Some Aspects of Fuzzy Algebraic Structures

This book deals with a comprehensive study of fuzzy algebraic structures. The objective of this book is to investigate fuzzy aspects of some algebraic structures. We attempt to study algebraic structures like modules, rings, hemirings in fuzzy and intuitionistic fuzzy setting. Small submodules of modules play a vital role in structure theorem. Study of fuzzy aspects of small submodules motivates us to study the concepts like fuzzy small epimorphism, fuzzy co-essential extension, Jacobson L-radical, fuzzy hollow submodules. The introduction of fuzzy point and neighbourhood relations leads to a new direction of research on fuzzy algebraic structure generalizing the conventional notion of studies. t - norms play a crucial role in several areas of mathematics and computer science. These studies motivate us to define fuzzy submodule with respect a t-norm which is based on neighbourhood relation. As an immediate consequence of degree of belongs to in fuzzy set, degree of not belongs to arises. This concept generalizes the concept of fuzzy set to intuitionistic fuzzy sets. These concepts inspire us to study about fuzzy modules, fuzzy rings and ideals, fuzzy hemirings intuitionistically.