直觉模糊三Ⅰ蕴涵的研究

Research on the Intuitionist Fuzzy Triple Implication

在Zadeh模糊集理论基础上,将传统模糊推理的合成推理方法(CAI)与王国俊教授的模糊推理全蕴涵三I算法进行分析和比较,得出了后者更加全面合理的结论,然后进一步对模糊三I全蕴涵进行研究,将其与Atanassov的直觉模糊集理论相结合,扩展为基于直觉模糊集的三I蕴涵,并论述了这一扩展的必要性和优点,从而得到了新的研究方向,接着给出了一个新的直觉模糊蕴涵算子,讨论了直觉模糊蕴含的运算性质,最后通过这一算子对直觉模糊三I蕴涵进行了直觉模糊取式问题(IFMP)的求解,得到了基于这一算子的IFMP问题求解算法,并用实例验证了该算法的正确性和合理性。

Compared with the common Fuzzy Sets, Intuitionist Fuzzy Sets （IFS） are good at describing the diversity and vagueness of the world, which has attracted many scholastics＇ attention. Extended from the Fuzzy Sets, Fuzzy Reasoning （FR） has been applied to many fields including vague control and artificial intelligence. However, it is explained that lntuitionist Fuzzy Reasoning （IFR） is more exquisite in finding out the inherent connections between the fuzzy objects. Originated by professor Wang, the Fuzzy Triple Implication （FTI） has deeply developed the theory of FR. Based on the above theories, and by researching on FTI, this paper extended FTI to Intuitionist Fuzzy Triple Implication （ IFTI）, and gave a dissertation about the necessity and strong point of it. Through proposing a new intuitionist fuzzy implication arithmetic operator, this paper solved the IFMP problem, and tested the argumentation by an example as well.