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Applications of Bimatrices to some Fuzzy and Neutrosophic Models

Research paper by WB Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral

Indexed on: 04 Sep '05Published on: 04 Sep '05Published in: Mathematics - General Mathematics



Abstract

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.