Fuzzy Cooperative Games with Coalition Values Based on Gaussian Fuzzy Numbers and Their Application to Energy Sharing in Residential Communities

Abstract Traditional cooperative game theory assumes precise coalition values and player payoffs. However, this assumption proves unrealistic in real-world applications that involve uncertainty. To address this, fuzzy cooperative games provide an effective framework by representing coalition values and player payoffs as fuzzy numbers. While triangular fuzzy numbers have been commonly used in these games, Gaussian fuzzy numbers (GFNs) present a robust alternative to modelling imprecision. This paper introduces an analytical solution for cooperative games with coalition values based on GFNs. The proposed method leverages the $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -cut set of fuzzy numbers and incorporates a quadratic programming model. This approach effectively avoids the subtraction operations between GFNs, which are known to increase uncertainty and compromise decision accuracy. The method’s applicability is demonstrated through a practical application of distributed energy sharing in a small residential community. A comparative analysis with interval Shapley-like and Hukuhara–Shapley values underscores the advantages and effectiveness of the proposed solution.