Fuzzy Relational Equations and Neutrosophic Relational Equations

TL;DR

This paper introduces Neutrosophic Relational Equations (NREs), extending fuzzy relational equations to handle indeterminacy in complex problems across various fields.

Contribution

It develops the concept of NREs, enhancing fuzzy relational models to analyze problems involving indeterminacy, with practical applications.

Findings

NREs can model problems with indeterminacy effectively.

NREs extend the applicability of FREs to new problem domains.

Practical applications demonstrate NREs' effectiveness.

Abstract

The introduction of Fuzzy Relational Equations (FREs) has made problems that were unsolvable using algebraic linear equations into solvable ones. FREs have been applied to problemsin medicine, industry, transportation and all types of social problems where the data is an unsupervised one. Yet, FREs lack the capacity to tackle problems where an element of indeterminacy is involved. This book develops the new concept of Neutrosophic Relational Equations (NREs) that have the capacity to analyze problems with indeterminacy. Here, earlier models on FREs are analyzed and new NRE models, with practical applications, are presented.