... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC... ... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATION... ...600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New M... ...dia e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gal... ...Mysore, Karnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by... ...rnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Meena Kan... ...ena Kandasamy. Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-86-1 ... ...re Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps (http://gallup.unm.edu/~smarandache/NCMs.pdf) and Analysis of Social Aspects of Migrant Labo... ...out his help this book would not have been possible. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE 9 Chapter One FUZZY RELATIONAL...

...36, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexic... ... e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup,... ...ity, Atlanta, GA 30302, USA Copyright 2005 by W. B. Vasantha Kandasamy, Florentin Smarandache and K. Ilanthenral Layout by Kama Kandasamy.... ...ta, GA 30302, USA Copyright 2005 by W. B. Vasantha Kandasamy, Florentin Smarandache and K. Ilanthenral Layout by Kama Kandasamy. Cover de... ...an be downloaded from this E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1931233-95-0 HEXIS Pu... ...of bialgebraic structures led to the invention of new notions like birings, Smarandache birings, bivector spaces, linear bialgebra, bigroupoids, bis... ... and Kama Kandasamy for formatting this book. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K. ILANTHENRAL 7 Chapter One BIMATRI... ...Kandasamy for formatting this book. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K. ILANTHENRAL 7 Chapter One BIMATRICES AND ... ...Linear Spaces, Prentice-Hall, Englewood Cliffs, NJ, 1961. 29. SMARANDACHE, Florentin, Collected Papers II, University of Kishinev Press, Kishinev, ...

.... vector spaces) form an inseparable component of each other. The study of bialgebraic structures led to the invention of new notions like birings, Smarandache birings, bivector spaces, linear bialgebra, bigroupoids, bisemigroups, etc. But most of these are abstract algebraic concepts except, the bisemigroup being used in the construction of biautomatons. So we felt it...

This book contains a collection of poems compiled by the author Florentin Smarandache.

...0036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mex... ...a e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallu... ..., Alaska, USA. Copyright 2005 by Hexis, W. B. Vasantha Kandasamy, Florentin Smarandache and K.Ilanthenral Layout by Kama Kandas... ...SA. Copyright 2005 by Hexis, W. B. Vasantha Kandasamy, Florentin Smarandache and K.Ilanthenral Layout by Kama Kandasamy. Cover... ...wnloaded from the following E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1931233-98-5 Stand... ...rt Kosko, the father of Fuzzy Cognitive Maps. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K.ILANTHENRAL 7 Chapter One ... ...the father of Fuzzy Cognitive Maps. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K.ILANTHENRAL 7 Chapter One BASIC C... ...loq. Pub., 24, Amer. Math. Soc., 1939. 4. Allen, J., S. Bhattacharya and F. Smarandache. Fuzziness and Funds allocation in Portfolio Optimization.... ...eutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics, Florentin Smarandache editor, Xiquan, Phoenix, ISBN: 1-931233- 55-1, 1...

...6, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico... ...e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, ... ...sore, Karnataka, India. Copyright 2005 by W. B. Vasantha Kandasamy, Florentin Smarandache and K. Ilanthenral Layout by Kama Kandasamy. ... ...ataka, India. Copyright 2005 by W. B. Vasantha Kandasamy, Florentin Smarandache and K. Ilanthenral Layout by Kama Kandasamy. Cover des... ...andasamy. Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1931233-97-7 ... ...LICATION 4.1 Some basic neutrosophic algebraic structures 131 4.2 Smarandache neutrosophic linear bialgebra 170 4.3 Smarandache representa... ...trosophic linear bialgebra 170 4.3 Smarandache representation of finite Smarandache bisemigroup 174 4.4 Smarandache... ...ent in every manner made this book possible. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K. ILANTHENRAL 7 Chapter One I... ...c linear bialgebra. 132 The notion of neutrosophic logic was created by Florentin Smarandache which is an extension / combination of the fuzzy lo...

...to applications. With the recent introduction of bimatrices (2005) we have ventured in this book to introduce new concepts like linear bialgebra and Smarandache neutrosophic linear bialgebra and also give the applications of these algebraic structures....

... Chief Editor Dmitri Rabounski rabounski@yahoo.com Associate Editors Prof. Florentin Smarandache smarand@unm.edu Dr. Larissa Borissova lborissova@yaho... ...tor Dmitri Rabounski rabounski@yahoo.com Associate Editors Prof. Florentin Smarandache smarand@unm.edu Dr. Larissa Borissova lborissova@yahoo.com Step... ...downloaded free from the E-library of Science: http://www.gallup.unm.edu/ smarandache ISSN: 1555-5534 (print) ISSN: 1555-5615 (online) Standard Addre... ...s. . . . . . . . . . . . . . . . . . . . 92 D. Rabounski, L. Borissova, F. Smarandache Quantum Causality Threshold in the General Theory of Relativity... ...ll, C. M. Klinger Bootstrap Universe from Self-Referential Noise. . 108 F. Smarandache Verifying Unmatter by Experiments, More Types of Unmatter, and ... ...d in the General Theory of Relativity Dmitri Rabounski, Larissa Borissova, Florentin Smarandache Dept. of Mathematics, University of New Mexico, 200 C... ...eneral Theory of Relativity Dmitri Rabounski, Larissa Borissova, Florentin Smarandache Dept. of Mathematics, University of New Mexico, 200 College Roa... ... Experiments, More Types of Unmatter, and a Quantum Chromodynamics Formula Florentin Smarandache Dept. of Mathematics, University of New Mexico, 200 C...

...n the Number Theory .82 -- Contributii la Studiul unor Functii §i Conjecturi in Teoria Numerelor .85 -- "The Function that You Bear its Name" .112 -- Smarandache Type Functions Obtained by Duality .113 -- Func!;ii Analitice .129 -- Funct;ii Prime §i Coprime .137 -- Asupra unor Conjecturi §i Probleme Nerezolvate Referitoare la 0 Funct;ie in Teoria l'\umerelor 138 -- K-Divis...

...ivity, 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 General Relativity, by Larissa Borissova and Florentin Smarandache, Progress in Phy...

...me 26 2.7. Magic square problem 27 2.8. Palindromic number and iteration 27 2.9. Non-Euclidean geometry by giving up its fifth postulate 28 2.10. Smarandache Geometry and Degree of Negation in Geometries 28 2.11. Non-Archimedean triangle theorem 33 2.12. The cubic Diophantine equation 33 2.13. Multispaces and applications in physics 34 3 Unsolved Problems in Astrop...

.......................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin Smarandache..15 2. On Recent Discovery of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in A...

.......................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin Smarandache..15 2. On Recent Discovery of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in A...

...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. ...