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  1. NeutroAlgebra is a Generalization of Partial Algebra.Florentin Smarandache - 2020 - International Journal of Neutrosophic Science 2 (1):8-17.
    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 (...)
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  • 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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  • Logic in reality.Joseph E. Brenner - 2008 - Dordrecht: Springer.
    The work is the presentation of a logical theory - Logic in Reality (LIR) - and of applications of that theory in natural science and philosophy, including ...
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  • 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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  • Isolated Single Valued Neutrosophic Graphs.Said Broumi, Assia Bakali, Mohamed Talea & Florentin Smarandache - 2015 - Neutrosophic Sets and Systems 11:74-78.
    Many results have been obtained on isolated graphs and complete graphs. In this paper, a necessary and sufficient condition will be proved for a single valued neutrosophic graph to be an isolated single valued neutrosophic graph.
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  • 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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  • 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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  • (1 other version)Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited).Florentin Smarandache - 2019 - In Advances of standard and nonstandard neutrosophic theories. Brussels, Belgium: Pons. pp. 240-265.
    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.
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  • 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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  • 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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  • Foundation of Revolutionary Topologies: An Overview, Examples, Trend Analysis, Research Issues, Challenges, and Future Directions.Florentin Smarandache - 2024 - Neutrosophic Systems with Applications 13:45-66.
    We now found nine new topologies, such as: NonStandard Topology, Largest Extended NonStandard Real Topology, Neutrosophic Triplet Weak/Strong Topologies, Neutrosophic Extended Triplet Weak/Strong Topologies, Neutrosophic Duplet Topology, Neutrosophic Extended Duplet Topology, Neutrosophic MultiSet Topology, and recall and improve the seven previously founded topologies in the years (2019-2023), namely: NonStandard Neutrosophic Topology, NeutroTopology, AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. They are called avantgarde topologies because of their innovative forms.
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  • Entropy of Polysemantic Words for the Same Part of Speech.Mihaela Colhon, Florentin Smarandache & Dan Valeriu Voinea - unknown
    In this paper, a special type of polysemantic words, that is, words with multiple meanings for the same part of speech, are analyzed under the name of neutrosophic words. These words represent the most dif cult cases for the disambiguation algorithms as they represent the most ambiguous natural language utterances. For approximate their meanings, we developed a semantic representation framework made by means of concepts from neutrosophic theory and entropy measure in which we incorporate sense related data. We show the (...)
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  • 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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  • (1 other version)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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  • Correlation Coefficient Measures of Interval Bipolar Neutrosophic Sets for Solving Multi-Attribute Decision Making Problems.Surapati Pramanik, Dey Partha Pratim & Florentin Smarandache - 2018 - Neutrosophic Sets and Systems 19:70-79.
    Interval bipolar neutrosophic set is a significant extension of interval neutrosophic set where every element of the set comprises of three independent positive membership functions and three independent negative membership functions. In this study, we first define correlation coefficient, and weighted correlation coefficient measures of interval bipolar neutrosophic sets and prove their basic properties. Then, we develop a new multi-attribute decision making strategy based on the proposed weighted correlation coefficient measure. Finally, we solve an investment problem with interval bipolar neutrosophic (...)
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  • An Evidence Fusion Method with Importance Discounting Factors based on Neutrosophic Probability Analysis in DSmT Framework.Qiang Guo, Haipeng Wang, You He, Yong Deng & Florentin Smarandache - 2017 - Neutrosophic Sets and Systems 17:64-73.
    To obtain effective fusion results of multi source evidences with different importance, an evidence fusion method with importance discounting factors based on neutrosopic probability analysis in DSmT framework is proposed. First, the reasonable evidence sources are selected out based on the statistical analysis of the pignistic probability functions of single focal elements. Secondly, the neutrosophic probability analysis is conducted based on the similarities of the pignistic probability functions from the prior evidence knowledge of the reasonable evidence sources. Thirdly, the importance (...)
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  • Uniform Single Valued Neutrosophic Graphs.S. Broumi, A. Dey, A. Bakali, M. Talea, F. Smarandache, L. H. Son & D. Koley - 2017 - Neutrosophic Sets and Systems 17:42-49.
    In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.
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  • 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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  • Neutrosophic Approach to Grayscale Images Domain.A. A. Salama, Florentin Smarandache & Hewayda ElGhawalby - 2018 - Neutrosophic Sets and Systems 21:13-19.
    In this paper, we propose a new technique for the enhancing images. It will work on removing the noise contained in the image as well as improving its contrast based on three different enhancing transforms, we commence by embedding the image into a neutrosophic domain; where the image will be mapped in three different levels, a level of trueness, a level of falseness and a level of indeterminacy. Hence, we act separately on each level using the enhancement transforms. Finally, we (...)
