Basic Neutrosophic Algebraic Structures and their Application to Fuzzy and Neutrosophic Models

TL;DR

This paper introduces neutrosophic algebraic structures and graphs, extending fuzzy models to incorporate indeterminacy, and demonstrates their application in neutrosophic cognitive and relational maps.

Contribution

It develops new neutrosophic algebraic structures and graph models, bridging fuzzy theory with neutrosophy to handle uncertainty and indeterminacy in complex systems.

Findings

Introduction of neutrosophic algebraic structures

Development of neutrosophic graph theory and models

Application to fuzzy and neutrosophic cognitive maps

Abstract

The involvement of uncertainty of varying degrees when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate. For the past two or more decades, Fuzzy Theory has become the potent tool to study and analyze uncertainty involved in all problems. But, many real-world problems also abound with the concept of indeterminacy. In this book, the new, powerful tool of neutrosophy that deals with indeterminacy is utilized. Innovative neutrosophic models are described. The theory of neutrosophic graphs is introduced and applied to fuzzy and neutrosophic models. This book is organized into four chapters. In Chapter One we introduce some of the basic neutrosophic algebraic structures essential for the further development of the other chapters. Chapter Two recalls basic graph theory definitions and results which has interested us and for which we give the neutrosophic analogues. In this chapter we give the application of graphs in fuzzy models. An entire section is devoted for this purpose. Chapter Three introduces many new neutrosophic concepts in graphs and applies it to the case of neutrosophic cognitive maps and neutrosophic relational maps. The last section of this chapter clearly illustrates how the neutrosophic graphs are utilized in the neutrosophic models. The final chapter gives some problems about neutrosophic graphs which will make one understand this new subject.