中文摘要：

定义了m-极模糊图上的并、联、合成、笛卡尔积、直积、强积、半强积及字典积运算,给出m-极模糊图能分解为两个m-极模糊图的并（联、合成、笛卡尔积、直积、强积、半强积、字典积）的必要或充分条件.由此得到m-极模糊图及两个有限m-极模糊图的并（联、合成、笛卡尔积、直积、强积、半强积、字典积）运算的等价定义.这些结果表明所定义的运算是合理的,同时也提供了一种模糊化通常数学运算（如两个拟阵的并、交等）的方法.

英文摘要：

The operations union, join, composition, cartesian product, direct product, strong product, semi strong product, and dictionary product on m-polar fuzzy graphs are defined, and some necessary or sufficient conditions under which an m-polar fuzzy graph can be decomposed into the union （resp., join, composition, cartesian product, direct product, strong product, semi strong product,dictionary product） of two m-polar fuzzy graphs are given. Based on these results, equivalent definitions of m-polar fuzzy graph and union （resp., join, composition, car- tesian product, direct product, strong product, semi strong product, dictionary product） of two finite m-polar fuzzy graphs are obtain. This not only exhibits the rationality of these operations defined on m-polar fuzzy graphs but also provides a way to fuzzify some crisp mathematical op- erations （e.g. union of two matroids, intersection of two matroids, etc.）.