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Florentin Smarandache
University of New Mexico
  1. [Book Chapter].Florentin Smarandache - 1999
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  2.  57
    A unifying field in logics: Neutrosophic logic.Florentin Smarandache - 1999 - In [Book Chapter].
    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”.
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  3.  37
    Rough Neutrosophic Sets.Said Broumi, Florentin Smarandache & Mamoni Dhar - 2014 - Neutrosophic Sets and Systems 3:60-65.
    Both neutrosophic sets theory and rough sets theory are emerging as powerful tool for managing uncertainty, indeterminate, incomplete and imprecise information .In this paper we develop an hybrid structure called “ rough neutrosophic sets” and studied their properties.
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  4.  11
    Neutrosophic Crisp Set Theory.A. A. Salama & Florentin Smarandache - 2015 - Columbus, OH, USA: Educational Publishers.
    In this book the authors introduce and study the following notions: Neutrosophic Crisp Points, Neutrosophic Crisp Relations, Neutrosophic Crisp Sets, Neutrosophic Set Generated by (Characteristic Function), alpha-cut Level for Neutrosophic Sets, Neutrosophic Crisp Continuous Function, Neutrosophic Crisp Compact Spaces, Neutrosophic Crisp Nearly Open Sets, Neutrosophic Crisp Ideals, Neutrosophic Crisp Filter, Neutrosophic Crisp Local Functions, Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals, Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity, Neutrosophic Topological Region, Neutrosophic Closed Set and Neutrosophic Continuous Function, etc. They compute (...)
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  5.  21
    Multi-attribute Decision Making based on Rough Neutrosophic Variational Coefficient Similarty Measure.Kalyan Modal, Surapati Pramanik & Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 13:3-17.
    The purpose of this study is to propose new similarity measures namely rough variational coefficient similarity measure under the rough neutrosophic environment. The weighted rough variational coefficient similarity measure has been also defined. The weighted rough variational coefficient similarity measures between the rough ideal alternative and each alternative are xxxxx calculated to find the best alternative. The ranking order of all the alternatives can be determined by using the numerical values of similarity measures. Finally, an illustrative example has been provided (...)
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  6.  18
    Filters via Neutrosophic Crisp Sets.A. Salama & Florentin Smarandache - 2013 - Neutrosophic Sets and Systems 1:34-37.
    In this paper we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.
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  7.  15
    Rough Neutrosophic TOPSIS for Multi-Attribute Group Decision Making.Kalyan Modal, Surapati Pramanik & Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 13:105-117.
    This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...)
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  8.  21
    An extended TOPSIS for multi-attribute decision making problems with neutrosophic cubic information.Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri & Florentin Smarandache - 2017 - Neutrosophic Sets and Systems 17:20-28.
    The paper proposes a new technique for dealing with multi-attribute decision making problems through an extended TOPSIS method under neutrosophic cubic environment. Neutrosophic cubic set is the generalized form of cubic set and is the hybridization of a neutrosophic set with an interval neutrosophic set. In this study, we have defined some operation rules for neutrosophic cubic sets and proposed the Euclidean distance between neutrosophic cubic sets. In the decision making situation, the rating of alternatives with respect to some predefined (...)
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  9.  15
    Interval Neutrosophic Rough Sets.Said Broumi & Florentin Smarandache - 2015 - Neutrosophic Sets and Systems 7:23-31.
    This Paper combines interval- valued neutrouphic sets and rough sets. It studies roughness in interval- valued neutrosophic sets and some of its properties. Finally we propose a Hamming distance between lower and upper approximations of interval valued neutrosophic sets.
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  10.  38
    Multi criteria decision making using correlation coefficient under rough neutrosophic environment.Surapati Pramanik, Rumi Roy, Tapan Kumar Roy & Florentin Smarandache - 2017 - Neutrosophic Sets and Systems 17:29-38.
    In this paper, we define correlation coefficient measure between any two rough neutrosophic sets. We also prove some of its basic properties.. We develop a new multiple attribute group decision making method based on the proposed correlation coefficient measure. An illustrative example of medical diagnosis is solved to demonstrate the applicability and effecriveness of the proposed method.
