Soft Neutrosophic Algebraic Structures and Their Generalization

TL;DR

This paper introduces soft neutrosophic algebraic structures, combining soft set theory and neutrosophic algebra, and explores their various forms and generalizations to handle uncertainty in mathematical structures.

Contribution

It develops the concept of soft neutrosophic algebraic structures and studies their various types and generalizations, expanding the application of soft set theory in algebra.

Findings

Defined soft neutrosophic groups, semigroups, loops, and LA-semigroups.

Explored the properties and relationships of these structures.

Provided a framework for further research in soft neutrosophic algebra.

Abstract

Study of soft sets was first proposed by Molodtsov in 1999 to deal with uncertainty in a non-parametric manner. The researchers did not pay attention to soft set theory at that time but now the soft set theory has been developed in many areas of mathematics. Algebraic structures using soft set theory are very rapidly developed. In this book we developed soft neutrosophic algebraic structures by using soft sets and neutrosophic algebraic structures. In this book we study soft neutrosophic groups, soft neutrosophic semigroups, soft neutrosophic loops, soft neutrosophic LA-semigroups, and their generalizations respectively.