Uncertain random multi-objective programming problem given general monotonic function and its solution under CESD criterion

• Published in: Soft computing (Berlin, Germany) Germany), 2022, Vol.26 (11), p.5297-5313
• Main Authors: Sun, Yun, Wang, Ying, Meng, Xiangfei
• Format: Article
• Language: English
• Subjects: Artificial Intelligence; Computational Intelligence; Control; Engineering; Mathematical Logic and Foundations; Mechatronics; Optimization; Robotics
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-022-06898-z

The classical uncertain random multi-objective programming is based on strictly monotonic functions, which limits the application of general monotonic functions. In order to overcome the problem, considering the general monotonic functions, this paper proposes a general uncertain random multi-objective programming, focusing on the multi-objective programming with correlation. Firstly, the solution of expected value and standard deviation value of uncertain random variables is extended to general monotonic functions. Secondly, considering the influence of correlation on the objective functions, the order relationship of expected values among comonotonic functions considering general monotonic functions is deduced. On this basis, the order relationship of expected values and standard deviation values of uncertain random multi-objective function with correlation is obtained, and the order relationship of uncertain random multi-objective function on the basis of the expected value-standard deviation value criterion (C ESD criterion) is derived. Then, for the two decision-making situations where the importance of the objective functions is known and the ideal points of the objective functions are known, two methods are proposed, respectively, which are proved that the methods can retain the uncertainty and randomness of the original problem. Finally, a numerical example is given to prove the effectiveness of the methods, which shows that the results obtained on the basis of the C ESD criterion can consider both the long-term stability and short-term volatility of decision-making.