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  11.  16
    Several Similarity Measures of Neutrosophic Sets.Said Broumi & Florentin Smarandache - 2013 - Neutrosophic Sets and Systems 1:54-62.
    Smarandache (1995) defined the notion of neutrosophic sets, which is a generalization of Zadeh's fuzzy set and Atanassov's intuitionistic fuzzy set. In this paper, we first develop some similarity measures of neutrosophic sets. We will present a method to calculate the distance between neutrosophic sets (NS) on the basis of the Hausdorff distance. Then we will use this distance to generate a new similarity measure to calculate the degree of similarity between NS. Finally we will prove some properties of the (...)
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  12.  14
    Multi-Attribute Decision Making Based on Several Trigonometric Hamming Similarity Measures under Interval Rough Neutrosophic Environment.Surapati Pramanik, Rumi Roy, Tapan Kumar Roy & Florentin Smarandache - 2018 - Neutrosophic Sets and Systems 19:110-118.
    In this paper, the sine, cosine and cotangent similarity measures of interval rough neutrosophic sets is proposed. Some properties of the proposed measures are discussed. We have proposed multi attribute decision making approaches based on proposed similarity measures. To demonstrate the applicability, a numerical example is solved.
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  13.  15
    Introduction to Develop Some Software Programs for Dealing with Neutrosophic Sets.A. Salama, Haitham A. El-Ghareeb, Ayman M. Manie & Florentin Smarandache - 2014 - Neutrosophic Sets and Systems 3:51-52.
    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. (...)
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  14.  74
    A Short Communication on Progress and Problems of ITER Fusion Project.Victor Christianto & Florentin Smarandache - 2022 - Bulletin of Pure and Applied Science 41 (2):111-115.
    In recent years, it becomes clear that ITER project in France, as one of the largest experimental fusion reactors underway, is far away from achieving net energy production. In this review article, we presented a short communication this week with Robert Neil Boyd, a senior physicist who happens to have his own working design of fusion reactor in the past. We hope that this transcript of our communication with him (as per 15-17th Nov. 2021) may be found useful for younger (...)
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  15.  16
    IN-cross Entropy Based MAGDM Strategy under Interval Neutrosophic Set Environment.Shyamal Dalapati, Surapati Pramanik, Shariful Alam, Florentin Smarandache & Tapan Kumar Roy - 2017 - Neutrosophic Sets and Systems 18:43-57.
    Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set environment.
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  16.  12
    GRA for Multi Attribute Decision Making in Neutrosophic Cubic Set Environment.Durga Banerjee, Bibhas C. Giri, Surapati Pramanik & Florentin Smarandache - 2017 - Neutrosophic Sets and Systems 15:60-69.
    In this paper, multi attribute decision making problem based on grey relational analysis in neutrosophic cubic set environment is investigated. In the decision making situation, the attribute weights are considered as single valued neutrosophic sets. The neutrosophic weights are converted into crisp weights. Both positve and negative GRA coefficients, and weighted GRA coefficients are determined. Hamming distances for weighted GRA coefficients and standard (ideal) GRA coefficients are determined. The relative closeness coefficients are derived in order to rank the alternatives. The (...)
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  17.  1
    Neutrosophic Crisp Set Theory.A. A. Salama & Florentin Smarandache - 2015 - New York, NY, USA: Education Publishing.
    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 (...)
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  18.  14
    Refined Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies.Florentin Smarandache - 2015 - Neutrosophic Sets and Systems 9:58-63.
    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.
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  19.  51
    How Violation of Newton’s Third Law Can Pave Way to New Space Propulsion Mechanism via Optical Diametric Drive Experiment.Victor Christianto & Florentin Smarandache - 2022 - Bulletin of Pure and Applied Science 41 (2):41-44.
    In our initial paper discussing plausible steps toward workable warp drive machines. The following article express our view on this debate. While there are still objections toward existing warp drive proposals, such as by G. Landis, Harold White etc., because they are all based on GTR, nonetheless we think it is possible by starting to see if it is possible to deviate from Newton's third law. And we discuss possible a propulsion method based on negative masses, and discuss how optical (...)
