## Set Linear Algebra and Set Fuzzy Linear Algebra

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Kandasamy, W. B. Vasantha

Smarandache, Florentin

Ilanthenral, K.

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In this book, the authors define the new notion of set vector spaces which is
the most generalized form of vector spaces. Set vector spaces make use of the
least number of algebraic operations, therefore, even a non-mathematician is
comfortable working with it. It is with the passage of time, that we can think
of set linear algebras as a paradigm shift from linear algebras. Here, the
authors have also given the fuzzy parallels of these new classes of set linear
algebras.
This book is divided into seven chapters. The first chapter briefly recalls
some of the basic concepts in order to make this book self-contained. Chapter
two introduces the notion of set vector spaces which is the most generalized
concept of vector spaces. Set vector spaces lends itself to define new classes
of vector spaces like semigroup vector spaces and group vector spaces. These
are also generalization of vector spaces. The fuzzy analogue of these concepts
are given in Chapter three. In Chapter four, set vector spaces are generalized
to biset bivector spaces and not set vector spaces. This is done taking into
account the advanced information technology age in which we live. As
mathematicians, we have to realize that our computer-dominated world needs
special types of sets and algebraic structures. Set n-vector spaces and their
generalizations are carried out in Chapter five. Fuzzy n-set vector spaces are
introduced in the sixth chapter. The seventh chapter suggests more than three
hundred problems.

Comment: 344 pages

Comment: 344 pages

##### Keywords

Mathematics - General Mathematics, 04-xx, 11-xx