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Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists

By: Florentin Smarandache
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Extenics in Higher Dimensions

By: Florentin Smarandache

... Finite Interval from one dimension (1D) to 2D, 3D, and in general n-D spaces. Then I used the Extenics, together with Victor Vlădăreanu, Mihai Liviu Smarandache, Tudor Păroiu, and Ştefan Vlăduţescu, in 2D and 3D spaces in technology, philosophy, and information theory....

...Contribution to Extenics (Preface by Florentin Smarandache): 4 1. Generalizations of the Distance and Dependent Function in Extenics to 2D, 3D, and n-D, by Florentin Smarandache: 22 2. Applications of Extenics to 2D-Space and 3D-Space, by Florentin Smarandache...

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Rank Distance Bicodes and Their Generalization

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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N-Linear Algebra of Type 2

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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N-Linear Algebra of Type 1 and Its Applications

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Non-Associative Linear Algebras

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Non Associative Algebraic Structures Using Finite Complex Numbers

By: Florentin Smarandache; W. B. Vasantha Kandasamy

...THEOREM 2.1: Let G = {C(Zn), *, (t, u); t, u ∈ Zn} be a complex modulo integer groupoid. If H ⊆ G is such that H is a Smarandache modulo integer subgroupoid, then G is a Smarandache complex modulo integer groupoid. But every subgroupoid of G need not be a Smarandache complex modulo interger subgroupoid even if G is a Smarandache groupoid. ...

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New Classes of Neutrosophic Linear Algebras

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Neutrosophic Rings

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Neutrosophic Interval Bialgebraic Structures

By: Florentin Smarandache; W. B. Vasantha Kandasamy

...roups or neutrosophic biinterval semigroups. We derive results pertaining to them. The new notion of quasi bisubsemigroups and ideals are introduced. Smarandache interval neutrosophic bisemigroups are also introduced and analysed. Also notions like neutrosophic interval bigroups and their substructures are studied in section two of this chapter. Neutrosophic interval bigro...

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Neutrosophic Bilinear Algebras and Their Generalizations

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Natural Product Xn On Matrices

By: Florentin Smarandache; W. B. Vasantha Kandasamy

...t defined on column matrices, m * n (m ≠ n) matrices. This extension is the same in case of row matrices. We make use of the notion of semigroups and Smarandache semigroups. Also the notion of semirings, Smarandache semirings, semi vector spaces and semifields are used....

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Groups as Graphs

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Auxiliary Information and A Priori Values in Construction of Improved Estimators

By: Florentin Smarandache; Rajesh Singh
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Dual Numbers

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Exploring the Extension of Natural Operations on Intervals, Matrices and Complex Numbers

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Finite Neutrosophic Complex Numbers

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry

By: Florentin Smarandache; M L. Perez, Editor

...Florentin Smarandache, an American mathematician of Romanian descent has generated a vast variety of mathematical problems. Some problems are easy, others medium, but many are interesting or unsolved and this is the reason wh...

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Quantization and Discretization at Large Scales

By: Florentin Smarandache, Editor; V. Christianto, Editor

...cs, and therefore we can think that the quantization of orbit distances can be caused by superfluid helium quantization. This issue is explored by F. Smarandache and V. Christianto. Moreover, F. Smarandache also discusses possible new era of research that is pertaining to superluminal physics and instantaneous physics. Ion Patrascu and D. Rabounski discuss superluminality ...

...RN. (I. Patrascu) Progress in Physics Vol.4, 2011...................127 Superluminal physics and Instantaneous physics as new trends in research (F. Smarandache) ...................129 The Hypergeometrical Universe: Cosmology and Standard Model. (M.A. Pereira). Jan. 2012...................134 On astrometric data and time-varying sun earth distance in light of Carmeli me...

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Research on Number Theory and Smarandache Notions : Proceedings of the Fifth International Conference on Number Theory and Smarandache Notions

By: Florentin Smarandache; Zhang Wenpeng, Editor

...This book contains 23 papers, most of which were written by participants to the fifth International Conference on Number Theory and Smarandache Notions held in Shangluo University, China, in March, 2009. In this Conference, several professors gave a talk on Smarandache Notions and many participants lectured on them both extensively and intensively. All th...