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  • Neutrosophic quadruple algebraic hyperstructures.A. A. A. Agboola, B. Davvaz & Florentin Smarandache - 2017 - Annals of Fuzzy Mathematics and Informatics 14.
    The objective of this paper is to develop neutrosophic quadruple algebraic hyperstructures. Specifically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them.
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  • An Overview of Neutrosophic and Plithogenic Theories and Applications.Florentin Smarandache & Maissam Ahmad Jdid - 2023 - Prospects for Applied Mathimatics and Data Analysis 2.
    We present this research to all researchers and scholars who have realized the existence of indeterminacy in all data, through the results they obtain and the values that are not accurate enough and that may cause loss to the systems and facilities under study, and we will present through it the emergence, foundations and development of Neutrosophic theories and their applications for more than two decades (1995- 2023) since it was defined and studied, along with its applications, in order to (...)
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  • Neutrosophic Soft Graphs.Nasir Shah & Asim Hussain - 2015 - Neutrosophic Sets and Systems 11:31-44.
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  • New Types of Neutrosophic Crisp Closed Sets.Ahmed B. Al-Nafee, A. A. Salama & Florentin Smarandache - 2020 - Neutrosophic Sets and Systems 36:175-183.
    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 (...)
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  • Pura Vida Neutrosophic Algebra.Ranulfo Paiva Barbosa & Florentin Smarandache - 2023 - Neutrosophic Systems with Applications 9.
    We introduce Pura Vida Neutrosophic Algebra, an algebraic structure consisting of neutrosophic numbers equipped with two binary operations namely addition and multiplication. The addition can be calculated sometimes with the function min and other times with the max function. The multiplication operation is the usual sum between numbers. Pura Vida Neutrosophic Algebra is an extension of both Tropical Algebra (also known as Min-Plus, or Min-Algebra) and Max-Plus Algebra (also known as Max-algebra). Tropical and Max-Plus algebras are algebraic structures included in (...)
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  • Graphical Method for Solving Neutrosophical Nonlinear Programming Models.Maissam Jdid & Florentin Smarandache - 2023 - Neutrosophic Systems with Applications 9.
    An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of the issue under (...)
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  • Neutrosophic Modal Logic.Florentin Smarandache - 2017 - Neutrosophic Sets and Systems 15:90-96.
    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.
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  • Aggregation of triangular fuzzy neutrosophic set information and its application to multi-attribute decision making.Pranab Biswas, Surapati Pramanik & Bibhas C. Giri - 2016 - Neutrosophic Sets and Systems 12:20-40.
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  • Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean.Florentin Smarandache & Subhash Kumar Yadav - 2023 - Neutrosophic Sets and Systems 53.
    One of the disadvantages of the point estimate in survey sampling is that it fluctuates from sample to sample due to sampling error, as the estimator only provides a point value for the parameter under discussion. The neutrosophic approach, pioneered by Florentin Smarandache, is an excellent tool for estimating the parameters under consideration in sampling theory since it yields interval estimates in which the parameter lies with a very high probability. As a result, the neutrosophic technique, which is a generalization (...)
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  • n-Cylindrical Fuzzy Neutrosophic Topological Spaces.Kumari R. Sarannya, Sunny Joseph Kalayathankal, George Mathews & Florentin Smarandache - 2023 - Journal of Fuzzy Extension and Applications 4 (2).
    The objective of this study is to incorporate topological space into the realm of n-Cylindrical Fuzzy Neutrosophic Sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper, we introduce n-Cylindrical Fuzzy Neutrosophic Topological Spaces (n-CyFNTS), n-Cylindrical Fuzzy Neutrosophic (n-CyFN) open sets, and n-CyFN closed sets. We also defined the n-CyFN base, n-CyFN subbase, and some related theorems here.
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  • Generalized plithogenic whole hypersoft set, PFHSS-Matrix, operators and applications as COVID-19 data structures.Shazia Rana, Muhammad Saeed, Madiha Qayyum & Florentin Smarandache - 2023 - Journal of Intelligent and Fuzzy Systems 44.
    This article is a preliminary draft for initiating and commencing a new pioneer dimension of expression. To deal with higher-dimensional data or information flowing in this modern era of information technology and artificial intelligence, some innovative super algebraic structures are essential to be formulated. In this paper, we have introduced such matrices that have multiple layers and clusters of layers to portray multi-dimensional data or massively dispersed information of the plithogenic universe made up of numerous subjects their attributes, and sub-attributes. (...)
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  • Neutrosophic Integer Programming Problem.Mai Mohamed, Mohamed Abdel-Basset, Abdel Nasser Zaied & Florentin Smarandache - 2017 - Neutrosophic Sets and Systems 15:3-7.
