Computational and Applied Mathematics

, Volume 37, Issue 3, pp 2943–2964

# An (R, S)-norm fuzzy information measure with its applications in multiple-attribute decision-making

• Rajesh Joshi
• Satish Kumar
Article

## Abstract

In this paper, we introduce a quantity measure which is called (RS)-norm entropy and discuss some of its major properties with Shannon’s and other entropies in the literature. Based on this (RS)-norm entropy, we have proposed a new (RS)-norm fuzzy information measure and discussed its validity and properties. Further, we have given its comparison with other fuzzy information measures to prove its effectiveness. Attribute weights play an important role in multiple-attribute decision-making problems. In the present communication, two methods of determining the attribute weights are introduced. First is the case when the information regarding attribute weights is incompletely known or completely unknown and second is when we have partial information about attribute weights. For the first case, the extension of ordinary entropy weight method is used to calculate attribute weights and minimum entropy principle method based on solving a linear programming model is used in the second case. Finally, two methods are explained through numerical examples.

## Keywords

R-norm entropy Shannon’s entropy Convex and concave function (RS)-norm information measure (RS)-norm fuzzy information measure MADM

## Mathematics Subject Classification

94A15 94A24 26D15

## Notes

### Acknowledgements

The authors are thankful to anonymous referees for their valuable comments and suggestions to improve this manuscript.

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