# Dice Index with Algebraic Product and Minimum t-Norm for Ranking Fuzzy Numbers

• Nazirah Ramli
• Fairuz Shohaimay
• Nurhalijah Bachik
Conference paper

## Abstract

In fuzzy environments, the ranking of fuzzy numbers (RFNs) is important for solving decision-making problems. Many ranking methods have been developed based on various techniques but no method can provide satisfactory solution to every situation and case. Some methods lack in certain aspects such as inconsistency with human intuition, non-discriminating results and difficulty of interpretation. In this paper, fuzzy preference relation ranking methods based on Dice index with algebraic product and minimum t-norm are proposed. The procedure of the ranking methods involves six steps which are determining fuzzy maximum and fuzzy minimum, intersection and union of fuzzy numbers (FNs), scalar cardinality of FNs, fuzzy evidences and total fuzzy evidences. The findings show that the type of t-norm used affects the ranking results of some FNs.

## Keywords

Decision making Dice index Fuzzy numbers (FNs) Ranking fuzzy numbers (RFNs)

## Notes

### Acknowledgments

The presentation of this paper is supported by the Department of Research & Industrial Linkages (PJI), Universiti Teknologi MARA Pahang under Tabung Penyelidikan Am.

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## Authors and Affiliations

• Nazirah Ramli
• 1
• Fairuz Shohaimay
• 1
Email author
• Nurhalijah Bachik
• 1
1. 1.Faculty of Computer and Mathematical SciencesUniversiti Teknologi MARAJengkaMalaysia