Banzhaf value for fuzzy cooperative games with coalition values based on gaussian fuzzy numbers

The Banzhaf value has been extensively studied in cooperative game theory under various representations of uncertainty. Existing methods in fuzzy cooperative games formulate the fuzzy Banzhaf value based on the α -cut interval subtraction of fuzzy numbers, the Hukuhara difference, or monotonicity assumptions. This paper introduces a fuzzy Banzhaf value for fuzzy cooperative games in which coalition values are represented by Gaussian fuzzy numbers (GFNs). The proposed method leverages basic operations from distribution theory, thereby preserving the location and variance information of GFNs. A cooperative energy-sharing scenario demonstrates the practical applicability of the proposed GFN-based Banzhaf value in assessing each player’s influence in the decision-making process. Comparative analysis with existing fuzzy Banzhaf values derived from Hukuhara-based approach shows that the proposed method remains applicable in cases where the Hukuhara difference is undefined, and it offers more realistic variance representations for players than α -cut based approaches that rely on Moore’s subtraction.