Applications of Bimatrices to some Fuzzy and Neutrosophic Models

WB Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral

Published:

This book, in order to generalize the two models of fuzzy cognitive maps and
neutrosophic cognitive maps, has systematically invented mathematical tools
like bimatrices, trimatrices, n-matrices, bigraphs, trigraphs and n-graphs and
describe some of its properties. These concepts are also extended
neutrosophically in this book. Using these new tools we define fuzzy cognitive
bimaps, fuzzy cognitive trimaps, fuzzy relational bimaps and fuzzy relational
trimaps which exploit the new notions of bimatrices, bigraphs, trimatrices and
trigraphs. It is worth mentioning that these can be extended to n-array models
as a simple exercise.
The main advantage of these models are:
1. Comparative study of the views stage-by-stage is possible. 2. Several
experts opinion can be compared not only at each stage but also the final
result can easily be compared. 3. Saves time and economy.
This book is organized into four chapters. The first chapter recalls the
basic concepts of bimatrices and neutrosophic bimatrices. Second chapter
introduces several new notions of graphs like bigraphs, trigraphs and their
properties. Chapter three illustrates how these new tools are used in the
construction of fuzzy cognitive bimaps, trimaps and n-maps and fuzzy relational
bimaps, trimaps and n-maps. The neutrosophic analogues of chapter 3 is carried
out in the fourth chapter. In this book, we have given nearly 95 examples to
make the reader easily follow the definitions. We have also provided 125
figures for help in easily understanding the definition and examples. We have
also given 25 real world problems as applications of Bimatrices to Fuzzy and
Neutrosophic models.