    In this paper, we introduce the integer programming in neutrosophic environment, by considering coffecients of problem as a triangulare neutrosophic numbers. The degrees of acceptance, indeterminacy and rejection of objectives are simultaneously considered. The Neutrosophic Integer Programming Problem (NIP) is transformed into a crisp programming model, using truth membership (T), indeterminacy membership (I), and falsity membership (F) functions as well as single valued triangular neutrosophic numbers. To measure the efficiency of the model, we solved several numerical examples.
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  • PCR5 and Neutrosophic Probability in Target Identification.Florentin Smarandache, N. Abbas, Y. Chibani, B. Hadjadji & Z. A. Omar - 2017 - Neutrosophic Sets and Systems 16:76-79.
    In this paper, we use PCR5 in order to fusion the information of two sources providing subjective probabilities of an event A to occur in the following form: chance that A occurs, indeterminate chance of occurrence of A, chance that A does not occur. -/- .
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  • Interval Neutrosophic Multi-Attribute Decision-Making Based on Grey Relational Analysis.Surapati Pramanik & Kalya Mondal - 2015 - Neutrosophic Sets and Systems 9:13-22.
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  • Parameterized Special Theory of Relativity (PSTR).Florentin Smarandache - 2012 - Apeiron: Studies in Infinite Nature 19 (2):115-122.
    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, (...)
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  • 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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  • Classical Logic and Neutrosophic Logic. Answers to K. Georgiev.Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 13:79-83.
    In this paper, we make distinctions between Classical Logic (where the propositions are 100% true, or 100 false) and the Neutrosophic Logic (where one deals with partially true, partially indeterminate and partially false propositions) in order to respond to K. Georgiev’s criticism [1]. We recall that if an axiom is true in a classical logic system, it is not necessarily that the axiom be valid in a modern (fuzzy, intuitionistic fuzzy, neutrosophic etc.) logic system.
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  • Neutrosophic Set Appriach for Characterizations of Left Almost Semigroups.Madad Khan, Florentin Smarandache & Sania Afzal - 2015 - Neutrosophic Sets and Systems 11:79-94.
    In this paper we have defined neutrosophic ideals, neutrosophic interior ideals, netrosophic quasi-ideals and neutrosophic bi-ideals (neutrosophic generalized bi-ideals) and proved some results related to them. Furthermore, we have done some characterization of a neutrosophic LA-semigroup by the properties of its neutrosophic ideals. It has been proved that in a neutrosophic intra-regular LA-semigroup neutrosophic left, right, two-sided, interior, bi-ideal, generalized bi-ideal and quasi-ideals coincide and we have also proved that the set of neutrosophic ideals of a neutrosophic intra-regular LA-semigroup forms (...)
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  • Neutrosophic LA-Semigroup Rings.Mumtaz Ali, Florentin Smarandache & Luige Vladareanu - 2015 - Neutrosophic Sets and Systems 7:81-88.
    Neutrosophic LA-semigroup is a midway structure between a neutrosophic groupoid and a commutative neutrosophic semigroup. Rings are the old concept in algebraic structures. We combine the neutrosophic LA-semigroup and ring together to form the notion of neutrosophic LA-semigroup ring. Neutrosophic LAsemigroup ring is defined analogously to neutrosophic group ring and neutrosophic semigroup ring.
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  • Neutosophic Quadruple Numbers, Refined Neutrosophic Quadruple Number, Absorbance Law, and the Multiplication of Neutrosophic Quadruple Numbers.Florentin Smarandache - 2015 - Neutrosophic Sets and Systems 10:96-98.
    In this paper, we introduce for the first time the neutrosophic quadruple numbers (of the form a + bT + cI + dF) and the refined neutrosophic quadruple numbers. Then we define an absorbance law, based on a prevalence order, both of them in order to multiply the neutrosophic components T, I, F, or their sub-components tJ, Ik, Fl and thus to construct the multiplication of neutrosophic quadruple numbers.
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  • A Study on Problems of Hijras in West Bengal Based on Neutrosophic Cognitive Maps.Kalyan Mondal & Surapati Pramanik - 2014 - Neutrosophic Sets and Systems 5:21-26.
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  • Neutrosophic Bi-LA-Semigroup and Neutrosophic N-LASemigroup.Mumtaz Ali, Florentin Smarandache, Muhammad Shabir & Munazza Naz - 2014 - Neutrosophic Sets and Systems 4:19-24.
