# Jaccard Ranking Index with Algebraic Product t-Norm Based on Second Function Principle in Handling Fuzzy Risk Analysis Problem

• Nazirah Ramli
• Norhuda Mohammed
• Fairuz Shohaimay
Conference paper

## Abstract

Jaccard set theoretic index based on the first function principle approach has been proposed for ranking fuzzy numbers. However, the arithmetic operations of the first function principle is not straightforward which consists of determining both the lower and upper limit of the fuzzy numbers and also the minimum and maximum values of the fuzzy numbers’ domain. In this paper, a simple point-wise arithmetic operation, namely the second function principle is applied in developing the Jaccard ranking index with algebraic product t-norm. Based on the proposed ranking index, a fuzzy risk analysis (FRA) is presented in dealing with FRA problem. The behavior of the proposed risk’s ranking order is investigated and compared with some of the previous studies.

## Keywords

Algebraic product t-norm Fuzzy risk Jaccard index Second function principle

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## Authors and Affiliations

• Nazirah Ramli
• 1
Email author
• Norhuda Mohammed
• 1
• Fairuz Shohaimay
• 1
1. 1.Department of Mathematics, Faculty of Computer & Mathematical SciencesUniversiti Teknologi MARAJengkaMalaysia