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Approximations of Fuzzy Numbers by Using r - s Piecewise Linear Fuzzy Numbers Based on Weighted Metric

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  • Haojie Lv

    (Institute of Operations Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Guixiang Wang

    (Institute of Operations Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018, China)

Abstract

Using simple fuzzy numbers to approximate general fuzzy numbers is an important research aspect of fuzzy number theory and application. The existing results in this field are basically based on the unweighted metric to establish the best approximation method for solving general fuzzy numbers. In order to obtain more objective and reasonable best approximation, in this paper, we use the weighted distance as the evaluation standard to establish a method to solve the best approximation of general fuzzy numbers. Firstly, the conceptions of I -nearest r - s piecewise linear approximation (in short, PLA) and the II -nearest r - s piecewise linear approximation (in short, PLA) are introduced for a general fuzzy number. Then, most importantly, taking weighted metric as a criterion, we obtain a group of formulas to get the I -nearest r - s PLA and the II -nearest r - s PLA. Finally, we also present specific examples to show the effectiveness and usability of the methods proposed in this paper.

Suggested Citation

  • Haojie Lv & Guixiang Wang, 2022. "Approximations of Fuzzy Numbers by Using r - s Piecewise Linear Fuzzy Numbers Based on Weighted Metric," Mathematics, MDPI, vol. 10(1), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:1:p:145-:d:717382
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    References listed on IDEAS

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    1. Savin Treanţă, 2021. "On a Class of Constrained Interval-Valued Optimization Problems Governed by Mechanical Work Cost Functionals," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 913-924, March.
    2. Rabia Ambrin & Muhammad Ibrar & Manuel De La Sen & Ihsan Rabbi & Asghar Khan & Feng Feng, 2021. "Extended TOPSIS Method for Supplier Selection under Picture Hesitant Fuzzy Environment Using Linguistic Variables," Journal of Mathematics, Hindawi, vol. 2021, pages 1-28, April.
    3. Yating Guo & Guoju Ye & Wei Liu & Dafang Zhao & Savin Treanţǎ, 2021. "Optimality Conditions and Duality for a Class of Generalized Convex Interval-Valued Optimization Problems," Mathematics, MDPI, vol. 9(22), pages 1-14, November.
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    Cited by:

    1. Yongjun Chen & Xiaojian Li & Jin Wang & Mei Liu & Chaoxun Cai & Yuefeng Shi, 2023. "Research on the Application of Fuzzy Bayesian Network in Risk Assessment of Catenary Construction," Mathematics, MDPI, vol. 11(7), pages 1-19, April.

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