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...introduction of neutrosophic theory has put forth a significant concept by giving representation to indeterminates. Uncertainty or indeterminacy happen to be one of the major factors in almost all real-world problems. When un...

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... 1 Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models W. B. Vasantha Kandasamy Departm... ...SBN: 1-931233-87-X Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS P r e f a c e ... ...America 3 CONTENTS P r e f a c e 5 Chapter One INTRODUCTION TO SOME NEUTROSOPHIC ALGEBRAIC STRUCTURES 1.1 Neutrosoph... ... CONTENTS P r e f a c e 5 Chapter One INTRODUCTION TO SOME NEUTROSOPHIC ALGEBRAIC STRUCTURES 1.1 Neutrosophic Fields 7 ... ... SUGGESTED PROBLEMS 127 BIBLIOGRAPHY 133 INDEX 141 ABOUT THE AUTHORS 149 5 Preface Study of neutrosophic alge... ...Preface Study of neutrosophic algebraic structures is very recent. The introduction of neutrosophic theory has put forth a significant concept ... ...ory. In 1847 Kirchoff developed the theory of trees, in order to solve the system of simultaneous linear equations, which give the current in each ... ...ing them if any, otherwise d (u, v) = ∞. In a connected graph distance is a metric i.e., for all points u, v and w 1. d(u, v) ≥ 0 with d (u, v) ... ...tion of NCM to this model. Figure 3.7.13 describes the Business performance metrics given by [30]. It is suggested that in the NCM model in which ...

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... ISBN: 1-931233-86-1 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS D e d i c a t i o n ... ...inear optimization problem with FRE constraints 48 1.7 Method of solution to fuzzy relation equations in a complete Brouwerian lattice 55 ... ... with fuzzy relation equation constraints 57 1.9 Neural fuzzy relational system with a new learning algorithm 63 1.10 Unattainable Sol... ...zy relational equations 70 1.12 FRE with defuzzification algorithm for the largest solution 75 1.13 Solvability and Unique solvability ... ...zy sets 146 1.26 Solvability criteria for systems of FRE 156 1.27 Infinite FRE to a complete browerian lattices 162 1.28 Semantics of implication o... ...ogous properties. This chapter has six sections which are solely devoted to the introduction of several neutrosophic concepts which are essential fo... ... a fuzzy relational equation. We use the notations in [46]. Let X be a compact metric space. We denote by 2 X the collection of all subsets of X, ... ...note by ζ (X) the collection of all closed subsets of X. Let ρ be the Hausdorff metric on 2 X . Then it is well-known [48] that (ζ(X), ρ) is a compa... ...ossible Figure 1.22.2 0 1 M M ~ (d) – M ~ (d) + Figure 1.22.3 135 The introduction of the smooth derivative by the authors have improved t...

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...The aim of this book is two fold. At the outset the book gives most of the available literature about Fuzzy Relational Equations (FREs) and its properties for there is no book that solely caters to FREs and its applications. ...

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... ISBN: 1-931233-86-1 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS D e d i c a t i o n ... ...inear optimization problem with FRE constraints 48 1.7 Method of solution to fuzzy relation equations in a complete Brouwerian lattice 55 ... ... with fuzzy relation equation constraints 57 1.9 Neural fuzzy relational system with a new learning algorithm 63 1.10 Unattainable Sol... ...zy relational equations 70 1.12 FRE with defuzzification algorithm for the largest solution 75 1.13 Solvability and Unique solvability ... ...zy sets 146 1.26 Solvability criteria for systems of FRE 156 1.27 Infinite FRE to a complete browerian lattices 162 1.28 Semantics of implication o... ...ogous properties. This chapter has six sections which are solely devoted to the introduction of several neutrosophic concepts which are essential fo... ... a fuzzy relational equation. We use the notations in [46]. Let X be a compact metric space. We denote by 2 X the collection of all subsets of X, ... ...note by ζ (X) the collection of all closed subsets of X. Let ρ be the Hausdorff metric on 2 X . Then it is well-known [48] that (ζ(X), ρ) is a compa... ...ossible Figure 1.22.2 0 1 M M ~ (d) – M ~ (d) + Figure 1.22.3 135 The introduction of the smooth derivative by the authors have improved t...

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...In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itself with the capability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of thi...

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...OPHIC COGNITIVE MAPS XIQUAN Phoenix 2003 CARE OF THE AIDS INFECTED PERSONS CREATION OF AWARENESS ABOUT AIDS PREVENTION... ...nm.edu Xiquan Phoenix 2003 2 The picture on the cover is a neutrosophic directed graph of the Neutrosoph... ... AND NEUTROSOPHIC RELATIONAL MAPS – PROPERTIES AND APPLICATIONS 2.1 An introduction to neutrosophy 123 2.2 Some basic neutrosophic structures 12... ...PHIC RELATIONAL MAPS – PROPERTIES AND APPLICATIONS 2.1 An introduction to neutrosophy 123 2.2 Some basic neutrosophic structures 125 2.3 Some b... ...ns of NRMs, Combined NRMs and the Introduction of linked NRMs 174 2.10 Neutrosophic Relational Maps versus N... ... DEDICATED TO ALL THE VOICES OF DISSENT 5 PREFACE In a world of chaotic alig... ...o reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Ou... ...hich tackles the complexity and allows the analysis and simulation of the metrics. The FCM proposed by Kardaras and Mentzas is called Impact Analy... ....) and polarity (positive or negative) of the impact of selected business metrics from business areas such as competition, customers, products, supp...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and surv...

