Der Artikel untersucht das Markusevangelium als kommunikative Handlung und fragt nach der Ausgangsfrage, auf die der Text eine Antwort ist. Die Analyse der Aussagen über die Zeit nach der im Text erzählten Zeit hinaus, der Charakterisierung der Jünger und der Erzähldynamik vom Anfang zum Schluss führt zu dem Ergebnis, dass sich das Markusevangelium der Herausforderung der Anfrage stellt, die Jesus am Kreuz hinausruft: „Mein Gott, mein Gott, warum hast du mich verlassen?" . Die grundlegende Antwort auf diese Frage ist die (...) markinische Rede von der Verborgenheit Gottes, seiner Herrschaft und seines Sohnes. Entsprechend möchte das Markusevangelium seine Leser auf einen Weg zu vertiefter Wahrnehmung führen, der sie erkennen lässt, dass sie nicht von Gott verlassen sind, sondern dass Gott ihnen verborgen nahe ist. Dieser Weg durch den Text wird in den drei entscheidenden Schritten beschrieben. Aufgrund der bleibenden Bedeutsamkeit seiner Ausgangsfrage erweist sich das Markusevangelium als ein auch heute noch aktueller und herausfordernder Text.The article examines the gospel of Mark as communicative act and asks for the initial question, to which the text is the answer. The analysis of the statements about the time beyond the time covered by the narrative, the characterization of the disciples and the narrative dynamics from beginning to end lead to the conclusion, that the gospel according to Mark takes up the challenge of the question, which Jesus cries on the cross: „My God, my God, why do you have forsaken me?".The fundamental answer to this challenge is the Markan emphasis on the concealment of God and his kingdom and the concealment of his son. Accordingly, the gospel of Mark wants to lead the reader on a way of deepened perception and awareness in order to recognize, that he is not forsaken by God, but that God is covertly near. This way is described in his three decisive steps. Because of the lasting significance of its initial question the gospel of Mark turns out to be of vital importance for present readers. (shrink)

This paper is an extension of “(t, i, f)-Neutrosophic Structures” applicability , where were introduced for the first time a new type of structures, called (t, i, f)- Neutrosophic Structures, presented from a neutrosophic logic perspective.

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let <A> be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to <A> and <antiA>, and one corresponding to neutral (indeterminate) <neutA> (also denoted <neutroA>) between the opposites}, which may (...) or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra is an algebra which has at least one NeutroOperation or one NeutroAxiom (axiom that is true for some elements, indeterminate for other elements, and false for the other elements). A Partial Algebra is an algebra that has at least one Partial Operation, and all its Axioms are classical (i.e. axioms true for all elements). Through a theorem we prove that NeutroAlgebra is a generalization of Partial Algebra, and we give examples of NeutroAlgebras that are not Partial Algebras. We also introduce the NeutroFunction (and NeutroOperation). (shrink)

The author makes an introduction to non-standard analysis, then extends the dialectics to “neutrosophy” – which became a new branch of philosophy. This new concept helps in generalizing the intuitionistic, paraconsistent, dialetheism, fuzzy logic to “neutrosophic logic” – which is the first logic that comprises paradoxes and distinguishes between relative and absolute truth. Similarly, the fuzzy set is generalized to “neutrosophic set”. Also, the classical and imprecise probabilities are generalized to “neutrosophic probability”.

ArgumentThis paper argues that the economics discipline is highly concentrated, which may inhibit scientific innovation and change in the future. The argument is based on an empirical investigation of six dimensions of concentration in economics between 1956 and 2016 using a large-scale data set. The results show that North America accounts for nearly half of all articles and three quarters of all citations. Twenty institutions reap a share of 42 percent of citations, five journals a share of 28.5 percent, and (...) 100 authors a share of 15.5 percent. A total of 2.8 percent of citations may be attributed to heterodox schools of thought. Also top articles are concentrated along these dimensions. Overall, concentration has strongly increased over the last six decades. (shrink)

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, Riad Khidr Al-hamido, Mohammad Akram, B. De Baets, Robert Neil Boyd, Said Broumi, Terman Frometa-Castillo, Yilmaz Ceven, D. Dubois, Harish Garg, L. Godo, Erik Gonzalez, Yanhui Guo, Mohammad Hamidi, E. Hüllermeier, W. B. Vasantha Kandasamy, Mary Jansi, Nivetha Martin, Mani Parimala, Akbar Rezaei, Bouzina Salah, Christy Vincent, Jun Ye.‬‬‬. (shrink)

Contributing to the fast growing new field of neutrosophy, this book provides a significant collection of unedited articles covering the latest ongoing research area. Neutrosopy is above all a new view on modelling, tailored to effectively address the uncertainties inherent of the real world. In short, Neutrosophy supersedes in logics the binary approach of true or false by introducing a third state: neutral, which can be also interpreted as indeterminate, uncertain, inconsistent.

In this short paper we extend the dialectical triad thesis-antithesis-synthesis to the neutrosophic tetrad thesis-antithesis-neutrothesis-neutrosynthesis. We do this for better reflecting our world, since the neutralities between opposites play an important role. The neutrosophic synthesis (neutrosynthesis) is more refined that the dialectical synthesis. It carries on the unification and synthesis regarding the opposites and their neutrals too.

