Characterizations of Hemirings Based on Probability Spaces

Abstract

The notion of falling fuzzy $h$-ideals of a hemiring is introduced on the basis of the theory of falling shadows and fuzzy sets. Then the relations between fuzzy $h$-ideals and falling fuzzy $h$-ideals are described. In particular, by means of falling fuzzy $h$-ideals, the charac-terizations of $h$-hemiregular hemirings are investigated based on independent (prefect positive correlation) probability spaces.