    In this paper we define neutrosophic bi-LAsemigroup and neutrosophic N-LA-semigroup. Infact this paper is an extension of our previous paper neutrosophic left almost semigroup shortly neutrosophic LAsemigroup. We also extend the neutrosophic ideal to neutrosophic biideal and neutrosophic N-ideal. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neutrosophy. We have given sufficient amount of examples to illustrate the theory of neutrosophic bi-LA-semigroup, neutrosophic N-LAsemigroup and display many properties of them (...)
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  • Soft Neutrosophic Ring and Soft Neutrosophic Field.Mumtaz Ali, Florentin Smarandache, Muhammad Shabir & Munazza Naz - 2014 - Neutrosophic Sets and Systems 3:53-59.
    In this paper we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and construct soft neutrosophic rings and soft neutrosophic fields. We also extend neutrosophic ideal theory to form soft neutrosophic ideal over a neutrosophic ring and soft neutrosophic ideal of a soft neutrosophic ring . We have given many examples to illustrate the theory of soft neutrosophic rings and soft neutrosophic fields and display many properties of of these. At the end of this paper we (...)
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  • Thesis-Antithesis-Neutrothesis, and Neutrosynthesis.Florentin Smarandache - 2015 - Neutrosophic Sets and Systems 8:57-58.
    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.
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  • Generalization of Neutrosophic Rings and Neutrosophic Fields.Mumtaz Ali, Florentin Smarandache, Muhammad Shabir & Luige Vladareanu - 2014 - Neutrosophic Sets and Systems 5:9-14.
    In this paper we present the generalization of neutrosophic rings and neutrosophic fields. We also extend the neutrosophic ideal to neutrosophic biideal and neutrosophic N-ideal. We also find some new type of notions which are related to the strong or pure part of neutrosophy. We have given sufficient amount of examples to illustrate the theory of neutrosophic birings, neutrosophic N-rings with neutrosophic bifields and neutrosophic N-fields and display many properties of them in this paper.
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  • Soft Neutrosophic Group.Muhammad Shabir, Mumtaz Ali, Munazza Naz & Florentin Smarandache - 2013 - Neutrosophic Sets and Systems 1:13-25.
    In this paper we extend the neutrosophic group and subgroup to soft neutrosophic group and soft neutrosophic subgroup respectively. Properties and theorems related to them are proved and many examples are given.
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  • The Neutrosophic Statistical Distribution- More Problems, More Solutions.S. K. Patro & Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 12:73-79.
    In this paper , the authors explore neutrosophic statistics, that was initiated by Florentin Smarandache in 1998 and developed in 2014, by presenting various examples of several statistical distributions, from the work [1]. The paper is presented with more case studies, by means of which this neutrosophic version of statistical distribution becomes more pronounced.
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  • Interval Valued Neutrosophic Soft Topological Spaces.Anjan Mukherjee, Mithun Datta & Florentin Smarandache - 2014 - Neutrosophic Sets and Systems 6:18-27.
    In this paper we introduce the concept of interval valued neutrosophic soft topological space together with interval valued neutrosophic soft finer and interval valued neutrosophic soft coarser topology. We also define interval valued neutrosophic interior and closer of an interval valued neutrosophic soft set. Some theorems and examples are cites. Interval valued neutrosophic soft subspace topology are studied. Some examples and theorems regarding this concept are presented.
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  • (I,T)-Standard neutrosophic rough set and its topologies properties.Nguyen Xuan Thao & Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 14:65-70.
    In this paper, we defined (I,T) − standard neutrosophic rough sets based on an implicator I and a t-norm T on I; lower and upper approximations of standard neutrosophic sets in a standard neutrosophic approximation are defined. Some properties of (I,T) − standard neutrosophic rough sets are investigated. We consider the case when the neutrosophic components (truth, indeterminacy, and falsehood) are totally dependent, single-valued, and hence their sum is ≤ 1.
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  • Soft Neutrosophic Loops and Their Generalization.Mumtaz Ali, Christopher Dyer, Muhammad Shabir & Florentin Smarandache - 2014 - Neutrosophic Sets and Systems 4:55-75.
    Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft neutrosophic loop,soft neutosophic biloop, soft neutrosophic N -loop with the discuission of some of their characteristics. We also introduced a new type of soft neutrophic loop, the so called soft strong neutrosophic loop which is of pure neutrosophic character. This notion also found in all the other corresponding notions of soft neutrosophic thoery. We also given some of (...)
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  • Regular Bipolar Single Valued Neutrosophic Hypergraphs.Muhammad Aslam Malik, Ali Hassan, Said Broumi & Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 13:84-89.
    In this paper, we define the regular and totally regular bipolar single valued neutrosophic hypergraphs, and discuss the order and size along with properties of regular and totally regular bipolar single valued neutrosophic hypergraphs. We extend work on completeness of bipolar single valued neutrosophic hypergraphs.
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