Results for 'interval valued neutrosophic set'

961 found
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  1. 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 (...)
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  2. Soft Interval-Valued Neutrosophic Rough Sets.Said Broumi & Florentin Smarandache - 2015 - Neutrosophic Sets and Systems 7:69-80.
    In this paper, we first defined soft intervalvalued neutrosophic rough sets(SIVN- rough sets for short) which combines interval valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of soft interval valued intuitionistic fuzzy rough sets( SIVIF- rough sets). Finally an illustartive example is given to verfy the developped algorithm and to demonstrate its practicality and effectiveness.
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  3. 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 (...)
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  4. 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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  5. 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 (...)
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  6. 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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  7. New Trends in Neutrosophic Theories and Applications, Volume III.Florentin Smarandache & Surapati Pramanik (eds.) - 2024
    The field of neutrosophic set theory and its applications has been rapidly expanding, particularly since the introduction of the journal "Neutrosophic Sets and Systems." New theories, techniques, and algorithms are being developed at a very high rate. One of the most notable trends in neutrosophic theory is its hybridization with other set theories such as rough set theory, bipolar set theory, soft set theory, hesitant fuzzy set theory, and more. Various hybrid structures like rough neutrosophic sets, (...)
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  8. 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 (...)
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  9. 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 (...)
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  10. 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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  11. Algebraic structures of neutrosophic triplets, neutrosophic duplets, or neutrosophic multisets. Volume I.Florentin Smarandache, Xiaohong Zhang & Mumtaz Ali - 2018 - Basel, Switzerland: MDPI. Edited by Florentin Smarandache, Xiaohong Zhang & Mumtaz Ali.
    The topics approached in the 52 papers included in this book are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power (...)
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  12. 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 (...)
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  13. Algebraic structures of neutrosophic triplets, neutrosophic duplets, or neutrosophic multisets. Volume II.Florentin Smarandache, Xiaohong Zhang & Mumtaz Ali - 2019 - Basel, Switzerland: MDPI.
    The topics approached in this collection of papers are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria (...)
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  14. A New Similarity Measure Based on Falsity Value between Single Valued Neutrosophic Sets Based on the Centroid Points of Transformed Single Valued Neutrosophic Values with Applications to Pattern Recognition.Mehmet Sahin, Necati Olgun, Vakkas Ulucay, Abdullah Kargin & Florentin Smarandache - 2017 - Neutrosophic Sets and Systems 15:31-48.
    In this paper, we propose some transfor mations based on the centroid points between single valued neutrosophic numbers. We introduce these trans formations according to truth, indeterminacy and falsity value of single valued neutrosophic numbers. We propose a new similarity measure based on falsity value between single valued neutrosophic sets. Then we prove some properties on new similarity measure based on falsity value between falsity value between single valued neutrosophic sets. Furthermore, we (...)
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  15. Interval neutrosophic sets applied to ideals in BCK/BCI-algebras.Seok-Zun Song, Madad Khan, Florentin Smarandache & Young Bae Jun - 2017 - Neutrosophic Sets and Systems 18:16-26.
    In this article, we apply the notion of interval neutrosophic sets to ideal theory in BCK/BCI-algebras.
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  16. Similarity Measure of Refined Single-Valued Neutrosophic Sets and Its Multicriteria Decision Making Method.Jun Ye & Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 12:41-44.
    This paper introduces a refined single-valued neutrosophic set (RSVNS) and presents a similarity measure of RSVNSs. Then a multicriteria decision-making method with RSVNS information is developed based on the similarity measure of RSVNSs. By the similarity measure between each alternative and the ideal solution (ideal alternative), all the alternatives can be ranked and the best one can be selected as well. Finally, an actual example on the selecting problems of construction projects demonstrates the application and effectiveness of the (...)
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  17. Single Valued Neutrosophic HyperSoft Set based on VIKOR Method for 5G Architecture Selection.Florentin Smarandache, M. Ali Ahmed & Ahmed Abdelhafeez - 2024 - International Journal of Neutrosophic Science 23 (2):42-52.
