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An original approach to ranking fuzzy numbers by inclusion index and Bitset Encoding

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Abstract

A variety of methods for ranking fuzzy sets has been suggested. Generally, these methods fall under two main categories: a fuzzy-real sets mapping, a dominance relation of one fuzzy set over another. The original approach proposed in this paper belongs to the second category, as the ranking is based on the degree of inclusion in the MIN of two fuzzy numbers. The novelty lies mainly in the intuitive connection between the topological relationship of fuzzy shapes (triangles, trapezoids, etc.) and the measure of inclusion or dominance referred as inclusion index. This connection led to the classification of different topological relationships into classes identified by a binary pattern. This operation is referred to as Bitset Encoding. Consequently, the outcome of a ranking is already decided for most cases by merely identifying its pattern. Ultimately, the method is validated by the axiomatic system of Wang and Kerre and proven to be a reliable, efficient and strong potential alternative to the other prominent methods.

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References

  • Abbasbandy, S., & Asady, B. (2006). Ranking of fuzzy numbers by sign distance. Information Sciences, 176(16), 2405–2416.

    Article  MathSciNet  MATH  Google Scholar 

  • Abbasbandy, S., & Hajjari, T. (2009). A new approach for ranking of trapezoidal fuzzy numbers. Computers & Mathematics with Applications, 57(3), 413–419.

    Article  MathSciNet  MATH  Google Scholar 

  • Adamo, J. (1980). Fuzzy decision trees. Fuzzy Sets and Systems, 4(3), 207–219.

    Article  MathSciNet  MATH  Google Scholar 

  • Asady, B., & Zendehnam, A. (2007). Ranking fuzzy numbers by distance minimization. Applied Mathematical Modelling, 31(11), 2589–2598.

    Article  MATH  Google Scholar 

  • Bordogna, G., Bosc, P., & Pasi, G. (1996). Fuzzy inclusion in database and information retrieval query interpretation. In Proceedings of the 1996 ACM symposium on applied computing (pp. 547–551). ACM

  • Boukezzoula, R., Galichet, S., & Foulloy, L. (2007). Min and max operators for fuzzy intervals and their potential use in aggregation operators. IEEE Transactions on Fuzzy Systems, 15(6), 1135–1144.

    Article  Google Scholar 

  • Boulmakoul, A. (2006). Fuzzy graphs modelling for hazmat telegeomonitoring. European Journal of Operational Research, 175(3), 1514–1525.

    Article  MATH  Google Scholar 

  • Chen, S. (1985). Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems, 17(2), 113–129.

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng, C. (1998). A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems, 95(3), 307–317.

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng, C. (1999). Evaluating weapon systems using ranking fuzzy numbers. Fuzzy Sets and Systems, 107(1), 25–35.

    Article  MATH  Google Scholar 

  • Chiu, C., & Wang, W. (2002). A simple computation of min and max operations for fuzzy numbers. Fuzzy Sets and Systems, 126(2), 273–276.

    Article  MathSciNet  MATH  Google Scholar 

  • Choobineh, F., & Li, H. (1993). An index for ordering fuzzy numbers. Fuzzy Sets and Systems, 54(3), 287–294.

    Article  MathSciNet  Google Scholar 

  • Chou, S., Dat, L., & Yu, V. (2011). A revised method for ranking fuzzy numbers using maximizing set and minimizing set. Computers & Industrial Engineering, 61(4), 1342–1348.

    Article  Google Scholar 

  • Chu, T., & Tsao, C. (2002). Ranking fuzzy numbers with an area between the centroid point and original point. Computers & Mathematics with Applications, 43(1), 111–117.

    Article  MathSciNet  MATH  Google Scholar 

  • Detyniecki, M., & Ronald, R. (2000). Ranking fuzzy numbers using \(\alpha \)-weighted valuations. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 8(05), 573–591.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois, D., & Prade, H. (1978). Operations on fuzzy numbers. International Journal of Systems Science, 9(6), 613–626.

    Article  MathSciNet  MATH  Google Scholar 

  • Ezzati, R., Allahviranloo, T., Khezerloo, S., & Khezerloo, M. (2012). An approach for ranking of fuzzy numbers. Expert Systems with Applications, 39(1), 690–695.

    Article  MATH  Google Scholar 

  • Facchinetti, G. (2002). Ranking functions induced by weighted average of fuzzy numbers. Fuzzy Optimization and Decision Making, 1(3), 313–327. doi:10.1023/A:1019692914431.

    Article  MATH  Google Scholar 

  • Klir, G., & Yuan, B. (1995). Fuzzy sets and fuzzy logic: Theory and applications. New Jersey: Prentice Hall.

    MATH  Google Scholar 

  • Kóczy, L., & Hirota, K. (1993). Approximate reasoning by linear rule interpolation and general approximation. International Journal of Approximate Reasoning, 9(3), 197–225.

    Article  MathSciNet  MATH  Google Scholar 

  • Laarabi, M. H., Boulmakoul, A., Mabrouk, A., Sacile, R., & Garbolino, E. (2014). Real-timefastest path algorithm using bidirectional point-to-point search on a fuzzy time-dependent transportation network. In 2014 international conference on advanced logistics and transport (ICALT) (pp. 78–84). IEEE

  • Wang, X., & Kerre, E. (2001). Reasonable properties for the ordering of fuzzy quantities (i). Fuzzy Sets and Systems, 118(3), 375–385.

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, Y. (2009). Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets. Computers & Industrial Engineering, 57(1), 228–236.

    Article  Google Scholar 

  • Yao, J., & Wu, K. (2000). Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and Systems, 116(2), 275–288.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang, X., & Xu, Z. (2012). A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making. Fuzzy Optimization and Decision Making, 11(2), 135–146. doi:10.1007/s10700-012-9118-9.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. LIM/IST Lab., Computer Sciences Department, Mohammedia Faculty of Sciences and Technologies (FSTM), Mohammedia, Morocco

    Azedine Boulmakoul

  2. Department of Computer science, Bioengineering, Robotics and Systems engineering (DIBRIS), University of Genoa (UNIGE), Genoa, Italy

    Mohamed Haitam Laarabi & Roberto Sacile

  3. Crisis Research Centre (CRC), Mines ParisTech, Sophia Antipolis, France

    Emmanuel Garbolino

Authors
  1. Azedine Boulmakoul
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  2. Mohamed Haitam Laarabi
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  3. Roberto Sacile
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  4. Emmanuel Garbolino
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Corresponding author

Correspondence to Mohamed Haitam Laarabi.

Appendices

Appendix 1: Encoding procedure

figure a

Appendix 2: Compare procedure

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Boulmakoul, A., Laarabi, M.H., Sacile, R. et al. An original approach to ranking fuzzy numbers by inclusion index and Bitset Encoding. Fuzzy Optim Decis Making 16, 23–49 (2017). https://doi.org/10.1007/s10700-016-9237-9

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  • DOI: https://doi.org/10.1007/s10700-016-9237-9

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