Normalized Fractional Order Entropy-Based Decision-Making Models under Risk

Abstract

Constructing efficient portfolios requires balancing expected returns with risk through optimal stock selection, while accounting for investor preferences. In a recent work by Paul and Kundu (2026), the fractional-order entropy due to Ubriaco was introduced as an uncertainty measure to capture varying investor attitudes toward risk. Building on this foundation, we introduce a novel normalized fractional order entropy aligned with investors' risk preferences that combines normalized fractional entropy with expected utility and variance. Risk sensitivity is modeled through the fractional parameter, interpolating between conservative or risk aversion and adventurous or high risk tolerance attitudes. Furthermore, the robustness and statistical significance of the fractional order entropy-based risk measure, termed normalized expected utility-fractional entropy (NEU-FE) and normalized expected utility-fractional entropy-variance (NEU-FEV) risk measures are explained with the help of machine learning tools, including Random forest, Ridge regression, Lasso Regression and artificial neural networks by using Indian stock market (NIFTY50). The results confirm that the proposed decision models support investors in making high-quality portfolio investments.