Interval Type-2 Gaussian Fuzzy Games: Energy Sharing in Distributed Systems with Electric Vehicle Integration under Uncertainty

Fuzzy cooperative games using Type-1 fuzzy numbers are commonly applied to model vagueness and imprecision in coalition values and player allocations. However, such models are less effective in capturing increased imprecision. This paper introduces interval Type-2 Gaussian fuzzy numbers (IT2 GFNs) to better represent increased imprecision in coalition values and player allocations in distributed energy systems (DES) caused by uncoordinated electric vehicle (EV) charging and discharging patterns. An analytical solution is proposed to ensure fair and efficient player allocations in IT2 Gaussian fuzzy cooperative games. The proposed method avoids the computational challenges of IT2 subtractions and the associated Type-1 fuzzy number subtractions, which tend to amplify the footprint of uncertainty (FOU) or restrict applicability. A comparative analysis with the interval-based Shapley value, computed using Moore’s subtraction operator, demonstrates that the proposed method achieves allocation efficiency by fully distributing the grand coalition value among players while overcoming the known limitations of the Hukuhara difference, which is not always well-defined.