Pointwise Fuzzy Powergroups And Fuzzy Power Ring

Since L.A .Zadeh , a famous American electronic engineering and cybernetics scientist , published 《Fuzzy sets》 in 1965, Fuzzy mathematics has developed quickly and displayed strong vitality in settling the fuzzy and uncertain questions. As a brand-new subject , Fuzzy mathematics extends mathematical basis of the classical mathematics, and it's brand-new mathematics thinking and method has been expanded to some mathematics field ,which makes some aspects of classic mathematics advancing more widely and more profoundly. For example .connecting classical algebra with fuzzy structure, a new mathematics branch-fuzzy algebra appears.Currently, there have been some articles on connecting fuzzy structure with algebra structure .The theoretics of F - group, and F-ring have developed perfectly. But with the development of fuzzy set theory, all kinds of the structure are upgraded not only from their universes to their power sets, but also from their universes to their fuzzy power sets.In the paper(2),Author firstly considered the question of the structural upgrade,concept of fuzzy power group was raised and the nature was considered ,in the paper(7)(8),the structure and homomorphism of fuzzy power group was considered. In the paper(9),the concept of fuzzy power ring was raised, the structure and homomorphism of fuzzy power group was considered.In this paper , Author firstly uses F- point to study F - group and F-ring .First, a new depication of F-power group and F-power ring has been found; Second, the structure of each fuzzy power group and fuzzy power ring have been considered systematically;Third, the transfer theorems of F-power group and F-power ring have been established, which disclose the relations of F-power group , F-power ring and power group, power ring;Finally, their homomorphism, isomorphism have been studied.