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RM approach for ranking of generalized trapezoidal fuzzy numbers

Author

Listed:
  • Amit Kumar

    (Thapar University)

  • Pushpinder Singh

    (Thapar University)

  • Amarpreet Kaur

    (Thapar University)

  • Parmpreet Kaur

    (Thapar University)

Abstract

Ranking of fuzzy numbers play an important role in decision making, optimization and 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 Systems with Applications 36 (3): 6833) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as an RM approach. The main advantage of the proposed approach is that the proposed approach provides the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach 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 and Systems 118 (3): 375).

Suggested Citation

  • Amit Kumar & Pushpinder Singh & Amarpreet Kaur & Parmpreet Kaur, 2010. "RM approach for ranking of generalized trapezoidal fuzzy numbers," Fuzzy Information and Engineering, Springer, vol. 2(1), pages 37-47, March.
    • Handle: RePEc:spr:fuzinf:v:2:y:2010:i:1:d:10.1007_s12543-010-0036-7
    DOI: 10.1007/s12543-010-0036-7
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    Citations

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    Cited by:

    1. Rezvani, S., 2015. "Ranking generalized exponential trapezoidal fuzzy numbers based on variance," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 191-198.
    2. P. Phani Bushan Rao & N. Ravi Shankar, 2013. "Ranking fuzzy numbers with an area method using circumcenter of centroids," Fuzzy Information and Engineering, Springer, vol. 5(1), pages 3-18, March.
    3. Anila Gupta & Amit Kumar & Mahesh Kumar Sharma, 2013. "Applications of fuzzy linear programming with generalized LR flat fuzzy parameters," Fuzzy Information and Engineering, Springer, vol. 5(4), pages 475-492, December.

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