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.... . . . 27 Some Remarks on Fuzzy N-Normed Spaces BY SAYED ELAGAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 σ-Coloring of the Monohedral Tiling BY M. E. BASHER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 The Forcing Domination Number of Hamiltonian Cubic Graphs BY H.ABDOLLAHZADEH AHANGAR AND PUSHPALATHA L. . . . . . ....

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and surv...

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...§1. Why is the WORLD a Combinatorial One? The multiplicity of the WORLD results in modern sciences overlap and hybrid, also implies its combinatorial structure. To see more clear, we present two meaningful proverbs following. Proverb ...

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...Contents Combinatorial Fields - An Introduction BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .01 A Spacetime Geodesics of the Schwarzschild Space and Its Deformation Retract BY H. RAFAT. . . . . . . . . . . . . . . . . . ...

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...g Progress in Physics template. This template can be downloaded from Progress in Physics home page http://www.geocities.com/ptep_online. Abstract and the necessary information about author(s) should be included into the papers. To submit a paper, mail the file(s) to Chief Editor. All submitted papers should be as brief as possible. Short articles are preferable. All that h...

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...nti-nucleons, while their life span was very short, no more than 10-20sec. Stable states of unmatter can be built on quarks and anti-quarks: applying the unmatter principle here it is obtained a quantum chromodynamics formula that gives many combinations of unmatter built on quarks and anti-quarks....

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...ics PROGRESSINPHYSICS A quarterly issue scientifc journal, registered with the Library of Congress (DC). This journal is peer reviewed and included in... ...he Library of Congress (DC). This journal is peer reviewed and included in the abstracting and indexing coverage of: Mathematical Reviews and MathSciN... ...m Electronic version of this journal: http://www.geocities.com/ptep_online To order printed issues of this journal, con- tact the Editor in Chief. Chi... .... Authors of articles published in Progress in Physics retain their rights to use their own articles in any other publications and in any way they see... ...nnot of itself be used directly to determine features of the feld from its metric. The appropriate quantities on the metric for the gravitational feld... ... gravitational feld, namely, the proper radius and the curvature radius. 1 Introduction The variabler has given rise to much confusion. In the con- ve... ... to much confusion. In the con- ventional analysis, based upon the Hilbert metric, which is almost invariably and incorrectly called the “Schwarzschil... ...of ther-parameter of a certain spacetime event depends upon the coordinate system chosen. However, the proper radiusR p (D(r)) and the curvature radiu... ...orld- geometry, in other words. This is a way to geometrize phys- ics. The introduction of his artifcial postulates became only of historical concern ...

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...A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interesting. Its function and role in mathematics are widely accepted by mathematicians today. On the last century, many works are concentrated on the com...

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...METRIES American Research Press Rehoboth, NM 2005 Linfan MAO Institute of Systems Science Academy of Mathematics and Systems Chinese Academy of Scien... ..., SURFACES AND SMARANDACHE GEOMETRIES Partially post-doctoral research for the Chinese Academy of Sciences American Research Press Rehoboth, NM 2005 ... ...nfan Mao Rehoboth, Box 141 NM 87322, USA Many books can be downloaded from the following E-Library of Science: http://www.gallup.unm.edu/˜ smarandache... ...he journals frequently today. All of those is surveyed in Liu’s book [33]. To deter- mine the embedding of a graph on surfaces, including coloring a m... ...as a kind of the decomposition of surfaces, should be given more attention to its role in surfaces theory, such as the Riemann surfaces, Klein surface... .... Thenumbersη O (Γ),η N (Γ)andη L (Γ)of non-equivalentembeddingsof anasym- metric underlying graph Γ are respective η O (Γ) = v∈V(Γ) (ρ(v)−1)!, η L ... ...iemann2-manifold. ARiemannn-manifold(M,g) is a n-manifold M with a Riemann metric g. Many important results in Riemann surfaces are generalized to Rie... ...rences 110 Discrete Math.248(2002),93-108. [32] L.Kuciuk and M.Antholy, An Introduction to Smarandache Geometries, Math- ematics Magazine, Aurora, Can... ... Com- puting, Vol.17(2005), 25-38. [52] W.S.Massey, Algebraic topology: an introduction, Springer-Verlag,New York, etc.(1977). [53] B.MoharandC.Thomas...

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...Research papers presented in this collection manifest only a few of many possible applications of neutrosophic logics to theoretical physics. Most of these applications target the theory of relativity and quantum physics, but other sections of physics are also possible to be considered....

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...We apply the S-denying procedure to signature conditions in a four-dimensional pseudo-Riemannian space — i. e. we change one (or even all) of the conditions to be partially true and partially false. We obtain five kinds of expanded sp...

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...Preface, by Dmitri Rabounski ............................5 General Relativity, Gravitation, and Cosmology................6 S-Denying of the Signature Conditions Expands General Relativity’s Space, by Dmitri Rabounski, Florentin Smarandache, Larissa Borissova, Progress in Physics, 13-19, Vol. 3, 2006.......7 Positive, Neutral, and Negative Mass-Charges in G...

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...Applications demonstrate the power of the DSmT framework. In this third Volume, DSmT is applied to the entire spectrum of the Information Fusion that would interest any reader in data, sensor, information, and mathematical fusion topics. Highlighted ...

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...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 fre...