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. (shrink)

In this book, we approach different topics related to neutrosophics, such as: Neutrosophic Set, Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set, Picture Fuzzy Set, Ternary Fuzzy Set, Pythagorean Fuzzy Set, Atanassov’s Intuitionistic Fuzzy Set of second type, Spherical Fuzzy Set, n-HyperSpherical Neutrosophic Set, q-Rung Orthopair Fuzzy Set, truth-membership, indeterminacy-membership, falsehood-nonmembership, Regret Theory, Grey System Theory, Three-Ways Decision, n-Ways Decision, Neutrosophy, Neutrosophication, Neutrosophic Probability, Refined Neutrosophy, Refined Neutrosophication, Nonstandard Analysis; (Theory, NeutroTheory, AntiTheory), S-denying an Axiom, Multispace with Multistructure, and so on.

We have introduced for the first time the degree of dependence (and consequently the degree of independence) between the components of the fuzzy set, and also between the components of the neutrosophic set in our 2006 book’s fifth edition [1]. Now we extend it for the first time to the refined neutrosophic set considering the degree of dependence or independence of subcomponets.

A simple, direct, fast point of view regarding my perception of Administration Philosophy, Teaching Philosophy, Research Philosophy, and What I Can Bring to This Institution.

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. (shrink)

Classes of linguistic paradoxes are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic.

La pensée eschatologique d'lsraël surgit et s'élabore au temps et sur les lieux de l'Exil, dans une population de personnes déplacées qui ont perdu leurs repères à leur passé et à leur terre. Elle inspire de rédiger un Livre pour redonner à ce peuple un lieu habitable, de lui restituer une histoire en lui transmettant des récits et des textes du passé réinterprétés par une vision d'avenir. Paradoxalement, l'espérance eschatologique se fait remémoration, historiographie. Faisant le deuil du passé en le (...) relisant, elle rend à nouveau possible l'histoire du peuple avec son Dieu, qui paraissait absent alors qu'il n'était que souffrant. Le « dernier jour » se profile dès le début de cette histoire, accomplissement inaugural, promesse d'un renouveau toujours possible. The eschatological thinking of Israel arose and was developed at the time and in the lands of the Exile. This took place in a population of displaced persons who had lost their connection with the past as well as their land. This thinking inspired them to compose a Book that would return a hospitable place and restore a history to them. This was done by the transmission of stories and texts reinterpreting the past, with a vision of the future. Paradoxically, eschatological hope became remembering, historiography. Burying the past through a rereading, hope again makes possible the history of a people with its God, who seemed absent while He was only suffering. The « Last Day » develops its profile from the start of this history, as an inaugural fulfilments, a renewal always possible. (shrink)

In this paper, we make a short history about: the neutrosophic set, neutrosophic numerical components and neutrosophic literal components, neutrosophic numbers, neutrosophic intervals, neutrosophic hypercomplex numbers of dimension n, and elementary neutrosophic algebraic structures. Afterwards, their generalizations to refined neutrosophic set, respectively refined neutrosophic numerical and literal components, then refined neutrosophic numbers and refined neutrosophic algebraic structures.

Neutrosophy considers a proposition, theory, event, concept, or entity, "A" in relation to its opposite, "Anti A" and that which is not A, "Non-A", and that which is neither "A" nor "Anti-A", denoted by "Neut-A". Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics.

The IndetermSoft Set is as an extension of the Soft Set, because the data, or the function, or the sets involved in the definition of the soft set have indeterminacy - as in our everyday life, and we still need to deal with such situations. And similarly, IndetermHyperSoft Set as extension of the HyperSoft Set, when there is indeterminate data, or indeterminate functions, or indeterminate sets. Herein, ‘Indeterm’ stands for ‘Indeterminate’ (uncertain, conflicting, incomplete, not unique outcome). We now introduce for (...) the first time the TreeSoft Set as extension of the MultiSoft Set. Several applications are presented for each type of soft set. (shrink)

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. (shrink)

We introduce now for the first time the neutrosophic modal logic. The Neutrosophic Modal Logic includes the neutrosophic operators that express the modalities. It is an extension of neutrosophic predicate logic and of neutrosophic propositional logic.

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. (shrink)

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. (shrink)

Essays in Romanian, English, French, and Portuguese, some of which are translations.

We recall and improve our 2019 and 2020 concepts of n-SuperHyperGraph, Plithogenic nSuperHyperGraph, n-Power Set of a Set, and we present some application from the real world. The nSuperHyperGraph is the most general form of graph today and it is able to describe the complex reality we live in, by using n-SuperVertices (groups of groups of groups etc.) and nSuperHyperEdges (edges connecting groups of groups of groups etc.).

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. (shrink)

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. (shrink)

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.

In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

This photo album contains images from a trip to Quebec city and Montreal, on the occasion of an international scientific conference I attended in the sumer of 2006. -/- Cet album photo contient des images d'un voyage à Québec et Montréal, à l'occasion d'une conférence scientifique internationale à laquelle j'ai participé l’été de l’année 2006.

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). (shrink)

In this paper one introduces for the first time the IndetermSoft Set, as extension of the classical (determinate) Soft Set, that deals with indeterminate data, and similarly the HyperSoft Set extended to IndetermHyperSoft Set, where ‘Indeterm’ stands for ‘Indeterminate’ (uncertain, conflicting, not unique outcome). They are built on an IndetermSoft Algebra that is an algebra dealing with IndetermSoft Operators resulted from our real world. Afterwards, the corresponding Fuzzy / Intuitionistic Fuzzy / Neutrosophic / and other fuzzy-extension IndetermSoft Set & IndetermHyperSoft (...) Set are presented together with their applications. (shrink)

In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined.