模糊过程熵的一些新结论

Some New Resules of Entropy of a Fuzzy Process

定义了模糊过程的熵,将模糊分割熵的一些结论推广到模糊过程熵上,得到一些新的结果:(1)H(P▽Q,T)≤H(P,T)+H(Q,T);(2)H(P,T)≤H(Q,T)+H(P|Q);(3)对任意的正整数k,有H(P,T)=H(▽i=ki=-k T-i P,T).这些结果对遍历论的发展起到一定的作用.

The entropy of fuzzy process is defined and some conclusions of fuzzy partition entropy are extended to fuzzy process entropy. We have some new results:(1)H(P▽ Q,T)≤H(P,T)+H(Q,T);(2)H(P,T)≤H(Q,T)+H(P|Q);(3)for any positive interger k,H(P,T)=H( ▽i=k i=-k T -i P,T).These results will play a certain role in the development of ergodic theory.