Fuzzy Power Ring

With a further progress and development of society and science & technology, we have come into a more complicated society with a recognizant stage characterized by "nature - society - thought" . Mathematics is necessitated to dealing with more complicated and indefinite phenomenon, especially in field of humanism science, social science and thinking science. Similarly, people need computer to automatically recognize and manage indefinite phenomenon in impersonal world, like human cerebra.L. A. Zadeh, a famous American electronic engineering and cybernetics scientist with profound insight, played emphasis on this kind of problem and published <> for resolving it in 1965. He amended and extended set theory - the basis of modern mathematics with a bold hand and brought forward the thinking of using Fuzzy set as a mathematical model to representing fuzzy business. It announced the birth of a new subject - Fuzzy mathematics.Fuzzy mathematics will grow along two directions in the future: first, it will research the inner rule of fuzzy character, i. e the fuzzy language and fuzzy logic. In this direction, computer would be more active and perform more excellent in simulating human thinking through the combination between fuzzy mathematics and some branches such as artificial intelligence, knowledge engineering and expert system. Second, we will regard fuzzy set as a frame that can generalize more kind of mathematical concept and establish definite mathematical theory which can deal with fuzzy phenomenon to extend mathematical basis. Consequently, some aspects of classic mathematics will be advanced more widely and more profoundly.With developing fuzzy mathematics, the importance of set value mapping has been highlighted, so that the upgrade of all kinds of the structures, such as ordered, topological measurable structure, etc, have been considered . The concept of HX ring was raised firstly in the paper[3] Paper[6][7]studied normal HX ring and uniform HX ring . The properties, structures, classifications, homomorphism and isomorphism of all kinds of HX ring have been considered in the paper [1] . 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[5], the concept of fuzzy power group was raised and in paper[8][9] the structure and homomorphism of fuzzy power group was considered.Enlightened by the structures of group and ring in algebra, in this paper , Author firstly raise the concept of fuzzy power ring . First, the properties of the fuzzy power ring will be considered. Second, the structure of each fuzzy power ring will be described systematically, and attempts will bo made to classify the fuzzy power ring and the chains of sub rings will bo constructed. Finally it's homoinorphism, isonmrphism and direct product will be considert-d.