Florentin Smarandache

Some years ago, Hidding et al. suggest that the emergence of intricate and pervasive weblike structure of the Universe on Megaparsec scales can be approximated by a well-known equation from fluid mechanics, the Burgers’ equation. The solution to this equation can be obtained from a geometrical formalism. The resulting Adhesion formalism provides deep insight into the dynamics and topology of the Cosmic Web. It uncovers a direct connection between the conditions in the very early Universe and the complex spatial patterns that emerged out of these under the influence of gravity. In the present paper, we describe a cellular automaton model of the Burgers’ equation, which can be investigated via a fast computer simulation. In the end, this suggests a Cellular Automata Adhesion Model of the Universe.

In the real word, in most cases, everything (an attribute, event, proposition, theory, idea, person, object, action, etc.) is evaluated in general by many sources (called experts), not only one. The more sources evaluate a subject, the better accurate result (after fusioning all evaluations). That’s why, in this paper, we straightforwardly extend the Refined Neutrosophic Set to the MultiNeutrosophic Set, and we show that the last two are isomorphic. A MultiNeutrosophic Set is a Neutrosophic Set whose all elements’ degrees of truth/indeterminacy/falsehood are evaluated by many (Multi) sources. Afterwards, we introduce a total order on the set of n-plets of the form (p, r, s), we build the operators on the (p, r, s)-plets, and show several applications of the MultiNeutrosophic Sets. Several particular cases of the MultiNeutrosophic Sets are presented: such as MultiFuzzy Set, MultiIntuitionistic Fuzzy Set, MultiPicture Fuzzy Set, and other Multi(Fuzzy Extension) Set.

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework. This paper can be considered as our second attempt towards such a complete description of the Universe based on soliton wave solution of cosmological KdV equation. Then we advance further this KdV equation by virtue of Cellular Automaton method to solve the PDEs. We submit wholeheartedly Robert Kurucz’s hypothesis that Big Bang should be replaced with a finite cellular automaton universe with no expansion. Nonetheless, we are fully aware that our model is far from being complete, but it appears the proposed cellular automaton model of the Universe is very close in spirit to what Konrad Zuse envisaged long time ago. It is our hope that the new proposed method can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details.

The n-th PowerSet of a Set {or Pn(S)} better describes our real world, because a system S (which may be a company, institution, association, country, society, set of objects/plants/animals/beings, set of concepts/ideas/propositions, etc.) is formed by sub-systems, which in their turn by sub-sub-systems, and so on. We prove that the SuperHyperFunction is a generalization of classical Function, SuperFunction, and HyperFunction. And the SuperHyperAlgebra, SuperHyperGraph are part of the SuperHyperStructure. Almost all structures in our real world are Neutrosophic SuperHyperStructures since they have indeterminate/incomplete/uncertain/conflicting data.

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.

For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems, etc.) are totally (100%) true. But, in the real world, many items are not totally true. The NeutroGeometry is a geometrical space that has some items that are only partially true (and partially indeterminate, and partially false), and no item that is totally false. The AntiGeometry is a geometrical space that has some item that are totally (100%) false. While the Non-Euclidean Geometries [hyperbolic and elliptic geometries] resulted from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom [and in general: theorem, concept, idea etc.] and even of more axioms [theorem, concept, idea, etc.] and in general from any geometric axiomatic system (Euclid’s five postulates, Hilbert’s 20 axioms, etc.), and the NeutroAxiom results from the partial negation of any axiom (or concept, theorem, idea, etc.). Clearly, the AntiGeometry is a generalization of Non-Euclidean Geometries.

Florentin Smarandache na ofron poezi të bukura, të frymëzuara dhe të shkarkuara nga zemra dhe shpirti. Autori shkruan një poezi reflektuese që shpaloset në disa shtresa medituese. Jehona e vargut të tij lind rezonanca të gjera dhe dërrmuese. Projektohen imazhe dhe tema përmes të cilave marrin formë ylberi lirika të reja, të artikuluara në përballje fjalësh që i bëjnë përshtypje të fortë poezisë dhe krijuesit të saj. Poezitë e mbretërimit të tij pasqyrojnë pikturën dhe kaligrafinë, dritën dhe hijen, një alkimi origjinale mes mendimit dhe tekstit, sepse poeti e mbart gjithmonë atë mister në tekst, duke rrjedhur si një ngjyrë fluide në faqen e kanavacës së mrekullueshme. (Përkthimi nga gjuha rumune: Baki Ymeri)

In this book, we present a study of linear models and algorithms to find the optimal solution for them using the concepts of neuroscientific science. We know that the linear programming method is one of the important methods of operations research, the science that was the product of the great scientific development that our contemporary world is witnessing. The name operations research is given to the group of scientific methods used. In analyzing problems and searching for optimal solutions, it is a science whose applications have achieved widespread success in various fields of life. What is meant by neutrosophic models are models in which the data are neutrosophic values, that is, variables such as in the objective function, which expresses profit if the model is a maximization model, and expresses a cost if the model is a minimization model, which in turn is affected by environmental conditions.

