Intuitionistic interval-valued hesitant fuzzy matrix games with a new aggregation operator for solving management problem

Matrix games involving interval-valued hesitant fuzzy linguistic sets and its application to electric vehicles

Game theory has been successfully applied in a variety of domains to deal with competitive environments between individuals or groups. The matrix games involving fuzzy, interval fuzzy, and intuitionistic fuzzy numbers exclusively examine the numeric components of an issue. However, several researchers have also examined various extensions of conventional game theory, considering the ambiguous situations for payoffs and goals. In many real-life scenarios, qualitative information is often critical in expressing the payoffs of a matrix game. Thus, the present work contributes to the field of matrix games where the payoffs have been quantified via qualitative variables, termed interval-valued hesitant fuzzy linguistic sets. The mathematical formulation and solution concept for matrix games involving interval-valued hesitant fuzzy linguistic numbers is designed by utilizing an aggregation operator supported by linguistic scale function and solving them by employing score function. Finally, the proposed approach is validated by applying it to electric vehicle sales.

Bi-Matrix Games with General Intuitionistic Fuzzy Payoffs and Application in Corporate Environmental Behavior

Uncertainty is common in miscellaneous decision-making problems, including bi-matrix games. The uncertainty of bi-matrix games is caused by the complexity of the game environment and the limitations of players’ cognition rather than the asymmetry of information. Therefore, it is hard for players to precisely give their crisp payoff values. In this paper, a new method considering the acceptance degree that the general intuitionistic fuzzy constraints may be violated is developed to solve general intuitionistic fuzzy bi-matrix games (GIFBMGs). In the method, a new asymmetric general intuitionistic fuzzy number (GIFN) and its cut sets are firstly defined. Then, the order relationship of GIFNs and the definitions of α and β-bi-matrix games are proposed. Afterwards, the constructed general intuitionistic fuzzy quadratic program is converted into an interval bi-objective program on the basis of the order relationship of GIFNs. Furthermore, the interval bi-objective program is converted into a multi-objective quadratic program based on the combination of interval order relationship and the player’s acceptance degree. A goal programming approach is put forward to solve the multi-objective quadratic program. Finally, the validity of the proposed method is verified with a numerical example for corporate environmental behavior (CEB), and some comparative analyses are conducted to show the superiority of the proposed method.