Results for 'Neutrosophic Probability'

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  1. New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic Plithogenic Optimizations.Florentin Smarandache & Yanhui Guo - 2022 - Basel, Switzerland: MDPI.
    This volume presents state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer (...)
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  2. 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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  3. 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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  4. 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 (...)
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  5. Neutrosophic overset, neutrosophic underset, and neutrosophic offset: similarly for neutrosophic over-/under-/off-logic, probability, and statistics.Florentin Smarandache - 2016 - Brussels: Pons Editions.
    Neutrosophic Over-/Under-/Off-Set and -Logic were defined for the first time by Smarandache in 1995 and published in 2007. They are totally different from other sets/logics/probabilities. He extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other (...)
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  6. 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 (...)
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  7. The Encyclopedia of Neutrosophic Researchers, 5th Volume.Florentin Smarandache - 2023
    Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational (...)
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  8. Neutrosophic Knowledge. Journal of Modern Science and Arts, vol. 1, 2020.A. A. Salama, Florentin Smarandache & Ibraheem Yasser (eds.) - 2020 - Gallup, NM, USA: University of New Mexico.
    “Neutrosophics Knowledge” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. The submitted papers should be professional, in good English and Arabic, containing a brief review of a problem and obtained results. Neutrosophy is a new branch of philosophy that studies the origin, nature, and (...)
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  9.  91
    The Basics of Neutrosophic Simulation for Converting Random Numbers Associated with a Uniform Probability Distribution into Random Variables Follow an Exponential Distribution.Maissam Jdid, Rafif Alhabib & A. A. Salama - 2023 - Neutrosophic Sets and Systems 53:358-366.
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  10. Neutrosophic Measure and Neutrosophic Integral.Florentin Smarandache - 2013 - Neutrosophic Sets and Systems 1:3-7.
    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 measure and neutrosophic integral. 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 (...)
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  11. The Encyclopedia of Neutrosophic Researchers. Volume I.Florentin Smarandache - 2016 - Gallup, NM, USA: Neutrosophic Science International Association.
    This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life (...)
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  12. The Encyclopedia of Neutrosophic Researchers. Volume III.Florentin Smarandache - 2019 - Gallup, NM, USA: Neutrosophic Science International Association.
    This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life (...)
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  13.  96
    The Encyclopedia of Neutrosophic Researchers. Volume IV.Florentin Smarandache & Maikel Leyva Vázquez - 2021 - Gallup, NM, USA: Neutrosophic Science International Association.
    This is the fourth volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life (...)
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  14.  88
    The Encyclopedia of Neutrosophic Researchers, 1st volume.Florentin Smarandache - 2016 - Gallup, NM, USA: Neutrosophic Science International Association.
    This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The 78 authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. -/- Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many (...)
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  15.  81
    The Encyclopedia of Neutrosophic Researchers, 6th Volume.Florentin Smarandache, Maikel Yelandi Leyva Vázquez & Jesús Estupiñán Ricardo - 2023
    Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational (...)
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  16. Advances of standard and nonstandard neutrosophic theories.Florentin Smarandache (ed.) - 2019 - Brussels, Belgium: Pons.
    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 (...)
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  17. 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 (...)
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  18. Collected Papers (on Neutrosophic Theory and Applications), Volume VI.Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    This sixth volume of Collected Papers includes 74 papers comprising 974 pages on (theoretic and applied) neutrosophics, written between 2015-2021 by the author alone or in collaboration with the following 121 co-authors from 19 countries: Mohamed Abdel-Basset, Abdel Nasser H. Zaied, Abduallah Gamal, Amir Abdullah, Firoz Ahmad, Nadeem Ahmad, Ahmad Yusuf Adhami, Ahmed Aboelfetouh, Ahmed Mostafa Khalil, Shariful Alam, W. Alharbi, Ali Hassan, Mumtaz Ali, Amira S. Ashour, Asmaa Atef, Assia Bakali, Ayoub Bahnasse, A. A. Azzam, Willem K.M. Brauers, Bui (...)