For long time, especially in the West, there is old paradigm that is strong separation between science and theology/religion matters. Especially, such a diverging path started from Galileo persecution, and also other patterns where religious authority seem to hold the last word on scientific issues. Other area of this World, seems to not hold such a diverging path, for instance it can be read in the works of physicist turned to religious philosopher, for instance Pavel Florensky and Nesteruk. That is why we also discuss shortly about those scientists in this book. In the last chapter, we discuss about eureka, an experience which for a long time was attributed to divine spark or “God’s favor to an artist or to a scientist, such luminaries like Newton, Pascal, Leibniz etc.” Nonetheless, new methodology appears to be able to be generated once we accept balanced brain approach, where left brain and right brain hemispheres of humans can work together.

Proza e shkurtër në këtë vëllim, e ribashkuar nën titullin „Me duar në xhepa të qepur”, tërheq konflikte midis ekzistencës dhe thelbit, duke projektuar ngërçe, aporie identitare dhe shëmbëlltyra komunikimi. 1-0 (?) është një satirë për futbollin dhe aranzhimet - në favor të skuadrave apo lojtarëve të caktuar - që u prodhuan intensivisht gjatë periudhës socialiste, të dominuara nga gënjeshtra, mistifikimi dhe faji. GIONÍ diskuton për komplekset adoleshente-adoleshente të disa krijesave me status të pasigurt, të përhumbur nga dështimi dhe dështimi, të cilat autori, në frymën amerikane, i shpëton në fund, duke i dërguar në punë (pa na shpjeguar sesi do të ishte i mundur shpëtimi ontologjik). Mekanizmi epik në XHAMANTANI BOJËALLI duket i huazuar nga Mircea Eliade, i zbatuar vetëm në dimensione deterministe, ndër të cilat zbulimi I paautenticitetit të një martese është më pak problematik. Tek KU ISHA NË VEND, strategjitë e fiksionit autobiografik funksionojnë me mjeshtëri, autori rikujtues na çon nëpër labirintin e fatit drejt arratisjes në brendësi. Katër tekstet e fundit (në anglisht) janë drafte për më vonë. Një sërë ilustrimeve mbështesin tekstet dhe, në tensionin e ideve, gjarpërimet e rrëfimit të Florentin Smarandache befasojnë këndshëm, duke shkaktuar keqardhje që autori, shumë më i tërhequr nga shkenca, por edhe nga avangarda, nuk kërkonte një konservator fati letrar në prozë. Kam bindjen se do të jetë një sukses.

Florentin Smarandache është një nga shkrimtarët më të talentuar në letërsinë rumune të diasporës. Dashuria e saj për librin ripërtërihet gjithmonë, duke arrdhur tani para lexuesve tanë me një libër të ri të ilustruar dhe të destinuar për lexuesit më të vegjël. Kjo është një befasi e re me disa tregime të bukura për shijen e fëmijëve të ditëve tona. Florentin Smarandache është një adhurues i leximit, një krijesë frymëzimesh të zjarrta për të cilin leximi është bërë një mënyrë e vërtetë jetese, një lloj zgjatje e qenies së tij. Nuk e dimë saktësisht se kur i imagjinonte krijimet e para, por e dimë se ai mësoi të lexonte e të shkruante, me hirin hyjnor, përpara se të hynte në shkollë. Ai ka qenë I magjepsur që atëherë nga fuqia e fjalës, nga mënyra se si u bashkuan për të formuar fjalë dhe nga kuptimet dhe fuqia që mund të sillnin. Pastaj e di se ai mezi priste të huazonte libra nga biblioteka e shkollës dhe se hyri në atë dhomë që dukej e madhe me shumë emocion. Florentini lexonte libër pas libri, duke dashur gjithmonë më shumë, duke pasur parasysh se nuk kalonte mjaftueshëm kohë në shoqërinë e miqve më të mirë që kishte pasur ndonjëherë. Në momentin që hap një libër të ilustruar për fëmijë, hyn në një botë tjetër, ndryshe nga ajo e të rriturve. Jeni të zhytur nga bukuria e botëve të pikturuara me ngjyra nga krijues dhe ilustrues të talentuar, pastaj takoni heronj fantastikë me të cilët gjithçka është e mundur. Autori gjithmonë i ka dashur fëmijët, poezitë dhe tregimet për të vegjlit, sepse librat për fëmijë e kanë magjepsur. Nëse e pyesni veten se si ka nisur të shkruajë, për krimtarin Florentin Smarandache, historia është shumë e bukur. Kur fëmijët filluan të shkonin në shkollë, kishin nevojë për përralla dhe poezi për raste të ndryshme, për vjeshtë, për Vitin e Ri, për dimër, për pranverë, dhe kështu ai filloi të shkruante poezi në letër, ku fëmijët ishin lexuesit dhe kritikët e saj të parë letrarë.

