Z-Number-Based Maximum Expected Linear Programming Model with Applications

Meng Yuan, Biao Zeng (), Jiayu Chen and Chenxu Wang
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Meng Yuan: School of Qian Weichang, Shanghai University, Shanghai 200444, China
Biao Zeng: School of Management, Shanghai University, Shanghai 200444, China
Jiayu Chen: School of Management, Shanghai University, Shanghai 200444, China
Chenxu Wang: School of Computer Science and Engineering, Tianjin University of Technology, Tianjin 300384, China

Mathematics, 2023, vol. 11, issue 17, 1-24

Abstract: In research of a better description for information uncertainty, Z-numbers, which are related to both the objective information and the subjective criticism, were first conceptualized by Zadeh. Because of its neologism, there have been multitudinous attempts toward continuation and expansion of the prototype. In this paper, we mainly study varieties of theoretical preparations for classical Z-numbers and derive the maximum expected linear programming model of Z-numbers, which are constructed on the basis of reliability conversion factors and proliferation on applications due to their simplicity. Firstly, by means of transforming Z-numbers into LR fuzzy intervals through their reliability variable, the credibility distribution and inverse distribution of converted Z-numbers are stated precisely. Then, the operational law of independent variables and its expected value can be derived via credibility distribution. The maximum expected Z-number linear programming model is determined on the basis of previous theoretical preparations, and it transforms from a classical Z-number chance-constrained model into a crisp one. Finally, with the aim of improving the programming method, its application in pragmatic practice with the realistic examples of a supplier section and optimal portfolio problems are enumerated to interpret the effectiveness of our model.

Keywords: Z-numbers; linear programming; expected value; maximum expected model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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