Research Of The Properties Of The Anti-fuzzy Subgroups

In recent years, group theory has been applied deeply into all practical areas of science and technology. Electronic engineering, control engineering, systems engineering and other developments in the field of science and technology are evolving with the application of modern mathematical discipline closely linked. Fuzzy math is based on fuzzy set theory, developed a new mathematical discipline, in 1965,Zadeh first proposed the fuzzy the concept of a collection of a few decades, fuzzy set theory has been rapid development, especially under the general theoretical nature of the classic fuzzy group, has been known to everyone . Yuanxue Hai teacher fuzzy nature of the study group, and achieved certain results.First proposed the concept of fuzzy subgroups, in 1971. When Rosenfeld fuzzy set theory applied to the Groups, and gradually formed an important branch of fuzzy mathematics - fuzzy algebra. History is always a striking similarity, the first views put forward the concept of anti-fuzzy subgroup, in 1990. R. biswas published a paper Fuzzy subgroups and anti-fuzzy subgroups [J] proposed the concept of anti-fuzzy subgroup, fuzzy algebra and created a new area of research.Anti-fuzzy subgroup of the currently made good progress. Yao Bing-science and other teachers, research in this area has achieved some results, after a Few Kinds of teachers in the classic definition of fuzzy group and Yuan Xuehai the nature of teacher research fuzzy group, based on fuzzy binary operation defined by the anti-fuzzy group, The corresponding equivalent definition is given, and discussed the nature of the corresponding anti-fuzzy group.On the basis of previous results, the anti-fuzzy subgroups were primary research, in this article, discussion of the anti-fuzzy subgroups of some relevant definitions and properties. The main product from the outer, cut set and homomorphisms three areas studied are the anti fuzzy subgroups of some equivalent definitions, and discussed the relations among the outer product, cut set and homomorphisms of the anti-fuzzy subgroups , which have goton some conclusions.