Probability feature of element transition and internal inverse P ρ -sets

Abstract

The concept of element transition probability and the structure of internal inverse $P_{ρ}$ -set ${\bar{X}}^{P_{F}}$ were proposed based on the inverse P-sets ( ${\bar{X}}^{F}$ , ${\bar{X}}^{\bar{F}}$ ) and the randomness of element transition. The relationship between internal inverse P-set ${\bar{X}}^{F}$ and internal inverse $P_{ρ}$ -set ${\bar{X}}^{p_{F}}$ was discussed, which showed ${\bar{X}}^{p_{F}}$ is the general forming of ${\bar{X}}^{F}$ while ${\bar{X}}^{F}$ is a special case of ${\bar{X}}^{p_{F}}$ . The relationship theorem between ${\bar{X}}^{p_{F}}$ and element transition probability, and the identification theorem between internal inverse $P_{ρ}$ -set family and internal inverse P-set family were presented. Furthermore analysis of the probability feature about internal inverse $P_{ρ}$ -set ${\bar{X}}^{p_{F}}$ was given at the end.

Keywords

Inverse P-set random properties about element transition