The Semiring Properties of Fuzzy Algebras

TL;DR

This paper investigates the connection between fuzzy algebras and semirings, introducing a new class of fuzzy structures similar to semirings and analyzing their algebraic properties and homomorphisms.

Contribution

It defines a new class of fuzzy structures akin to semirings and explores their algebraic properties, including partial ordering and homomorphism characteristics.

Findings

Partial ordering on fuzzy algebras established

Zero-sum free property of fuzzy semirings demonstrated

Semiring properties of homomorphisms mapped to fuzzy structures

Abstract

The relationship between fuzzy algebras and semirings is explored with fuzzy algebra operators replacing the arithmetic operators of semirings. A new class of fuzzy structures which are similar to semirings is defined. Results of partial ordering on fuzzy algebras are shown. The zero-sum free property of semirings on fuzzy structures is shown. The semiring property of homomorphism is mapped to fuzzy structures and results like order- and operator-preservation are described.