Smarandache Fuzzy Algebra

TL;DR

This paper explores Smarandache Fuzzy Algebra, extending fuzzy algebraic structures to better model real-world uncertainties, and introduces new concepts across various fuzzy algebraic systems.

Contribution

It provides a comprehensive analysis of eleven fuzzy algebraic concepts and introduces new definitions and properties within Smarandache Fuzzy Algebra.

Findings

Analysis of eleven fuzzy algebraic concepts

Introduction of new fuzzy algebraic definitions

Extensive properties of fuzzy algebra structures

Abstract

The author studies the Smarandache Fuzzy Algebra, which, like its predecessor Fuzzy Algebra, arose from the need to define structures that were more compatible with the real world where the grey areas mattered, not only black or white. This book has seven chapters, which are divided into two parts. Part I contains the first chapter, and Part II encloses the remaining six chapters. In the first chapter (which also forms the first part), which is subdivided into twelve sections, we deal with eleven distinct fuzzy algebraic concepts and in the concluding section list the miscellaneous properties of fuzzy algebra. The eleven fuzzy algebraic concepts which we analyze are fuzzy sets, fuzzy subgroups, fuzzy sub-bigroups, fuzzy rings, fuzzy birings, fuzzy fields, fuzzy semirings, fuzzy near-rings, fuzzy vector spaces, fuzzy semigroups and fuzzy half-groupoids. The results used in these sections are extensive and we have succeeded in presenting new concepts defined by several researchers.