## Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models

**Authors:** W. B. Vasantha Kandasamy, Florentin Smarandache

Study of neutrosophic algebraic structures is very recent. The
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 uncertainty is modeled we use fuzzy
theory and when indeterminacy is involved we use neutrosophic
theory. Most of the fuzzy models which deal with the analysis and
study of unsupervised data make use of the directed graphs or
bipartite graphs. Thus the use of graphs has become inevitable in
fuzzy models. The neutrosophic models are fuzzy models that
permit the factor of indeterminacy. It also plays a significant role,
and utilizes the concept of neutrosophic graphs. Thus
neutrosophic graphs and neutrosophic bipartite graphs plays the
role of representing the neutrosophic models. Thus to construct
the neutrosophic graphs one needs some of the neutrosophic
algebraic structures viz. neutrosophic fields, neutrosophic vector
spaces and neutrosophic matrices. So we for the first time
introduce and study these concepts. As our analysis in this book is
application of neutrosophic algebraic structure we found it deem
fit to first introduce and study neutrosophic graphs and their
applications to neutrosophic models.

**Comments:** 149 pages

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### Submission history

[v1] 10 Mar 2010

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