    This work introduces the framework for selecting architecture in 5G networks, considering various technological, performance, economic, and operational factors. With the emergence of 5G technology, the architecture selection process has become pivotal in meeting diverse requirements for ultra-high-speed connectivity, low latency, scalability, and diverse service demands. The evaluation comprehensively analyses different architecture options, including centralized, distributed, cloud-based, and virtualized architectures. Factors such as network performance, scalability, cost-effectiveness, security, and compatibility are considered within a multi-criteria decision-making framework. Findings reveal each architecture (...)
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  18. Neutrosophic logics: prospects and problems.Umberto Rivieccio - 2008 - Fuzzy Sets and Systems 159 (14):1860-1868.
    Neutrosophy has been introduced some years ago by Florentin Smarandache as a new branch of philosophy dealing with “the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra”. A variety of new theories have been developed on the basic principles of neutrosophy: among them is neutrosophic logics, a family of many-valued systems that can be regarded as a generalization of fuzzy logics. In this paper we present a critical introduction to neutrosophic (...)
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  19. Multiple Criteria Evaluation Model Based on the Single Valued Neutrosophic Set.Dragisa Stanujkic, Florentin Smarandache, Edmundas Kazimieras Zavadskas & Darjan Karabasevic - 2016 - Neutrosophic Sets and Systems 14:3-6.
    Gathering the attitudes of the examined respondents would be very significant in some evaluation models. Therefore, a multiple criteria approach based on the use of the neutrosophic set is considered in this paper. An example of the evaluation of restaurants is considered at the end of this paper with the aim to present in detail the proposed approach.
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  20. 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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  21. 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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  22. 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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  23. A New Type of Neutrosophic Set in Pythagorean Fuzzy Environment and Applications to Multi-criteria Decision Making.Mahmut Can Bozyigit, Florentin Smarandache, Murat Olgun & Mehmet Unver - 2023 - International Journal of Neutrosophic Science 20 (2):107-134.
    In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and (...)
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  24. A Bipolar Single Valued Neutrosophic Isolated Graphs: Revisited.Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache & Mohsin Khan - 2017 - International Journal of New Computer Architectures and Their Applications 7 (3):89-94.
    In this research paper, the graph of the bipolar single-valued neutrosophic set model (BSVNS) is proposed. The graphs of single valued neutrosophic set models is generalized by this graph. For the BSVNS model, several results have been proved on complete and isolated graphs. Adding, an important and suitable condition for the graphs of the BSVNS model to become an isolated graph of the BSVNS model has been demonstrated.
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  25. 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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  26. 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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  27. Regular Single Valued Neutrosophic Hypergraphs.Muhammad Aslam Malik, Ali Hassan, Said Broumi & Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 13:18-23.
    In this paper, we define the regular and totally regular single valued neutrosophic hypergraphs, and discuss the order and size along with properties of regular and totally regular single valued neutrosophic hypergraphs. We also extend work on completeness of single valued neutrosophic hypergraphs.
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  28. On single-valued neutrosophic soft uniform spaces.Yaser Saber, Hanan Alohali, Tawfik Elmasry & Florentin Smarandache - 2023 - AIMS Mathematics 9 (1).
    In this paper, we introduce the notion of single-valued neutrosophic soft uniform spaces as a view point of the entourage approach. We investigate the relationship among single-valued neutrosophic soft uniformities, single-valued neutrosophic soft topologies and single-valued neutrosophic soft interior operators. Also, we study several single-valued neutrosophic soft topologies induced by a single-valued neutrosophic soft uniform space.
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  29. 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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  30. Ambiguous Set is a subclass of the Double Refined Indeterminacy Neutrosophic Set, and of the Refined Neutrosophic Set in general.Florentin Smarandache - 2023 - Neutrosophic Sets and Systems 58.
    In this short note we show that the so-called Ambiguous Set (2019) is a subclass of the Double Refined Indeterminacy Neutrosophic Set (2017) and is a particular case of the Refined Neutrosophic Set (2013). Also, the Ambiguous Set is similar to the Quadripartitioned Neutrosophic Set (2016), and Belnap’s Four-Valued Logic (1975).
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  31. Introduction to the Complex Refined Neutrosophic Set.Florentin Smarandache - 2017 - Critical Review: A Journal of Politics and Society 14 (1):5-9.
    In this paper, one extends the single-valued complex neutrosophic set to the subsetvalued complex neutrosophic set, and afterwards to the subset-valued complex refined neutrosophic set.
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  32. Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets – Revisited.Florentin Smarandache - 2018 - Neutrosophic Sets and Systems 21:153-166.