...J. Wang : An equation related to the Smarandache power function 1 X. Lu and J. Hu : On the F.Smarandache 3n-digital sequence 5 B. Cheng : An equation involving the Smarandache double factorial function and Euler function 8 A. A. K. Majumdar : S-perfect and c...

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Innovative Uses of Matrices

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Fuzzy Analysis of School Dropouts and Their Life After

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Erasure Techniques in MRD Codes

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Artificial Intelligence and Responsive Optimization (Second Edition)

By: Florentin Smarandache; M. Khoshnevisan
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Vedic Mathematics : 'Vedic' or 'Mathematics' : A Fuzzy & Neutrosophic Analysis

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Neutrality and Many-Valued Logics

By: Florentin Smarandache; Andrew Schumann
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Quantization in Astrophysics, Brownian Motion, and Supersymmetry

By: Florentin Smarandache, Editor; V. Christianto, Editor
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Fuzzy Linguistic Topological Spaces

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Cultural Advantages for Cities : An Alternative for Developing Countries

By: Florentin Smarandache; V. Christianto
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Neutrosophic Book Series : Neutrosophic Methods in General Relativity : Volume 10

By: Florentin Smarandache; Dmitri Rabounski

...c to the General Theory of Relativity to obtain a generalisation of Einstein’s four dimensional pseudo-Riemannian differentiable manifold in terms of Smarandache Geometry (Smarandache manifolds), by which new classes of relativistic particles and non-quantum teleportation are developed....

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Introduction to N-Adaptive Fuzzy Models to Analyze Public Opinion on Aids

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Fuzzy Interval Matrices, Neutrosophic Interval Matrices and Their Applications

By: Florentin Smarandache; W. B. Vasantha Kandasamy
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Multi-Valued Logic, Neutrosophy, and Schrödinger Equation

By: Florentin Smarandache; V. Christianto
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Advances and Applications of DSmT for Information Fusion (Collected Works) : Volume 3

By: Florentin Smarandache; Jean Dezert

...Part I Advances on DSmT 1 Chapter 1 An introduction to DSmT 3 by J. Dezert and F. Smarandache 1.1 Introduction . . . . . . . . . . 4 1.2 Foundations of DSmT . . . . . . . . . 4 1.2.1 The power set, hyper-power set and super-power set . . 6 1.2.2 Notion of free and hybrid DSm models . . . . 18 1.2.3 Ge...

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Advances and Applications of DSmT for Information Fusion (Collected Works) : Volume 2

By: Florentin Smarandache; Jean Dezert

...This second book devoted on advances and applications of Dezert-Smarandache Theory (DSmT) for information fusion collects recent papers from different researchers working in engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical investigation...

...Preamble iii Prefaces v Part I Advances on DSmT 1 Chapter 1 Proportional Conflict Redistribution Rules for Information Fusion 3 by Florentin Smarandache and Jean Dezert 1.1 Introduction . . . . . . . . . . . 3 1.2 The principal rules of combination . . . . . . . 6 1.2.1 Notion of total and partial conflicting masses . . . . . 6 1.2.2 The conjunctive ...

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Advances and Applications of DSmT for Information Fusion (Collected Works) : Volume 1

By: Florentin Smarandache; Jean Dezert

...n the information provided by the sources is both uncertain and (highly) conflicting. This approach, known in literature as DSmT (standing for Dezert-Smarandache Theory), proposes new useful rules of combinations. We gathered in this volume a presentation of DSmT from the beginning to the latest development. Part 1 of this book presents the current state-of-the-art on theo...

...57 8.2.1 Preliminary: about probability . . . 157 8.2.2 Dempster Shafer Theory . . . . 161 8.2.3 Transferable Belief Model . . . . 162 8.3 Dezert Smarandache Theory (DSmT) . . . 163 8.3.1 Dezert Smarandache model . . . . 164 8.3.2 Fusion rule . . . . . 166 8.4 Probability over logical propositions . . . . 167 8.4.1 Definition . . . . . 167 8.4.2 Property . . . . ....

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DSm Super Vector Space of Refined Labels : Volume 2

By: W. B. Vasantha Kandasamy; Florentin Smarandache
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Algebraic Structures Using Super Interval Matrices

By: W. B. Vasantha Kandasamy; Florentin Smarandache
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DSm Vector Spaces of Refined Labels

By: W. B. Vasantha Kandasamy; Florentin Smarandache
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