Florentin Smarandache

Fotografiile acestui album s-au adunat, neprogramatic și fără pretenții artistice, în timpul recentei vizite pe care am făcut-o în România, în vara anului 2023. O vizită cu inima îngreunată de dor. Drumurile mele s-au întins mai mult pe Dunăre și pe Olt, de-a stânga și de-a dreapta acestor ape care au desenat și determinat o bună parte din istoria românilor. Instanțele foto sunt surprinse în și împrejurul Orșovei, Drobetei Turnu Severin, Cazanelor Dunării, Craiovei și Bălceștilor natali. Textele însoțitoare sunt eboșe cu tentă poetică, așa cum le-au inspirat, instant, locurile văzute, oamenii (re)întâlniți și sentimentele prezente/trezite/reamintite în sufletul autorului.

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 to avoid losses. For this, the linear programming method was used, which is one of the research methods. Processes, where the problem data is converted into a linear mathematical model for which the optimal solution achieves the desired goal. Since these models are linear models, we can solve them using the direct simplex method and its modifications, but the specificity that these models enjoy has enabled scholars and researchers to find special methods that help us in obtaining the optimal solution. Whatever the method used, the goal is to determine the number of units transferred from any material from production centers to consumption centers, or to allocate a machine or person to do a job so that the cost or time is as short as possible. These issues were addressed according to classical logic, but the ideal solution was a specific value appropriate to the conditions in which the data was collected and does not take into account the changes that may occur in the work environment. In order to obtain results that are more accurate and enjoy a margin of freedom, we present in this book a study of transport issues and neutrosophic allocation issues and some methods for solving them. By neutrosophic issues we mean These are the problems in which the data are neutrosophic values, i.e. the required quantities and the available quantities.

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 book.

The n-th PowerSet is used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. This first volume collects original research and applications from different perspectives covering different areas of neutrosophic studies, such as decision-making, neutroalgebra, neutro metric, and some theoretical papers.

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 to avoid losses. For this, the linear programming method was used, which is one of the research methods. Processes, where the problem data is converted into a linear mathematical model for which the optimal solution achieves the desired goal. Since these models are linear models, we can solve them using the direct simplex method and its modifications, but the specificity that these models enjoy has enabled scholars and researchers to find special methods that help us in obtaining the optimal solution. Whatever the method used, the goal is to determine the number of units transferred from any material from production centers to consumption centers, or to allocate a machine or person to do a job so that the cost or time is as short as possible. These issues were addressed according to classical logic, but the ideal solution was a specific value appropriate to the conditions in which the data was collected and does not take into account the changes that may occur in the work environment. In order to obtain results that are more accurate and enjoy a margin of freedom, we present in this book a study of transport issues and neutrosophic allocation issues and some methods for solving them. By neutrosophic issues we mean These are the problems in which the data are neutrosophic values, i.e. the required quantities and the available quantities.

Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements. There are about 7,000 neutrosophic researchers, within 89 countries around the globe, that have produced about 4,000 publications and tenths of PhD and MSc theses, within more than two decades. This is the fifth volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation, with an introduction contains a short history of neutrosophics, together with links to the main papers and books.

Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements. There are about 7,000 neutrosophic researchers, within 89 countries around the globe, that have produced about 4,000 publications and tenths of PhD and MSc theses, within more than two decades. This is the sixth volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation, with an introduction contains a short history of neutrosophics, together with links to the main papers and books. ES: 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 los últimos años, los campos de la neutrosófica se han ampliado y aplicado en diversos campos, tales como: inteligencia artificial, minería de datos, software informática, toma de decisiones en forma incompleta / indeterminada / inconsistente sistemas de información, procesamiento de imágenes, modelado computacional, robótica, diagnóstico médico, ingeniería biomédica, problemas de inversión, previsión económica, ciencias sociales, humanística y la validación y consolidación del conocimiento científico.

This book is written for middle and high school students, for teachers and for those with a passion for math, containing 150+1 problems (which are followed by solutions) to make it more accessible to the reader. The last problem (150+1), a very interesting one, leaves some space for comments and generalizations. The book is a collaboration between a multi-awarded student at Romania’s National Mathematics Olympiad (Carina Maria Viespescu, student in year 10 at Liceul International of Informatics Bucuresti), a teacher from Colegiul National “Fratii Buzesti” din Cravoia and prof. Dr. Emeritus Florentin Smarandache from the University of New Mexico. A couple of problems are proposed by colleagues, and their names indicated in footnotes.

