中文摘要：

针对传统突变模糊归一化公式的问题,在适当设定指标参照值和指标值的规范变换式基础上,使同类环境不同指标同级标准的规范值差异尽可能小,而不同标准的指标规范值差异尽可能大,从而可以认为用规范值表示的同类环境的各指标皆等效于某个规范指标。而任意m项指标的突变模型可用多个尖点突变（m=2）和（或）燕尾突变（m=3）两种突变模型组合表示,且具有可规范的指数分级标准值。基于指标规范值的环境质量突变模糊指数公式具有普适、统一和简单、适用的特点。

英文摘要：

According to the problems of the tradtional catastrophe fuzzy normalized formulae,the present study set the proper reference values and transformed forms for each index or environment,and made the difference in the same grade standard values with different indexes could be weakened,whereas,the difference in the different grade standard values could be strengthened after the normal transformation.Furthermore,the different indexes with normalized values were equivalent to a certain normalized index.Therefore,the catastrophe theory model of any m environmental indexes can be represented with multi-composition models of cusp catastrophe（m=2） and swallowtail catastrophe（m=3）,and the catastrophe exponent values have the normalized classified standard values.Indexes formulae of environmental quality evaluation with normalized index values based on catatrophe theory exhibit the characteristics of universality,unity,simplicity as well as practicality.