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  20.  16
    Neutrosophic Refined Similarity Measure Based on Cosine Function.Said Broumi & Florentin Smarandache - 2014 - Neutrosophic Sets and Systems 6:42-48.
    In this paper, the cosine similarity measure of neutrosophic refined (multi-) sets is proposed and its properties are studied. The concept of this cosine similarity measure of neutrosophic refined sets is the extension of improved cosine similarity measure of single valued neutrosophic. Finally, using this cosine similarity measure of neutrosophic refined set, the application of medical diagnosis is presented.
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  21.  16
    Neutrosophic Crisp Set Theory.A. Salama & Florentin Smarandache - 2014 - Neutrosophic Sets and Systems 5:27-35.
    The purpose of this paper is to introduce new types of neutrosophic crisp sets with three types 1, 2, 3. After given the fundamental definitions and operations, we obtain several properties, and discussed the relationship between neutrosophic crisp sets and others. Also, we introduce and study the neutrosophic crisp point and neutrosophic crisp relations. Possible applications to database are touched upon.
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  22.  13
    Cosine Similarity Measure of Interval Valued Neutrosophic Sets.Said Broumi & Florentin Smarandache - 2014 - Neutrosophic Sets and Systems 5:15-20.
    In this paper, we define a new cosine similarity between two interval valued neutrosophic sets based on Bhattacharya’s distance [19]. The notions of interval valued neutrosophic sets (IVNS, for short) will be used as vector representations in 3D-vector space. Based on the comparative analysis of the existing similarity measures for IVNS, we find that our proposed similarity measure is better and more robust. An illustrative example of the pattern recognition shows that the proposed method is simple and effective.
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  23.  44
    Neutrosophic Statistics is an extension of Interval Statistics, while Plithogenic Statistics is the most general form of statistics (second version).Florentin Smarandache - 2022 - International Journal of Neutrosophic Science 19 (1):148-165.
    In this paper, we prove that Neutrosophic Statistics is more general than Interval Statistics, since it may deal with all types of indeterminacies (with respect to the data, inferential procedures, probability distributions, graphical representations, etc.), it allows the reduction of indeterminacy, and it uses the neutrosophic probability that is more general than imprecise and classical probabilities and has more detailed corresponding probability density functions. While Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to (...)
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  24.  16
    Taylor Series Approximation to Solve Neutrosophic Multiobjective Programming Problem.Ibrahim Hezam, Mohamed Abdel-Baset & Florentin Smarandache - 2015 - Neutrosophic Sets and Systems 10:39-45.
    In this paper, Taylor series is used to solve neutrosophic multi-objective programming problem (NMOPP). In the proposed approach, the truth membership, Indeterminacy membership, falsity membership functions associated with each objective of multi-objective programming problems are transformed into a single objective linear programming problem by using a first order Taylor polynomial series. Finally, to illustrate the efficiency of the proposed method, a numerical experiment for supplier selection is given as an application of Taylor series method for solving neutrosophic multi-objective programming problem (...)
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  25.  35
    Extension of Soft Set to Hypersoft Set, and then to Plithogenic Hypersoft Set.Florentin Smarandache - 2018 - Neutrosophic Sets and Systems 22 (1):168-170.
    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.
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  26.  34
    The Paradoxism in Mathematics, Philosophy, and Poetry.Florentin Smarandache - 2022 - Bulletin of Pure and Applied Sciences 41 (1):46-48.
    This short article pairs the realms of “Mathematics”, “Philosophy”, and “Poetry”, presenting some corners of intersection of this type of scientocreativity. Poetry have long been following mathematical patterns expressed by stern formal restrictions, as the strong metrical structure of ancient Greek heroic epic, or the consistent meter with standardized rhyme scheme and a “volta” of Italian sonnets. Poetry was always connected to Philosophy, and further on, notable mathematicians, like the inventor of quaternions, William Rowan Hamilton, or Ion Barbu, the creator (...)