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  19. Collected Papers (on Neutrosophic Theory and Applications), Volume VII.Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    This seventh volume of Collected Papers includes 70 papers comprising 974 pages on (theoretic and applied) neutrosophics, written between 2013-2021 by the author alone or in collaboration with the following 122 co-authors from 22 countries: Mohamed Abdel-Basset, Abdel-Nasser Hussian, C. Alexander, Mumtaz Ali, Yaman Akbulut, Amir Abdullah, Amira S. Ashour, Assia Bakali, Kousik Bhattacharya, Kainat Bibi, R. N. Boyd, Ümit Budak, Lulu Cai, Cenap Özel, Chang Su Kim, Victor Christianto, Chunlai Du, Chunxin Bo, Rituparna Chutia, Cu Nguyen Giap, Dao The (...)
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  20. Collected Papers (on Neutrosophic Theory and Its Applications in Algebra), Volume IX.Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxin Bo, Rakhal Das, Bijan Davvaz, R. Dhavaseelan, B. Elavarasan, Fahad Alsharari, (...)
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  21. Collected Papers (on Neutrosophic Theory and Applications), Volume VIII.Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    This eighth volume of Collected Papers includes 75 papers comprising 973 pages on (theoretic and applied) neutrosophics, written between 2010-2022 by the author alone or in collaboration with the following 102 co-authors (alphabetically ordered) from 24 countries: Mohamed Abdel-Basset, Abduallah Gamal, Firoz Ahmad, Ahmad Yusuf Adhami, Ahmed B. Al-Nafee, Ali Hassan, Mumtaz Ali, Akbar Rezaei, Assia Bakali, Ayoub Bahnasse, Azeddine Elhassouny, Durga Banerjee, Romualdas Bausys, Mircea Boșcoianu, Traian Alexandru Buda, Bui Cong Cuong, Emilia Calefariu, Ahmet Çevik, Chang Su Kim, Victor (...)
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  22. Introduction to Neutrosophic Genetics.Florentin Smarandache - 2021 - International Journal of Neutrosophic Science 1 (1):1-5.
    Neutrosophic Genetics is the study of genetics using neutrosophic logic, set, probability, statistics, measure and other neutrosophic tools and procedures. In this paper, based on the Neutrosophic Theory of Evolution (that includes degrees of Evolution, Neutrality (or Indeterminacy), and Involution) – as extension of Darwin’s Theory of Evolution, we show the applicability of neutrosophy in genetics, and we present within the frame of neutrosophic genetics the following concepts: neutrosophic mutation, neutrosophic speciation, and (...)
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  23. 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 (...)
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  24. 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}, (...)
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  25. Nidus Idearum. Scilogs, XIV: SuperHyperAlgebra.Florentin Smarandache - 2024 - BiblioPublishing.
    In this fourteenth book of scilogs – one may find topics on examples where neutrosophics works and others don’t, law of included infinitely-many-middles, decision making in games and real life through neutrosophic lens, sociology by neutrosophic methods, Smarandache multispace, algebraic structures using natural class of intervals, continuous linguistic set, cyclic neutrosophic graph, graph of neutrosophic triplet group , how to convert the crisp data to neutrosophic data, n-refined neutrosophic set ranking, adjoint of a square (...)
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  26. 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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  27. A Neutrosophic Binomial Factorial Theorem with their Refrains.Huda E. Khalid, Florentin Smarandache & Ahmed K. Essa - 2016 - Neutrosophic Sets and Systems 14:7-11.
    The Neutrosophic Precalculus and the Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the method used to deal with such indeterminacy. This article is innovative since the form of neutrosophic binomial factorial theorem was constructed in addition to its refrains. Two other important theorems were proven with their corollaries, and numerical examples as well. As a conjecture, we use ten (indeterminate) forms in neutrosophic calculus taking an (...)
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  28. 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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  29. Neutrosophic Regular Filters and Fuzzy Regular Filters in Pseudo-BCI Algebras.Xiaohong Zhang, Yingcan Ma & F. Smarandache - 2017 - Neutrosophic Sets and Systems 17:10-15.
    Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indetermi nacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI al gebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts of neutrosophic regular filter, neutrosophic closed filter and fuzzy regular filter in pseudo-BCI algebras are introduced, and some basic properties (...)
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  30. 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 (...)
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  31. 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 (...)
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  32. 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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  33. 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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  34. 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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  35. Soft Neutrosophic Bigroup and Soft Neutrosophic N-Group.Mumtaz Ali, Florentin Smarandache, Muhammad Shabir & Munazza Naz - 2014 - Neutrosophic Sets and Systems 2:55-81.
