SMARANDACHE-GALOIS FIELDS

In this paper we study the notion of Smarandache-Galois fields and homomorphism and the Smarandache quotient ring. Galois fields are nothing but fields having only a finite number of elements. We also propose some interesting problems

SMARANDACHE LOOPS

In this paper we study the notion of Smarandache loops. We obtain some interesting results about them. The notion of Smarandache semigroups homomorphism is studied as well in this paper. Using the definition of homomorphism of Smarandache semigroups we give the classical theorem of Cayley for Smarandache semigroups. We also analyze the Smarandache loop homomorphism. We pose the problem of finding a Cayley theorem for Smarandache loops

Interval Algebraic Bistructures

This book has four chapters. In the first chapter interval bistructures (biinterval structures) such as interval bisemigroup, interval bigroupoid, interval bigroup and interval biloops are introduced. Throughout this book we work only with the intervals of the form [0, a] where a \in Zn or Z+ \cup {0} or R+ \cup {0} or Q+ \cup {0} unless otherwise specified. Also interval bistructures of the form interval loop-group, interval groupgroupoid so on are introduced and studied. In chapter two n-interval structures are introduced. n-interval groupoids, n-interval semigroups, n-interval loops and so on are introduced and analysed. Using these notions n-interval mixed algebraic structure are defined and described. Some probable applications are discussed. Only in due course of time several applications would be evolved by researchers as per their need. The final chapter suggests around 295 problems of which some are simple exercises, some are difficult and some of them are research problems.Comment: 208 page

Neutrosophic Rings

This book has four chapters. Chapter one is introductory in nature, for it recalls some basic definitions essential to make the book a self-contained one. Chapter two, introduces for the first time the new notion of neutrosophic rings and some special neutrosophic rings like neutrosophic ring of matrix and neutrosophic polynomial rings. Chapter three gives some new classes of neutrosophic rings like group neutrosophic rings,neutrosophic group neutrosophic rings, semigroup neutrosophic rings, S-semigroup neutrosophic rings which can be realized as a type of extension of group rings or generalization of group rings. Study of these structures will throw light on the research on the algebraic structure of group rings. Chapter four is entirely devoted to the problems on this new topic, which is an added attraction to researchers. A salient feature of this book is that it gives 246 problems in Chapter four. Some of the problems are direct and simple, some little difficult and some can be taken up as a research problem.Comment: 154 page

Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists

This book introduces the concept of fuzzy super matrices and operations on them. This book will be highly useful to social scientists who wish to work with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy Relational Maps, Bidirectional Associative Memories and Fuzzy Associative Memories are defined here. The authors introduce 13 multi-expert models using the notion of fuzzy supermatrices. These models are described with illustrative examples. This book has three chapters. In the first chaper, the basic concepts about super matrices and fuzzy super matrices are recalled. Chapter two introduces the notion of fuzzy super matrices adn their properties. The final chapter introduces many super fuzzy multi expert models.Comment: 280 page

Fuzzy and Neutrosophic Analysis of Periyar's views on Untouchability

This book is organized into four chapters. In Chapter One we just introduce the basic Fuzzy and Neutrosophic tools used in the analysis of the social evil of Untouchability. Since the notion of caste is based on themind, it is appropriate to use Fuzzy and Neutrosophic theory. In Chapter Two we use the opinion of several experts to analyze the various aspects of untouchability. Here, we use the tools that have been described in Chapter One. Fuzzy Directed Graphs and Neutrosophic Directed Graphs of these Fuzzy and Neutrosophic models happen to be very dense. We have represented 16 such graphs in this book. In Chapter Three we give a brief introduction about the life and struggle of Periyar. The fourth and concluding chapter gives observations drawn from our mathematical results based on the Fuzzy and Neutrosophic analysis.Comment: 385 pages, 16 figure