Journal of Applied Mathematics and Computing

, Volume 59, Issue 1–2, pp 91–127

# Rough fuzzy digraphs with application

• Fariha Zafar
Original Research

## Abstract

Rough set theory is a mathematical tool to deal with incomplete and vague information. Fuzzy set theory deals the problem of how to understand and manipulate imperfect knowledge. The aim of this research is to construct a framework for handling vague information by applying some new concept of rough fuzzy digraphs. In this research study, we present certain new aspects of rough fuzzy digraphs (RFDs) based on rough fuzzy set model. We discuss complement and $$\mu$$-complement of RFDs. We discuss the concept of isomorphisms between RFDs and the irregularity of RFDs in detail. We consider an application of our proposed hybrid decision-making method: RFDs. We also describe our hybrid decision-making method as an algorithm.

## Keywords

Rough fuzzy relation Irregular rough fuzzy digraphs Hybrid decision-making method Algorithm

## Mathematics Subject Classification

03E72 68R10 68R05

## Notes

### Acknowledgements

The authors are very thankful to the Editor and referees for their valuable comments and suggestions for improving the paper.

### Conflict of interest

The authors declare that they have no conflict of interest regarding the publication of the research article.

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