft Set, Indetermsoft Set, Indetermhypersoft Set, And Treesoft Set - An Improved Version, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This is an improved paper of [10], where we recall the definitions together with practical applications of the Soft Set and its extensions to HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set.

Pura Vida Neutrosophic Algebra, Florentin Smarandache, Ranulfo Paiva Barbosa (Sobrinho)

Branch Mathematics and Statistics Faculty and Staff Publications

We introduce Pura Vida Neutrosophic Algebra, an algebraic structure consisting of neutrosophic numbers equipped with two binary operations namely addition and multiplication. The addition can be calculated sometimes with the function min and other times with the max function. The multiplication operation is the usual sum between numbers. Pura Vida Neutrosophic Algebra is an extension of both Tropical Algebra (also known as Min-Plus, or Min-Algebra) and Max-Plus Algebra (also known as Max-algebra). Tropical and Max-Plus algebras are algebraic structures included in semirings and their operations can be used in matrices and vectors. Pura Vida Neutrosophic Algebra is included in Neutrosophic …

Lagrange Multipliers And Neutrosophic Nonlinear Programming Problems Constrained By Equality Constraints, Maissam Jdid, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Operations research science is defined as the science that is concerned with applying scientific methods to complex problems in managing and directing large systems of people, including resources and tools in various fields, private and governmental work, peace and war, politics, administration, economics, planning and implementation in various domains. It uses scientific methods that take the language of mathematics as a basis for it and uses computer, without which it would not have been possible to achieve numerical solutions to the raised problems, those that need correct solutions, when the solutions abound and the options are multiple, so we need …

The Use Of Neutrosophic Methods Of Operation Research In The Management Of Corporate Work, Maissam Jdid, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The science of operations research is one of the modern sciences that have made a great revolution in all areas of life through the methods provided by it, suitable and appropriate to solve most of the problems that were facing researchers, scholars and those interested in the development of societies, and the most beneficiaries of this science were companies and institutions that are looking for scientific methods that help them manage their work so that they achieve the greatest profit and the lowest cost, and one of the important methods that have been used in the management of companies we …

N-Cylindrical Fuzzy Neutrosophic Topological Spaces, Sarannya Kumari R, Sunny Joseph Kalayathankal, Mathews George, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The objective of this study is to incorporate topological space into the realm of n-Cylindrical Fuzzy Neutrosophic Sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper, we introduce n-Cylindrical Fuzzy Neutrosophic Topological Spaces (n-CyFNTS), n-Cylindrical Fuzzy Neutrosophic (n-CyFN) open sets, and n-CyFN closed sets. We also defined the n-CyFN base, n-CyFN subbase, and some related theorems here.

Complex Fermatean Neutrosophic Graph And Application To Decision Making, Said Broumi, Swaminathan Mohanaselvi, Tomasz Witczak, Mohamed Talea, Assia Bakali, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Original scientific paper Abstract: A new growing area of the neutrosophic set theory called complex neutrosophic sets (CNS) provides useful tools for dealing with uncertainty in complex valued physical variables that are observed in the actual world. A CNS takes values for the truth, indeterminacy and falsity membership functions in the complex plane's unit circle. In this research, a novel concept of complex fermatean neutrosophic graph (CFNG) is established and various basic graphical ideas such as the order, size, degree and total degree of a vertex of it are introduced. Also, set theoretical operations such as complement, union, join, ring-sum …

On Neutro-La-Semihypergroups And Neutro-Hv-La-Semigroup, Saeid Mirvakili, Akbar Rezaei, Omaima Al-Shanqiti, Florentin Smarandache, Bijan Davvaz

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we extend the notion of LA-semihypergroups (resp. Hv-LA-semigroups) to neutro-LA-semihypergroups (respectively, neutro-Hv-LA-semigroups). Anti-LA-semihypergroups (respectively, anti-Hv-LA-semigroups) are studied and investigated some of their properties. We show that these new concepts are different from classical concepts by several examples. These are particular cases of the classical algebraic structures generalized to neutroalgebraic structures and antialgebraic structures (Smarandache, 2019).

A New Type Of Neutrosophic Set In Pythagorean Fuzzy Environment And Applications To Multi-Criteria Decision Making, Mahmut Can Bozyıgıt, Murat Olgun, Florentin Smarandache, Mehmet Unver

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker …

Applications Of Extended Plithogenic Sets In Plithogenic Sociogram, S. Sudha, Nivetha Martin, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The theory of plithogeny developed by Smarandache is described as a more generalized form of representing sets of different nature such as crisp, fuzzy, intuitionistic and neutrosophic. Plithogenic set comprises degree of appurtenance and contradiction degree with respect only to the dominant attribute. This paper introduces extended plithogenic sets comprising degrees of appurtenance and contradiction with respect to both dominant and recessive attributes. The extension of the 5-tuple Plithogenic sets to a 7- tuple plithogenic sets helps in developing a more comprehensive kind of Plithogenic sociogram. The newly developed plithogenic sets and its implications in Plithogenic sociogram is validated by …

[Research Note] The Random Somatic Mutation Is Not Quite Random, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This research note challenges the idea that Random Somatic Mutations are entirely random, highlighting their non-equiprobable nature and their influence on evolution, involution, or indeterminacy. It recalls the Neutrosophic Theory of Evolution, extending Darwin’s theory, and emphasizes the importance of distinguishing between different senses of “random mutation” in evolutionary theory.