We present a study of linear models using the concepts of neutrosophic science, the science that was built on the basis that there is no absolute truth, there is no confirmed data, issues cannot be limited to right and wrong only. There is a third state between error and right, an indeterminate, undetermined, uncertain state. It is indeterminacy. Neutrosophic science gave each issue three dimensions, namely (T, I, F), correctness in degrees, indeterminacy in degrees, and error in degrees. It was founded by the American philosopher and mathematician Florentin Smarandache, in 1995 and came as a generalization of fuzzy logic that was founded by the scientist Lotfi. A. Zadeh, in 1965.

We have parameterized Einstein’s thought experiment with atomic clocks, supposing that we knew neither if the space and time are relative or absolute, nor if the speed of light was ultimate speed or not. We have obtained a Parameterized Special Theory of Relativity (PSTR) (1982). Our PSTR generalized not only Einstein’s Special Theory of Relativity, but also our Absolute Theory of Relativity, and introduced three more possible Relativities to be studied in the future. After the 2011 CERN’s superluminal neutrino experiments, we recall our ideas and invite researchers to deepen the study of PSTR, ATR, and check the three new mathematically emerged Relativities 4.3, 4.4, and 4.5.

The neutrosophic sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these the concepts to define a new types of neutrosophic crisp closed sets and limit points in neutrosophic crisp topological space, namly [neutrosophic crisp Gem sets and neutrosophic crisp Turig points] respactvely, we stady their properties in details and join it with topological concepts. Finally we used [neutrosophic crisp Gem sets and neutrosophic crisp Turig points] to introduce of topological concepts as: neutrosophic crisp closed (open) sets, neutrosophic crisp closure, neutrosophic crisp interior, neutrosophic crisp extrior and neutrosophic crisp boundary which are fundamental for further reserch on neutrosophic crisp topology and will setrengthen the foundations of theory of neutrosophic topological spaces.

Product acceptance determination using similarity measure index by neutrosophic statistics / Muhammad Aslam and Rehan Ahmed Khan Sherwani -- New concepts of strongly edge irregular interval-valued neutrosophic graphs / A.A.Talebi, Hossein Rashmanlou and Masoomeh Ghasemi -- The link between neutrosophy and learning : through the related concepts of representation and compression / Philippe Schweizer -- Neutrosophic soft cubic M-subalgebras of B-algebras / Mohsin Khalid, Neha Andaleeb Khalid and Hasan Khalid -- Alpha, beta and gamma product of neutrosophic graphs / Nasir Shah, Said Broumi, Abdul Raheem and Tahir Imran -- Neutrosophic cubic normal ideal and neutrosophic cubic closed normal ideal of PS-algebra / Mohsin Khalid, Hasan khalid and Neha Andaleeb Khalid -- Neutrosophic multisets : an overview / Vakkas Uluçay -- Neutrosophy as a model for knowledge : the influence of representative models on thinking / Philippe Schweizer -- When neutrosophic theory meets three-way decisions / Rui Ren, Chao Zhang and Deyu Li -- Neutrosophic economic order quantity model with more than one price breaks / R. Surya, M. Mullai and G. Madhan Kumar -- General non-square systems of linear equations in single-valued triangular neutrosophic number environment / S.A. Edalatpanah -- Hesitant neutrosophic soft set relations / Abhijit Saha -- Computer application of neutrosophic set operations / S. Saranya, M. Vigneshwaran, Said Broumi -- Triangular bipolar neutrosophic based transportation problem / Avishek Chakraborty -- Studying neutrosophic variables / Rafif Alhabib and Ahmad Salama -- Decision making for logistics center location selection in trapezoidal neutrosophic environment / Kalyan Mondal and Surapati Pramanik -- Weighted similarity measure and decision making model for clinical application of single valued neutrosophic set / R.Binu and P. Isaac -- Rough neutrosophic set : an overview / Surapati Pramanik -- Some new concepts on normalized SVTN-number and multiple criteria decision making / İrfan Deli and Emel Kırmızı Öztürk.

