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Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews

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  • Thanh-Lam Nguyen

Abstract

Fuzzy set theory, extensively applied in abundant disciplines, has been recognized as a plausible tool in dealing with uncertain and vague information due to its prowess in mathematically manipulating the knowledge of imprecision. In fuzzy-data comparisons, exploring the general ranking measure that is capable of consistently differentiating the magnitude of fuzzy numbers has widely captivated academics’ attention. To date, numerous indices have been established; however, counterintuition, less discrimination, and/or inconsistency on their fuzzy-number rating outcomes have prohibited their comprehensive implementation. To ameliorate their manifested ranking weaknesses, this paper proposes a unified index that multiplies weighted-mean and weighted-area discriminatory components of a fuzzy number, respectively, called centroid value and attitude-incorporated left-and-right area. From theoretical proof of consistency property and comparative studies for triangular, triangular-and-trapezoidal mixed, and nonlinear fuzzy numbers, the unified index demonstrates conspicuous ranking gains in terms of intuition support, consistency, reliability, and computational simplicity capability. More importantly, the unified index possesses the consistency property for ranking fuzzy numbers and their images as well as for symmetric fuzzy numbers with an identical altitude which is a rather critical property for accurate matching and/or retrieval of information in the field of computer vision and image pattern recognition.

Suggested Citation

  • Thanh-Lam Nguyen, 2017. "Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews," Complexity, Hindawi, vol. 2017, pages 1-13, July.
    • Handle: RePEc:hin:complx:3083745
    DOI: 10.1155/2017/3083745
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    1. Chalco-Cano, Y. & Román-Flores, H., 2008. "On new solutions of fuzzy differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 112-119.
    2. Chou, Shuo-Yan & Chang, Yao-Hui & Shen, Chun-Ying, 2008. "A fuzzy simple additive weighting system under group decision-making for facility location selection with objective/subjective attributes," European Journal of Operational Research, Elsevier, vol. 189(1), pages 132-145, August.
    3. Abbasbandy, S. & Nieto, Juan J. & Alavi, M., 2005. "Tuning of reachable set in one dimensional fuzzy differential inclusions," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1337-1341.
    4. 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.
    5. Rezvani, S., 2015. "Ranking generalized exponential trapezoidal fuzzy numbers based on variance," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 191-198.
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