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  27.  20
    An Extended TOPSIS Method for the Multiple Attribute Decision Making Problems Based on Interval Neutrosophic Uncertain Linguistics Variables.Said Broumi & Florentin Smarandache - 2015 - Neutrosophic Sets and Systems 8:22-31.
    The interval neutrosophic uncertain linguistic variables can easily express the indeterminate and inconsistent information in real world, and TOPSIS is a very effective decision making method more and more extensive applications. In this paper, we will extend the TOPSIS method to deal with the interval neutrosophic uncertain linguistic information, and propose an extended TOPSIS method to solve the multiple attribute decision making problems in which the attribute value takes the form of the interval neutrosophic uncertain linguistic variables and attribute weight (...)
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  28.  10
    The Characteristic Funcation of a Neutrosophic Set.A. Salama, Florentin Smarandache & S. A. Alblowi - 2014 - Neutrosophic Sets and Systems 3:14-17.
    The purpose of this paper is to introduce and study the characteristic function of a neutrosophic set. After given the fundamental definitions of neutrosophic set operations generated by the characteristic function of a neutrosophic set ( Ng for short), we obtain several properties, and discussed the relationship between neutrosophic sets generated by Ng and others. Finally, we introduce the neutrosophic topological spaces generated by Ng . Possible application to GIS topology rules are touched upon.
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  29.  12
    Multi Attribute Decision Making Strategy on Projection and Bidirectional Projection Measures of Interval Rough Neutrosophic Sets.Surapati Pramanik, Rumi Roy, Tapan Kumar Roy & Florentin Smarandache - 2018 - Neutrosophic Sets and Systems 19:101-109.
    In this paper, we define projection and bidirectional projection measures between interval rough neutrosophic sets and prove their basic properties. Then two new multi attribute decision making strategies are proposed based on interval rough neutrosophic projection and bidirectional projection measures respectively. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.
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  30.  29
    A Unifying Field in Logics: Neutrosophic Logic: Neutrosophy, Neutrosophic Set, Neutrosophic Probability.Florentin Smarandache (ed.) - 2007 - Ann Arbor, MI, USA: InfoLearnQuest.
    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.
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  31.  15
    Degree of Dependence and Independence of the Components of Fuzzy Set and Neutrosophic Set.Florentin Smarandache - 2015 - Neutrosophic Sets and Systems 11:95-97.
    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.
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  32.  23
    New Neutrosophic Crisp Topological Concepts.A. Salama, Florentin Smarandache & S. A. Alblowi - 2014 - Neutrosophic Sets and Systems 4:50-54.
    In this paper, we introduce the concept of ""neutrosophic crisp neighborhoods system for the neutrosophic crisp point ". Added to, we introduce and study the concept of neutrosophic crisp local function, and construct a new type of neutrosophic crisp topological space via neutrosophic crisp ideals. Possible application to GIS topology rules are touched upon.
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  33.  22
    Bipolar Neutrosophic Projection Based Models for Solving Multi-Attribute Decision-Making Problems.Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri & Florentin Smarandache - 2017 - Neutrosophic Sets and Systems 15:70-79.
    Bipolar neutrosophic sets are the extension of neutrosophic sets and are based on the idea of positive and negative preferences of information. Projection measure is a useful apparatus for modelling real life decision making problems. In the paper, we define projection, bidirectional projection and hybrid projection measures between bipolar neutrosophic sets. Three new methods based on the proposed projection measures are developed for solving multi-attribute decision making problems. In the solution process, the ratings of performance values of the alternatives with (...)
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  34.  1
    Filters via Neutrosophic Crisp Sets.A. A. Salama & Florentin Smarandache - 2013 - Neutrosophic Sets and Systems 1:34-37.
    In this paper we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.
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  35.  17
    Small Tech, High Touch: A Permutation.Victor Christianto & Florentin Smarandache - 2022 - Bio-Science Research Bulletin 38 (2):81-85.