Graph theory is a specific concept that has numerous applications throughout many industries. Despite the advancement of this technique, graph theory can still yield ambiguous and imprecise results. In order to cut down on these indeterminate factors, neutrosophic logic has emerged as an applicable solution that is gaining significant attention in solving many real-life decision-making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. However, empirical research on this specific graph set is lacking. Neutrosophic Graph Theory and Algorithms is a collection of innovative research on the methods and applications of neutrosophic sets and logic within various fields including systems analysis, economics, and transportation. While highlighting topics including linear programming, decision-making methods, and homomorphism, this book is ideally designed for programmers, researchers, data scientists, mathematicians, designers, educators, researchers, academicians, and students seeking current research on the various methods and applications of graph theory.

Since the world is full of indeterminacy, the Neutrosophics found their place into contemporary research. We now introduce for the first time the notions of Neutrosophic Crisp Sets and Neutrosophic Topology on Crisp Sets. We develop the 2012 notion of Neutrosophic Topological Spaces and give many practical examples. Neutrosophic Science means development and applications of Neutrosophic Logic, Set, Measure, Integral, Probability etc., and their applications in any field. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Indeterminacy is different from randomness. Indeterminacy can be caused by physical space, materials and type of construction, by items involved in the space, or by other factors. In 1965 [51], Zadeh generalized the concept of crisp set by introducing the concept of fuzzy set, corresponding to the situation in which there is no precisely defined set;there are increasing applications in various fields, including probability, artificial intelligence, control systems, biology and economics. Thus, developments in abstract mathematics using the idea of fuzzy sets possess sound footing. In accordance, fuzzy topological spaces were introduced by Chang [12] and Lowen [33]. After the development of fuzzy sets, much attention has been paid to the generalization of basic concepts of classical topology to fuzzy sets and accordingly developing a theory of fuzzy topology [1-58]. In 1983, the intuitionistic fuzzy set was introduced by K. Atanassov [55, 56, 57] as a generalization of the fuzzy set, beyond the degree of membership and the degree of non-membership of each element. In 1999 and 2002, Smarandache [71, 72, 73, 74] defined the notion of Neutrosophic Sets, which is a generalization of Zadeh’s fuzzy set and Atanassov's intuitionistic fuzzy set. Some neutrosophic concepts have been investigated by Salama et al. [61-70]. Forwarding the study of neutrosophic sets, this book consists of seven chapters, targeting to:  generalize the previous studies in [1-59], and[91-94] so to define the neutrosopic crisp set and neutrosophic set concepts;  discuss their main properties; A. A. Salama & Florentin Smarandache  introduce and study some concepts of neutrosophic crisp and neutrosophic topological spaces and deduce their properties;  deduce many types of functions and give the relationships between different neutrosophic topological spaces, which helps to build new properties of neutrosophic topological spaces;  stress once more the importance of Neutrosophic Ideal as a nontrivial extension of neutrosophic set and neutrosophic logic [71, 72, 73, 74];  propose applications on computer sciences by using neutrosophic sets.

In this paper, we have developed an Excel package to be utilized for calculating neutrosophic data and analyze them. The use of object oriented programming techniques and concepts as they may apply to the design and development a new framework to implement neutrosophic data operations, the c# programming language, NET Framework and Microsoft Visual Studio are used to implement the neutrosophic classes. We have used Excel as it is a powerful tool that is widely accepted and used for statistical analysis. Figure 1 shows Class Diagram of the implemented package. Figure 2 presents a working example of the package interface calculating the complement. Our implemented Neutrosophic package can calculate Intersection, Union, and Complement of the neutrosophic set. Figure 3 presents our neutrosophic package capability to draw figures of presented neutrosophic set. Figure 4 presents charting of Union operation calculation, and figure 5 Intersection Operation. neutrosophic set are characterized by its efficiency as it takes into consideration the three data items: True, Intermediate, and False.