The Shapley Value of Cooperative Games on Concept Lattices With the Worth of Coalitions Represented by Intuitionistic Fuzzy Values

This article focuses on cooperative games where coalition worths are characterized by intuitionistic fuzzy values (IFVGs). A Shapley value is defined for such games, and this value for strongly monotonic IFVGs satisfies some core properties and serves as the unique solution meeting efficiency (EF), symmetry (SYM), and marginality (MA) axioms. For games where coalitions are restricted to a concept lattice and worths remain intuitionistic fuzzy values (IFVCGs), two distinct Shapley values are developed. The first follows traditional frameworks (focusing on postcoalition benefit allocation) and, for strongly monotonic IFVCGs, satisfies core properties but lacks uniqueness. Drawing on concept lattice reduction theory, we categorize players into indispensable players, relatively necessary players, and absolutely unnecessary players. Based on this classification, a second Shapley value based player reduction is proposed. Compared with conventional methods, it offers three advantages: assigning higher profits to indispensable players, ensuring relatively necessary players get legitimate allocations, and setting absolutely unnecessary players profits to $0_{IFV}$ (precluding unwarranted benefits). We further prove that this novel Shapley value is unique if the traditional Shapley value on its reduction is unique.