    In an earlier paper published in a neutrosophic math journal (IJNS), we discussed a new approach to technology, which may be called as ‘opti-realism’ or ‘pess-optimism’ as alternative to utopianism based on technocracy, which may lead the world into global technototalitarianism. In this article, we submit a new approach to Nature and technology, which is more modest and humble, rather than a techno-utopianism version of reality that most futurists argue for. Our proposed approach resembles more to Myer-Briggs 16 types of (...)
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  36.  9
    Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces.A. A. Salama, Florentin Smarandache & Valeri Kroumov - 2014 - Neutrosophic Sets and Systems 2:25-30.
    In this paper, we generalize the crisp topological spaces to the notion of neutrosophic crisp topological space, and we construct the basic concepts of the neutrosophic crisp topology.
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  37.  16
    Introducción a los conjuntos IndetermSoft e IndetermHyperSoft.Florentin Smarandache - 2022 - Neutrosophic Computing and Machine Learning 22 (1):1-22.
    This paper presents for the first time the IndetermSoft Set, as an extension of the classical (determinate) Soft Set, which operates on indeterminate data, and similarly the HyperSoft Set extended to the IndetermHyperSoft Set, where 'Indeterm' means 'Indeterminate' (uncertain, conflicting, non-unique result). They are built on an IndetermSoft Algebra which is an algebra dealing with IndetermSoft Operators resulting from our real world. Subsequently, the IndetermSoft and IndetermHyperSoft Sets and their Fuzzy/Fuzzy Intuitionistic/Neutrosophic and other fuzzy extensions and their applications are presented.
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  38.  88
    Neutrosophy: Neutrosophic Probability, Set, and Logic: Analytic Synthesis & Synthetic Analysis.Florentin Smarandache - 1998 - American Research Press.
  39.  15
    Improved Definition of NonStandard Neutrosophic Logic and Introduction to Neutrosophic Hyperreals (Fifth version).Florentin Smarandache - 2022 - Neutrosophic Sets and Systems 51 (1):1-20.
    In the fifth version of our response-paper [26] to Imamura’s criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the NonStandard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy – otherwise they (...)
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  40.  15
    Introduction to SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra.Florentin Smarandache - 2022 - Journal of Algebraic Hyperstructures and Logical Algebras 3 (2):17-24.
    In this paper we recall our concepts of n th-Power Set of a Set, SuperHyperOperation, SuperHyperAxiom, SuperHyperAlgebra, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one actually encounters SuperHyperStructures (or more accurately (m, n)- SuperHyperStructures).
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  41.  15
    Practical Applications of IndetermSoft Set and IndetermHyperSoft Set and Introduction to TreeSoft Set as an extension of the MultiSoft Set.Florentin Smarandache - 2022 - Neutrosophic Sets and Systems 51 (1):939-947.
    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 (...)
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  42.  32
    Neutrosophic Closed Set and Neutrosophic Continuous Functions.A. A. Salama, Florentin Smarandache & Valeri Kroumov - 2014 - Neutrosophic Sets and Systems 4:4-8.
    In this paper, we introduce and study the concept of" neutrosophic closed set" and" neutrosophic continuous function". Possible application to GIS topology rules are touched upon.
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  43.  14
    Definición Mejorada de Lógica Neutrosófica No Estándar e Introducción a los Hiperreales Neutrosóficos (Quinta versión). Improved Definition of Non-Standard Neutrosophic Logic and Introduction to Neutrosophic Hyperreals (Fifth Version).Florentin Smarandache - 2022 - Neutrosophic Computing and Machine Learning 23 (1):1-20.
    In the fifth version of our reply article [26] to Imamura's critique, we recall that Neutrosophic Non-Standard Logic was never used by the neutrosophic community in any application, that the quarter-century old (1995-1998) neutrosophic operators criticized by Imamura were never used as they were improved soon after, but omits to talk about their development, and that in real-world applications we need to convert/approximate the hyperreals, monads and bi-nads of Non-Standard Analysis to tiny intervals with the desired precision; otherwise they would (...)
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  44.  13
    Introduction to the n-SuperHyperGraph - the most general form of graph today.Florentin Smarandache - 2022 - Neutrosophic Sets and Systems 48 (1):483-485.
