多重模糊蕴涵关于三角模的分配性

Distributivity of Multiple Fuzzy Implications about Triangle Module

通过对模糊蕴涵进行多重迭代可以得到新的模糊蕴涵,新蕴涵保持原蕴涵的许多性质。主要讨论这些模糊蕴涵满足相互交换律,以及一些与分配律相关的逻辑重言式,给出了这些重言式成立的充分必要条件。这些结论进一步表明了多重迭代方法生成新蕴涵的优点,为模糊蕴涵在其它领域的应用有一定的指导意义。

Some new fuzzy implications can be gained by multiple iterations of fuzzy implications. The new fuzzy implications maintain many properties of original implications. In this paper, based on the multiple fuzzy implications, we mainly discuss the mutual exchange law and logical tautologies about distribution. Some necessary and sufficient conditions are given for these logical tautologies. These results will further indicate the advantages of new implications generated by multiple iterations and have certain guidance significance for application of fuzzy implications in related fields.