    Soft neutrosophic group and soft neutrosophic subgroup are generalized to soft neutrosophic bigroup and soft neutrosophic N-group respectively in this paper. Different kinds of soft neutrosophic bigroup and soft neutrosophic N-group are given. The structural properties and theorems have been discussed with a lot of examples to disclose many aspects of this beautiful man made structure.
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  36. Neutrosophic Cubic MCGDM Method Based on Similiarity Measure.Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy & F. Smarandache - 2017 - Neutrosophic Sets and Systems 16:44-56.
    The notion of neutrosophic cubic set is originated from the hybridization of the concept of neutrosophic set and interval valued neutrosophic set. We define similarity measure for neutrosophic cubic sets and prove some of its basic properties. We present a new multi criteria group decision making method with linguistic variables in neutrosophic cubic set environment. Finally, we present a numerical example to demonstrate the usefulness and applicability of the proposed method.
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  37. A Note on Square Neutrosophic Fuzzy Matrices.Mamouni Dhar, Said Broumi & Florentin Smarandache - 2014 - Neutrosophic Sets and Systems 3:37-41.
    In this article, we shall define the addition and multiplication of two neutrosophic fuzzy matrices. Thereafter, some properties of addition and multiplication of these matrices are also put forward.
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  38. 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 (...)
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  39. Neutrosophic Lattices.Vasantha Kandasamy & Florentin Smarandache - 2014 - Neutrosophic Sets and Systems 2:42-47.
    In this paper authors for the first time define a new notion called neutrosophic lattices. We define few properties related with them. Three types of neutrosophic lattices are defined and the special properties about these new class of lattices are discussed and developed. This paper is organised into three sections. First section introduces the concept of partially ordered neutrosophic set and neutrosophic lattices. Section two introduces different types of neutrosophic lattices and the final section studies (...)
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  40. On Neutrosophic Semi Alpha Open Sets.Qays Hatem Imran, F. Smarandache, Riad K. Al-Hamido & R. Dhavaseelan - 2017 - Neutrosophic Sets and Systems 18:37-42.
    In this paper, we presented antoher concept of neutrosophic open sets called neutrosophic semi-α-open sets and studied their fundamental poperties in neutrosophic topological spaces. We also present neutrospohic semi-α-interior and neutrosophic semi-α-closure and study some of their fundamental properties.
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  41. Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models.Maissam Jdid & Florentin Smarandache - 2023 - International Journal of Neutrosophic Science 23.
    Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available (...)
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  42. 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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  43. Neutrosophic Association Rule Mining Algorithm for Big Data Analysis.Mohamed Abdel-Basset, Mai Mohamed, Florentin Smarandache & Victor Chang - 2018 - Symmetry 10 (4):1-19.
    Big Data is a large-sized and complex dataset, which cannot be managed using traditional data processing tools. Mining process of big data is the ability to extract valuable information from these large datasets. Association rule mining is a type of data mining process, which is indented to determine interesting associations between items and to establish a set of association rules whose support is greater than a specific threshold. The classical association rules can only be extracted from binary data where an (...)
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  44. 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 (...)
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  45. Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm.Maissam Jdid & Florentin Smarandache - 2023 - Prospects for Applied Mathematics and Data Analysis 2 (1).
    One of the most important theories in linear programming is the dualistic theory and its basic idea is that for every linear model has dual linear model, so that solving the original linear model gives a solution to the dual model. Therefore, when we solving the linear programming model, we actually obtain solutions for two linear models. In this research, we present a study of the models. The neutrosophic dual and the binary simplex algorithm, which works to find the (...)
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  46. 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 (...)
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  47. 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 (...)
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  48. Support-Neutrosophic Set: A New Concept in Soft Computing.Nguyen Xuan Thao, Florentin Smarandache & Nguyen Van Dinh - 2017 - Neutrosophic Sets and Systems 16:93-98.
    Today, soft computing is a field that is used a lot in solving real-world problems, such as problems in economics, finance, banking... With the aim to serve for solving the real problem, many new theories and/or tools which were proposed, improved to help soft computing used more efficiently. We can mention some theories as fuzzy sets theory (L. Zadeh, 1965), intuitionistic fuzzy set (K Atanasov, 1986), neutrosophic set (F. Smarandache 1999). In this paper, we introduce a new notion of (...)
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  49. 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. (...)
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  50. 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 (...)
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