The solution for type-2 fuzzy linear programming model based on the nearest interval approximation

Article type: Research Article

Authors: Li, Xiaofei | Ye, Binhua | Liu, Xinwang^{; *}

Affiliations: Southeast University, Jiangning District, Nanjing, Jiangsu, China

Correspondence: [*] Corresponding author. Xinwang Liu, Southeast University, 2 Southeast University Road, Jiangning District, Nanjing, Jiangsu, China. E-mail: xwliu@seu.edu.cn.

Abstract: Linear programming is an important branch of operations research. The model is mature in theory and widely used in real life. However, various complex realistic scenarios involve fuzzy information. In this paper, we consider a fuzzy linear programming (FLP) model in which all parameters are trapezoidal interval type-2 fuzzy numbers (IT2FNs) and propose a solution method based on the nearest interval approximation and the best-worst cases (BWC) method. We prove the nearest interval approximation interval of trapezoidal IT2FNs, then the trapezoidal IT2FNs in the model are transformed into interval numbers which both upper and lower limits are interval numbers. With the help of best-worst cases (BWC) method, the sub-models of the transformed interval linear programming model are proposed, and four sub-solutions with different specific meanings can be obtained by solving them respectively. Finally, an application example is presented to show the rationality and practical significance of the method.

Keywords: Fuzzy linear programming (FLP), Trapezoidal interval type-2 fuzzy numbers (IT2FNs), Best-worst cases (BWC) method, The nearest interval approximation

DOI: 10.3233/JIFS-211568

Journal: Journal of Intelligent & Fuzzy Systems, vol. 42, no. 3, pp. 2275-2285, 2022