A New Method of Teaching Quality Evaluation Based on the α-Pessimistic Shapley Value

Coalitional game with uncertain payoffs driven by uncertain variables stands for uncertain coalitional game. A α-pessimistic Shapley value as the solution of uncertain coalitional game is proposed in this paper, which can be played an important role in solving the problem of profit allocation. Moreover, the α-pessimistic Shapley value is proved to be the only value satisfying symmetry, dummy and additivity. Based on the α-pessimistic Shapley value, a new method of teaching quality evaluation in the institutions of higher learning is presented. In order to obtain the index of teaching quality evaluation in uncertain environments, an α-pessimistic multilinear extension is defined. Meanwhile, some properties of α-pessimistic multilinear extension are investigated successfully. Moreover, the problem of teaching quality evaluation are considered in this paper.