In this paper, Difference-Similitude Set Theory is proposed which is fundamental different from the known algorithms. Two new concepts in this subject, “Available Member Set” and “Upper-approximate Set” are defined. In the framework of Difference Similitude Set Theory (DSST), the knowledge reduction on any information system is equivalent to the serials calculations on difference set and similitude set of both the whole information system and each object. It is concluded and demonstrated that: 1. The attribute reduction process is just to find an upper-approximate set of the available set of difference set with minimal cardinality as possible. 2. The rule construction of certain object is just to find an upper-approximate set of available set of the object’s difference set with minimal cardinality as possible. The algorithms about these two jobs are also described. The first process can be separated into two steps: a) to find the base attribute. b) to find an upper-approximate set of available member set of no-base set. The union of this two steps’ results is the reserved attribute. The second process can be also separated into two steps: a) to find the object’s base attribute. b) to find an upper-approximate set of the object’s no-base set. By comparing the overlapness of each rule and rejecting the object one by one which the reserved rules suit, the synthesized rules as less as possible should be found.
"Difference-similitude set theory", Proc. SPIE 5803, Intelligent Computing: Theory and Applications III, (28 March 2005); doi: 10.1117/12.603140; https://doi.org/10.1117/12.603140