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RM approach for ranking of L–R type generalized fuzzy numbers

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Abstract

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Syst Appl 36:6833–6842, 2009) is incorrect. The main aim of this paper is to propose a new approach for the ranking of L–R type generalized fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as RM approach. The main advantage of the proposed approach is that it provides the correct ordering of generalized and normal fuzzy numbers and it is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets Syst 118:375–385, 2001).

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Acknowledgments

The authors would like to thank Editor-in-Chief “Professor Antonio D. Nola” and anonymous referees for the various suggestions that have led to an improvement in both the quality and clarity of the paper. Dr. Amit Kumar want to acknowledge the innocent blessings of Mehar without whom it was not possible to think the idea proposed in this manuscript. Mehar is a lovely daughter of Parmpreet Kaur (Research scholar under the supervision of Dr. Amit Kumar).

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Authors and Affiliations

  1. School of Mathematics and Computer Applications, Thapar University, Patiala, 147 004, India

    Amit Kumar, Pushpinder Singh, Parmpreet Kaur & Amarpreet Kaur

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  1. Amit Kumar
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  2. Pushpinder Singh
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  3. Parmpreet Kaur
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  4. Amarpreet Kaur
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Correspondence to Pushpinder Singh.

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Kumar, A., Singh, P., Kaur, P. et al. RM approach for ranking of L–R type generalized fuzzy numbers. Soft Comput 15, 1373–1381 (2011). https://doi.org/10.1007/s00500-010-0676-x

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  • DOI: https://doi.org/10.1007/s00500-010-0676-x

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