Fuzzy extension of n-persons games based on pseudo-Boolean functions

Boolean functions and pseudo-Boolean functions have been widely used in different fields,whose polynomial representations contribute to depicting their some characteristic properties.

A kind of Boolean algebra and its application;

The Boolean Algebra Definited on the Partial Order Set;

The n_ary Boole polynomial f(x_,…,x_n) can be denoted by the form off(x_1,…,x_n)=∑f(α_1,…,α_n)x~~~(α_1)_1…x~~~(α_n)_nLet F_n and_m is respectively the set of all n-ary Boole functions and all n_ary Boole polynomials on Boole algebra B,then F_n=_n iff |B|=2.

In this paper we construct a functor from the category o f Boole algebras to the category of double Stone algebras satisfying the complem ent property and show that this functor has a left adjoint.

From this, the consistent signals in the logic circuits will be transformed into the global minimal points of quadratic pseudo Boolean functions.

A method of auto tuning parameters for PID controller based on the Pan Boolean algebra is introduced according to its parameters which affect the performance of the PID controller.

Aiming at incompletely information, based on Pan Boolean algebra, applying the method of "acquire according to uncomformed information" to library inquiry system can form a kind of new library inquiry system.

Pan Boolean algebra-based logical control model of the traffic light is designed in this paper,with an illustration of crossroads in the urban trunk roads.