This book contains concrete examples from history, economy, biology, digital world, nuclear physics, agriculture and so on about breaking a neutrosophic dynamic system (i.e. a dynamic system that has indeterminacy) from inside. We define a neutrosophic mathematical model using a system of ordinary differential equations and the neutrosophic probability in order to approximate the process of breaking from inside a neutrosophic complex dynamic system. It shows that for breaking from inside it is needed a smaller force than for breaking from outside the neutrosophic complex dynamic system. Methods that have been used in the past for breaking from inside are listed. Simulation and animation of this neutrosophic dynamical system are needed for the future since, by changing certain parameters, various types of breaking from inside may be simulated. Abstract: Această carte conține exemple concrete din istorie, economie, biologie, spațiu digital, fizică nucleară, agricultură și altele, de distrugere unui sistem neutrosofic dinamic (adică a unui sistem care are indeterminări), acționând din interiorul acestuia. Descriem un model neutrosofic matematic folosind un sistem de ecuații diferențiale ordinare și probabilitatea neutrosofică, cu scopul de a aproxima procesul de distrugere din interior a unui sistem neutrosofic dinamic complex. Se demonstrează că, pentru distrugerea din interior a unui astfel de sistem, este necesară o forță mai mică decât pentru distrugerea din exterior. Sunt enumerate metode folosite în trecut pentru distrugerea din interior. Simularea și animația acestui sistem neutrosofic dinamic sunt necesare pentru viitor, deoarece, schimbând diferiți parametri, se pot simula diferite tipuri de distrugeri din interior.

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world.

In this twelfth book of scilogs – called seed & heed –, one may find topics on Neutrosophy, Superluminal Physics, Mathematics, Information Fusion, Philosophy, or Sociology – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on. Exchanging ideas with Pritpal Singh, Mohamed Abobala, Muhammad Aslam, Ervin Goldfain, Dmitri Rabounski, Victor Christianto, Steven Crothers, Jean Dezert, Tomasz Witczak (in order of reference in the book).

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. Exchanging ideas with Prem Kumar Singh, Feng Liu, Nicolae Bălașa, Jimmy Quellet, Minodora Rușchița, Frank Gelli, A. R. Vătuiu, Victor Christianto, Vladimir I. Rogozhin, Robert Neil Boyd, Akira Kanda, Stefan Spaarmann, Oliver Consa, Yabin Shao, Junle Zhuo, Nivetha Martin, Said Broumi, Jean Dezert, Erick González, Tomasz Witczak, B. De Baets, I. Couso, D. Dubois, L. Good, Mihaela Colhon, Atiqe Ur Rahman, Muhammad Saeed, Muhammad Ihsan, Edeline Nancy, Shawkat Alkhazaleh, Shazia Rana, Vasantha Kandasamy, Santanu Acharjee, Mohamed Al-Shmrani, Parimala Manie, Mehmet Unver, Murat Olgun, Adel Aleidhri, Akira Kanda, Ilanthenral Kandasamy, Mircea Zărnescu, R. Tayebi Khorami, Arsham Borumand Saeid, Maisam Jdid, M. Abobala, Riad Hamido, Rafael Rojas, Esmaeil Zarei, Faisal Khan, Rouzbeh Abbassi, Adel Al-Odhari, Henry Garrett, Ackbar Rezaei, Saeid Jafari, Karthika Muthusamy, Harish Garg, Huda E. Khalid, Gonca D. Güngör, Muslim A. Noah Zainal, Fakhry Asad Agusfrianto, Madeleine Al-Tahan, Mariam Hariri, Yudi Mahatma, Masoud Ghods, Marco Brigliadori, Luis Enrique Aponte Pérez, Amr Mohammed, M. Aslam (in order of reference in the book).

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 to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations.

The purpose of this book is to extend the foundation and application range of 'Tao TeChing'. The reasons for this are as follows. Firstly, we are willing to point out that 'Tao TeChing' already has some limitation, because many questions we are interested in cannot beanswered within 'Tao Te Ching'. For example, 'Tao Te Ching' basically discussed the matters in China, however considering all possible situations it should matter in foreign countries as well, i.e. the global village. This was impossible in Lao Tzu s time. Secondly, if the original Tao Te Ching is regarded as Positive Tao Te Ching, its opposite is Negative Tao TeChing, while the intermediate or compound state is Neutral Tao Te Ching. Thus, our book presents the way to extend the original Tao Te Ching in various neutrosophic interpretations. In a same way it is possible to neutrosophically interpret any theory T in any field: positive T, negative T, and Neutrosophic T.

This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements.