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Ranking Fuzzy Number Based On Lexicographic Screening Procedure

Author

Listed:
  • MIAO-LING WANG

    (Department of Industrial Engineering and Management, Ming Hsin University of Science & Technology, Hsinchu, Taiwan, Republic of China)

  • HSIAO-FAN WANG

    (Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan, Republic of China)

  • CHIH-LUNG LIN

    (Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan, Republic of China)

Abstract

Fuzzy numbers are used for representing the numerical quantities in a vague environment. Their ranking order has been an important issue for application purposes. Most of the existing ranking methods transform a fuzzy number into a real number based on certain criteria. There is yet no method that can always give a satisfactory solution. This study pointed out that it cannot be avoided for different fuzzy numbers to be corresponding to the same real number by any type of ranking functions. Therefore, sequential screening approach would be necessary for a complete order of fuzzy numbers. We summarize the properties for a sufficient and necessary set of ranking criteria. Then, based on the ranking order of these criteria, aLexicographical Screening Procedureis proposed, which has shown to be promising in ranking fuzzy number with efficient computation and ease of understanding. Six counterexamples of the existing methods were used for comparison.

Suggested Citation

  • Miao-Ling Wang & Hsiao-Fan Wang & Chih-Lung Lin, 2005. "Ranking Fuzzy Number Based On Lexicographic Screening Procedure," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 663-678.
    • Handle: RePEc:wsi:ijitdm:v:04:y:2005:i:04:n:s0219622005001696
    DOI: 10.1142/S0219622005001696
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    Citations

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    Cited by:

    1. Carlo Alberto Magni & Stefano Malagoli & Giovanni Mastroleo, 2006. "An Alternative Approach To Firms' Evaluation: Expert Systems And Fuzzy Logic," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 195-225.
    2. Magni, Carlo Alberto, 2004. "Rating and ranking firms with fuzzy expert systems: the case of Camuzzi," MPRA Paper 5889, University Library of Munich, Germany.
    3. Thanh-Lam Nguyen, 2017. "Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews," Complexity, Hindawi, vol. 2017, pages 1-13, July.
    4. R. A. Aliev & O. H. Huseynov & R. Serdaroglu, 2016. "Ranking of Z-Numbers and Its Application in Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1503-1519, November.

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