| Since LA .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 theoreies of fuzzy semigroups, fuzzy groups , fuzzy rings and the fuzzy ideals on fuzzy semigroups have developed perfectly. But, most of the results are studied based on the belonging function of fuzzy set.In this paper, Author firstly uses fuzzy points to study the fuzzy ideals on fuzzy semigroups and a new characterizations of fuzzy ideals on fuzzy semigroups is obtained.First, the pointwise definitions of fuzzy ideals are given .Then,the author discuss the relations of the definitions of fuzzy ideals defined by fuzzy points and the definitions defined by the belonging function of fuzzy set and testify that the two definitions of fuzzy ideals are equivalent which indicates the study by fuzzy points is reasonable. Also,the relations of fuzzy ideals on fuzzy semigroups and crisps ideals on crisps semigroups is discussed, and the connections of them are obtained.Finally,the properties of fuzzy ideals are studied and the relations among varies ideals are discussedThe results indicates that the studies of fuzzy ideals on fuzzy semigroups by fuzzy points are more intuitive and the results are more significant. |
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