    In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes (parameters)’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for (...)
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  33. 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. (...)
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  34. 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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  35. 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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  36. (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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  37. 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 (...)
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  38. Neutrosophic Algebraic Structures and Their Applications.Florentin Smarandache, Memet Şahin, Derya Bakbak, Vakkas Uluçay & Abdullah Kargın - 2022 - Gallup, NM, USA: NSIA Publishing House.
    Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, (...)
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  39. A short history of fuzzy, intuitionistic fuzzy, neutrosophic and plithogenic sets.Akbar Rezaei, T. Oner, T. Katican, Florentin Smarandache & N. Gandotra - 2022 - International Journal of Neutrosophic Science 18.
    Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough stud ies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set whose elements are (...)
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  40. Neutrosophic Triplet Structures. Volume I.Florentin Smarandache & Memet Şahin (eds.) - 2019 - Brussels, Belgium, EU: Pons editions.
    Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world (...)
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  41. Neutrosophic SuperHyperAlgebra and New Types of Topologies.Florentin Smarandache - 2023 - Infinite Study. Edited by Florentin Smarandache, Memet Şahin, Derya Bakbak, Vakkas Uluçay & Abdullah Kargın.
    The n-th PowerSet is used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. Neutrosophic set has been derived from a (...)
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  42. Quadruple neutrosophic theory and applications.Florentin Smarandache, Memet Şahin, Vakkas Uluçay & Abdullah Kargın - 2020 - Brussels, Belgium: Pons Editions.
    Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific (...)
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  43. 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 (...)
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  44. Novel Concepts on Domination in Neutrosophic Incidence Graphs with Some Applications.Florentin Smarandache, Siti Nurul Fitriah Mohamad & Roslan Hasni - 2023 - Journal of Advanced Computational Intelligence and Intelligent Informatics 27 (5).
    In graph theory, the concept of domination is essential in a variety of domains. It has broad applications in diverse fields such as coding theory, computer net work models, and school bus routing and facility lo cation problems. If a fuzzy graph fails to obtain acceptable results, neutrosophic sets and neutrosophic graphs can be used to model uncertainty correlated with indeterminate and inconsistent information in arbitrary real-world scenario. In this study, we consider the concept of domination as it (...)
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  45. CSsEv: Modelling QoS Metrics in Tree Soft Toward Cloud Services Evaluator based on Uncertainty Environment.Mona Gharib, Florentin Smarandache & Mona Mohamed - 2024 - International Journal of Neutrosophic Science 23 (2):32-41.
    Cloud computing (ClC) has become a more popular computer paradigm in the preceding few years. Quality of Service (QoS) is becoming a crucial issue in service alteration because of the rapid growth in the number of cloud services. When evaluating cloud service functioning using several performance measures, the issue becomes more complex and non-trivial. It is therefore quite difficult and crucial for consumers to choose the best cloud service. The user's choices are provided in a quantifiable manner in the current (...)
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  46. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Second volume.Takaaki Fujita & Florentin Smarandache - 2024
    The second volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents a deep exploration of the progress in uncertain combinatorics through innovative methodologies like graphization, hyperization, and uncertainization. This volume integrates foundational concepts from fuzzy, neutrosophic, soft, and rough set theory, among others, to further advance the field. Combinatorics and set theory, two central pillars of mathematics, focus on counting, arrangement, and the study of collections under defined rules. Combinatorics excels (...)
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  47.  86
    Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Third volume.Florentin Smarandache - 2024
    The third volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents an in-depth exploration of the cutting-edge developments in uncertain combinatorics and set theory. This comprehensive collection highlights innovative methodologies such as graphization, hyperization, and uncertainization, which enhance combinatorics by incorporating foundational concepts from fuzzy, neutrosophic, soft, and rough set theories. These advancements open new mathematical horizons, offering novel approaches to managing uncertainty within complex systems. Combinatorics, a discipline focused on (...)
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  48. 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 (...)
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  49.  86
    Algebraic Structures in the Universe of Neutrosophic: Analysis with Innovative Algorithmic Approaches.Florentin Smarandache, Derya Bakbak, Vakkas Uluçay, Abdullah Kargın & Necmiye Merve Şahin (eds.) - 2024
    Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, (...)
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  50. 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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