正则剩余格上的模糊理想及模糊蕴涵理想  

Fuzzy Ideals and Fuzzy Implicative Ideals of Regular Residuated Lattices

作　　者：郝加兴[1] 吴洪博[1] 

机构地区：[1]陕西师范大学数学与信息科学学院

出　　处：《模糊系统与数学》2011年第4期8-17,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10871121)

摘　　要：对正则剩余格的结构作进一步研究。利用正则剩余格上、算子并结合模糊数学的思想和方法,在正则剩余格上引入了模糊理想和模糊蕴涵理想的概念,讨论了它们的基本性质。主要结果是:(1)给出了模糊理想和模糊蕴涵理想的等价刻画;(2)证明了模糊蕴涵理想一定是模糊理想,模糊理想不必是模糊蕴涵理想;(3)证明了全体模糊理想之集在给定的运算下是一个完备的分配格。The structure of regular residuated lattices is further studied. With the help of the thought ana methods of fuzzy mathematics, the notions of fuzzy ideals and fuzzy implicative ideals are introduced by ⊕-operator and -operator on regular residuated lattices and some related properties of them are investigated. The main results of this paper are： [l-]Several equivalent characterizations for fuzzy ideals and fuzzy implicative ideals are given; [2] It is proved that fuzzy implicative ideals must be fuzzy ideals, but the converse does not hold; [3]It is proved that the set of all the fuzzy ideals in regular residuated lattices forms a complete distribution lattice in terms of the given operations.

关 键 词：模糊逻辑 正则剩余格 模糊理想 模糊蕴涵理想 模糊布尔理想 

分 类 号：O141[理学—数学]