17 found
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  1. Modified Collatz conjecture or + I Conjecture for Neutrosophic Numbers.W. B. Vasantha Kandasamy, K. Ilanthenaral & Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 14:44-46.
    In this paper, a modified form of Collatz conjecture for neutrosophic numbers n ∈ (Z U I) is defined. We see for any n ∈ (Z U I) the related sequence using the formula (3a + 1) + (3b + 1)I converges to any one of the 55 elements mentioned in this paper. Using the akin formula of Collatz conjecture viz. (3a- 1) + (3b -1)I the neutrosophic numbers converges to any one of the 55 elements mentioned with appropriate modifications. (...)
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  2. Algebraic Structures using Super Interval Matrices.W. B. Vasantha Kandasamy & Florentin Smarandache - 2011 - Columbus, OH, USA: Educational Publisher.
    In this book authors for the first time introduce the notion of super interval matrices using special intervals. The advantage of using super interval matrices is that one can build only one vector space using m × n interval matrices, but in case of super interval matrices we can have several such spaces depending on the partition on the interval matrix.
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  3.  96
    DSm Super Vector Space of Refined Labels.W. B. Vasantha Kandasamy & Florentin Smarandache - 2011 - Columbus, OH, USA: Zip Publishing.
    In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m × n matrix of refined labels are introduced and studied.
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  4. Linguistic Functions.W. B. Vasantha Kandasamy, K. Ilanthenral & Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    In this book, for the first time, authors try to introduce the concept of linguistic variables as a continuum of linguistic terms/elements/words in par or similar to a real continuum. For instance, we have the linguistic variable, say the heights of people, then we place the heights in the linguistic continuum [shortest, tallest] unlike the real continuum (–∞, ∞) where both –∞ or +∞ is only a non-included symbols of the real continuum, but in case of the linguistic continuum we (...)
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  5. Linguistic Graphs and their Applications.W. B. Vasantha Kandasamy, K. Ilanthenral & Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    In this book, the authors systematically define the new notion of linguistic graphs associated with a linguistic set of a linguistic variable. We can also define the notion of directed linguistic graphs and linguistic-weighted graphs. Chapter two discusses all types of linguistic graphs, linguistic dyads, linguistic triads, linguistic wheels, complete linguistic graphs, linguistic connected graphs, disconnected linguistic graphs, linguistic components of the graphs and so on. Further, we define the notion of linguistic subgraphs of a linguistic graph. However, like usual (...)
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  6. Linguistic Geometry and its Applications.W. B. Vasantha Kandasamy, K. Ilanthenral & Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    The notion of linguistic geometry is defined in this book. It is pertinent to keep in the record that linguistic geometry differs from classical geometry. Many basic or fundamental concepts and notions of classical geometry are not true or extendable in the case of linguistic geometry. Hence, for simple illustration, facts like two distinct points in classical geometry always define a line passing through them; this is generally not true in linguistic geometry. Suppose we have two linguistic points as tall (...)
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  7. Linguistic Matrices.W. B. Vasantha Kandasamy, K. Ilanthenral & Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    In this book, the authors introduce the linguistic set associated with a linguistic variable and the structure of matrices, which they define as linguistic matrices. The authors build linguistic matrices only for those linguistic variables which yield a linguistic continuum or an ordered linguistic set. This book is organised into three chapters. The first chapter is introductory, in which we introduce all the basic concepts of linguistic variables and the associated linguistic set to make this book self-contained. Chapter two introduces (...)
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  8. Linguistic Multidimensional Spaces.W. B. Vasantha Kandasamy, Ilanthenral K. & Florentin Smarandache - 2023
    This book extends the concept of linguistic coordinate geometry using linguistic planes or semi-linguistic planes. In the case of coordinate planes, we are always guaranteed of the distance between any two points in that plane. However, in the case of linguistic and semi-linguistic planes, we can not always determine the linguistic distance between any two points. This is the first limitation of linguistic planes and semi-linguistic planes.
