Abstract: With respect to cooperative n-person games with judgement worth, the Multiplicative-Shapley is proposed based on the 1-9 judgement scale. Firstly, the average payoff function is defined, and two types of consistent and their adjustment are introduced simultaneously. Secondly, some concepts of cooperative n-person games, such as domination, pseudoconvex, Multiplicative-Shapley value and unit element, are defined based on the corresponding characteristic function, and then the Multiplicative-Shapley value is proposed according to three axioms. Finally, a numeral example is illustrated to show the feasibility and availability of the Multiplicative-Shapley value.

Key words: cooperative games, judgement worth, Multiplicative-Shapley value, unit element