    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.).
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  45.  13
    The SuperHyperFunction and the Neutrosophic SuperHyperFunction (revisited again).Florentin Smarandache - 2022 - Neutrosophic Sets and Systems 49 (1):594-600.
    In this paper, one recalls the general definition of the SuperHyperAlgebra with its SuperHyperOperations and SuperHyperAxioms [2, 6]. Then one introduces for the first time the SuperHyperTopology and especially the SuperHyperFunction and Neutrosophic SuperHyperFunction. One gives a numerical example of a Neutro-SuperHyperGroup.
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  46.  9
    Degrees of Membership > 1 and < 0 of the Elements with Respect to a Neutrosophic OffSet.Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 12:3-8.
    We have defined the Neutrosophic Over- /Under-/Off-Set and -Logic for the first time in 1995 and published in 2007. During 1995-2016 we presented them to various national and international conferences and seminars ([16]-[37]) and did more publishing during 2007-2016 ([1]-[15]). These new notions are totally different from other sets/logics/probabilities. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, to Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some (...)
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  47.  12
    La Neutro-Geometría y la Anti-Geometría como Alternativas y Generalizaciones de las Geometrías no Euclidianas.Florentin Smarandache - 2022 - Neutrosophic Computing and Machine Learning 20 (1):91-104.
    In this paper we extend Neutro-Algebra and Anti-Algebra to geometric spaces, founding Neutro/Geometry and AntiGeometry. While Non-Euclidean Geometries resulted from the total negation of a specific axiom (Euclid's Fifth Postulate), AntiGeometry results from the total negation of any axiom or even more axioms of any geometric axiomatic system (Euclidean, Hilbert, etc. ) and of any type of geometry such as Geometry (Euclidean, Projective, Finite, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.), and Neutro-Geometry results from the partial negation of one (...)
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  48.  11
    Introducción a la Super-Hiper-Álgebra y la Super-HiperÁlgebra Neutrosófica.Florentin Smarandache - 2022 - Neutrosophic Computing and Machine Learning 20 (1):1-6.
    In this article, the concepts of Nth Power Set of a Set, Super-Hyper-Oper-Operation, Super-Hyper-Axiom, SuperHyper-Algebra, and their corresponding Neutrosophic Super-Hyper-Oper-Operation, Neutrosophic Super-Hyper-Axiom and Neutrosophic Super-Hyper-Algebra are reviewed. In general, in any field of knowledge, really what are found are Super-HyperStructures (or more specifically Super-Hyper-Structures (m, n)).
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  49.  17
    Introduction to Image Processing via Neutrosophic Techniques.A. A. Salama, Florentin Smarandache & Mohamed Eisa - 2014 - Neutrosophic Sets and Systems 5:59-64.
    This paper is an attempt of proposing the processing approach of neutrosophic technique in image processing. As neutrosophic sets is a suitable tool to cope with imperfectly defined images, the properties, basic operations distance measure, entropy measures, of the neutrosophic sets method are presented here. İn this paper we, introduce the distances between neutrosophic sets: the Hamming distance, the normalized Hamming distance, the Euclidean distance and normalized Euclidean distance. We will extend the concepts of distances to the case of neutrosophic (...)
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  50.  9
    La Estadística Neutrosófica es una extensión de la Estadística de Intervalos, mientras que la Estadística Plitogénica es la forma más general de estadística. (Cuarta versión). Neutrosophic Statistics is an extension of Interval Statistics, while Plitogenic Statistics is the most general form of statistics (Fourth version).Florentin Smarandache - 2022 - Neutrosophic Computing and Machine Learning 23 (1):21-38.
    In this paper we show that Neutrosophic Statistics is an extension of Interval Statistics, since it deals with all kinds of indeterminacy (with respect to data, inferential procedures, probability distributions, graphical representations, etc.), allows for indeterminacy reduction, and uses neutrosophic probability which is more general than imprecise and classical probabilities, and has more detailed corresponding probability density functions. Whereas Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments of Woodall et al (...)
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