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  9. Linguistic Semilinear Algebras and Linguistic Semivector Spaces.W. B. Vasantha Kandasamy, K. Ilanthenral & Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    Algebraic structures on linguistic sets associated with a linguistic variable are introduced. The linguistics with single closed binary operations are only semigroups and monoids. We describe the new notion of linguistic semirings, linguistic semifields, linguistic semivector spaces and linguistic semilinear algebras defined over linguistic semifields. We also define algebraic structures on linguistic subsets of a linguistic set associated with a linguistic variable. We define the notion of linguistic subset semigroups, linguistic subset monoids and their respective substructures. We also define as (...)
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  10. Reservation for Other Backward Classes In Indian Central Government Institutions – A Study of The Role of Media Using Fuzzy Super FRM Models.W. B. Vasantha Kandasamy, Florentin Smarandache & K. Kandasamy - 2007 - Slatina, Romania: CuArt.
    The new notions of super column FRM model, super row FRM model and mixed super FRM model are introduced in this book. These three models are introduced specially to analyze the biased role of the print media on 27 percent reservation for the Other Backward Classes (OBCs) in educational institutions run by the Indian Central Government.
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  11.  96
    Superbimatrices and Their Generalizations.W. B. Vasantha Kandasamy & Florentin Smarandache - 2009 - Slatina, Romania: CuArt.
    The systematic study of supermatrices and super linear algebra has been carried out in 2008. These new algebraic structures find their applications in fuzzy models, Leontief economic models and data-storage in computers.
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  12. Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists.W. B. Vasantha Kandasamy, Florentin Smarandache & K. Amal - 2008 - Ann Arbor, MI, USA: ProQuest Information & Learning.
    The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. This book will be highly useful to social scientists who wish to (...)
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  13. Super Linear Algebra.W. B. Vasantha Kandasamy & Florentin Smarandache - 2008 - Ann Arbor, MI, USA: ProQuest Information & Learning.
    In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). Many theorems on super linear algebra and its properties are proved. Some theorems are left as exercises for the reader. These new class of super linear algebras which can be thought of as a set of linear algebras, following a stipulated condition, will find applications in several fields using computers. The authors feel that such (...)
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  14. Super Special Codes using Super Matrices.W. B. Vasantha Kandasamy, Florentin Smarandache & K. Ilanthenral - 2010 - Stockholm, Sweden: Svenska fysikarkivet.
    The new classes of super special codes are constructed in this book using the specially constructed super special vector spaces. These codes mainly use the super matrices. These codes can be realized as a special type of concatenated codes.
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  15.  93
    Special Subset Linguistic Topological Spaces.W. B. Vasantha Kandasamy, Ilanthenral K. & Florentin Smarandache - 2023 - Infinite Study.
    In this book, authors, for the first time, introduce the new notion of special subset linguistic topological spaces using linguistic square matrices. This book is organized into three chapters. Chapter One supplies the reader with the concept of ling set, ling variable, ling continuum, etc. Specific basic linguistic algebraic structures, like linguistic semigroup linguistic monoid, are introduced. Also, algebraic structures to linguistic square matrices are defined and described with examples. For the first time, non-commutative linguistic topological spaces are introduced. The (...)
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  16. Neutrosophic Super Matrices and Quasi Super Matrices.Florentin Smarandache & W. B. Vasantha Kandasamy - 2012 - Columbus, OH, USA: Zip Publishing.
    In this book authors study neutrosophic super matrices. The concept of neutrosophy or indeterminacy happens to be one the powerful tools used in applications like FCMs and NCMs where the expert seeks for a neutral solution. Thus this concept has lots of applications in fuzzy neutrosophic models like NRE, NAM etc. These concepts will also find applications in image processing where the expert seeks for a neutral solution.
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  17. Supermodular Lattices.Iqbal Unnisa, W. B. Vasantha Kandasamy & Florentin Smarandache - 2012 - Columbus, OH, USA: Educational Publisher.
    In lattice theory the two well known equational class of lattices are the distributive lattices and the modular lattices. All distributive lattices are modular however a modular lattice in general is not distributive. In this book, new classes of lattices called supermodular lattices and semi-supermodular lattices are introduced and characterized.
     
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