f(X0, X1 ,……,Xn) is a random selection function relying on X0, X1, ……,Xn.

The application of random selection in ranked set sampling;

A strong limit theorem on random selection for independent identical distribution random variables;

A strong limit theorem on random selection for the sequence of N-valued random variables;

Then,some maximal element theorems in stochastic choice problems and other theorems with respect to incomplete preference are obtained.

Stochastic utility theory and multinomial logit model are used to analyze stochastic choice in demand market,while the influence of region and brand is treated as stochastic variable.

A market equilibrium model is proposed for differentiated multi product with stochastic choice, in which, multinomial logit is used as the probabilities of the stachastic choice and the supply of differentiated products is subjected to the total demand function of all products.

Furthermore, by allowing the selection function to take values in an interval, the conception of random selection is generalized.

It explained how the selection function D divided the power consumption curves into .

An analysis of the correlation between the choice function and consistency condition;

The Characterization of Fuzzy Choice Functions Rationality and Quasi-transitive Rationality;

Study on choice function and its preference structure based on a matching market;