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Ranking Triangular Fuzzy Numbers Using Fuzzy Set Inclusion Index

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Fuzzy Logic and Applications (WILF 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8256))

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Abstract

In this paper, an original ranking operator is introduced for Triangular Fuzzy Numbers. The purpose is to elaborate fast and efficient algorithms dealing with complicated operations and big data in fuzzy decision-making. The proposed ranking operator takes advantage of the topological relationship of two triangles, besides the Inclusion Index concept — which is an index indicating the Degree of Inclusion in the MIN of two Fuzzy Numbers, a way to approach the ”strongly included in”. Consequently, the ranking result can mostly be deduced directly, allowing an efficient ranking process.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Wang, Y., Yang, J., Xu, D., Chin, K.: On the centroids of fuzzy numbers. Fuzzy Sets and Systems 157(7), 919–926 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Lee-Kwang, H., Lee, J.: A method for ranking fuzzy numbers and its application to decision-making. IEEE Transactions on Fuzzy Systems 7(6), 677–685 (1999)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  6. Boulmakoul, A.: Generalized path-finding algorithms on semirings and the fuzzy shortest path problem. Journal of Computational and Applied Mathematics 162(1), 263–272 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Boulmakoul, A., Laurini, A., Mouncif, H., Taqafi, G.: Path-finding operators for fuzzy multimodal spatial networks and their integration in mobile gis. In: Proceedings of the 2nd IEEE International Symposium on Signal Processing and Information Technology (2002)

    Google Scholar 

  8. Laarabi, M.H., Sacile, R., Boulmakoul, A., Garbolino, E., et al.: An overview of a multiagent-based simulation system for dynamic management of risk related to dangerous goods transport. In: Proceedings IEEE International Systems Conference in Engineering of Complex Systems, pp. 830–835 (April 2013)

    Google Scholar 

  9. Roncoli, C., Bersani, C., Sacile, R.: A decentralised control model for the risk-based management of dangerous good transport flows on road. In: 2012 IEEE International Systems Conference (SysCon), pp. 1–5. IEEE (April 2012)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  13. Bordogna, G., Bosc, P., Pasi, G.: Fuzzy inclusion in database and information retrieval query interpretation. In: Proceedings of the 1996 ACM symposium on Applied Computing, pp. 547–551. ACM (1996)

    Google Scholar 

  14. Beg, I., Ashraf, S.: Fuzzy set of inclusion under kleene implicator. Applied and Computational Math. 10(1), 65–77 (2011)

    MathSciNet  MATH  Google Scholar 

  15. Puri, M.L., Ralescu, D.A.: Fuzzy random variables. Journal of Mathematical Analysis and Applications 114(2), 409–422 (1986)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  27. Wang, Y., Luo, Y.: Area ranking of fuzzy numbers based on positive and negative ideal points. Computers & Mathematics with Applications 58(9), 1769–1779 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  29. Wang, Y., Lee, H.: The revised method of ranking fuzzy numbers with an area between the centroid and original points. Computers & Mathematics with Applications 55(9), 2033–2042 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

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

    Azedine Boulmakoul

  2. Department of Computer science, Bioengineering, Robotics and Systems Engineering (DIBRIS), University of 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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Editor information

Editors and Affiliations

  1. DIBRIS, University of Genoa, Via Dodecaneso 35, 16146, Genoa, Italy

    Francesco Masulli

  2. Dept. of Informatics, Systems, and Communication, University of Milano Bicocca, Viale Sarca 336, 20126, Milan, Italy

    Gabriella Pasi

  3. Dept. of Information Systems, Iona College, 710 North Ave, 10801, New Rochelle, NY, USA

    Ronald Yager

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© 2013 Springer International Publishing Switzerland

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Boulmakoul, A., Laarabi, M.H., Sacile, R., Garbolino, E. (2013). Ranking Triangular Fuzzy Numbers Using Fuzzy Set Inclusion Index. In: Masulli, F., Pasi, G., Yager, R. (eds) Fuzzy Logic and Applications. WILF 2013. Lecture Notes in Computer Science(), vol 8256. Springer, Cham. https://doi.org/10.1007/978-3-319-03200-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-03200-9_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03199-6

  • Online ISBN: 978-3-319-03200-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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