A local multi-granularity fuzzy rough set method for multi-attribute decision making based on MOSSO-LSTM and its application in stock market

Multi-attribute decision-making, based on historical data of attributes, considers multiple attributes and strives to find the optimal solution among numerous possible choices. Historical data cannot accurately reflect future situations of the attributes. To address this issue, this paper proposes a local multi-granularity fuzzy rough set (LMGFRS) method for multi-attribute decision making based on long short-term memory (LSTM) neural networks. Firstly, the LSTM is conducted to forecast the future trends of key attributes. And an algorithm of multi-objective salp swarm optimization (MOSSO) is employed to optimize the hyper-parameters of the LSTM. Then, based on the MOSSO-LSTM forecasting attribute trends, the prospect theory and grey relation analysis are utilized to construct different prospect value matrices and the objective concept. The risk preference, risk aversion, and risk neutral of decision-makers in the actual decision-making process are characterized. Next, by integrating the local rough set and multi-granularity fuzzy rough set, a LMGFRS method is constructed. The calculation of approximations of the LMGFRS based on the information granules of the objective concept can greatly reduce calculation complexity. Additionally, the overfitting problems are avoided by tuning the values of (alpha,beta)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha , \beta )$$\end{document}. Finally, the proposed LMGFRS decision-making method is applied to stock market. The results indicate that the LMGFRS method enriches rough set theory and decision-making methodology, and provides a feasible decision-making solution for investment institutions in practice.