Abstract: How to present complex numerical relations is difficult in software modeling, since accurate complex numeri- cal relations representation always leads to high complexity in software model reasoning. hhis paper pointed out an ex- tended fuzzy description logic based framework to approximately represent numerical relations by comparisons over fuzzy functions, which contains three core modules: fuzzification from software numerical domain to fuzzy domain, con- struction of software numerical knowledge bases (SNKI3s) and reasoning with SNKI3s. This paper gave some common fuzzification functions and two fuzzification principles to guarantee sufficiency, talked about construction steps and pro- cedures of cut concepts,assertions and inclusions in SNKBs,and discussed some implementation mechanisms in design, optimization and segmentation of reasoning algorithms.

Key words: Software, Model, Semantics, Description logic