Paper:

# An Application of Discernibility Functions to Generating Minimal Rules in Non-Deterministic Information Systems

## Hiroshi Sakai^{*} and Michinori Nakata^{**}

^{*}Department of Mathematics and Computer Aided Science, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan

^{**}Faculty of Management and Information Science, Josai International University, Gumyo, Togane, Chiba 283-8555, Japan

Minimal rule generation in Non-deterministic Information Systems (NISs), which follows rough sets based rule generation in Deterministic Information Systems (DISs), is presented. According to certain rules and possible rules in NISs, minimal certain rules and minimal possible rules are defined. Discernibility functions are also introduced into NISs for generating minimal certain rules. Like minimal rule generation in DISs, the condition part of a minimal certain rule is given as a solution of an introduced discernibility function. As for generating minimal possible rules, there may be lots of discernibility functions to be solved. So, an algorithm based on an order of attributes is proposed. A tool, which generates minimal certain rules and minimal possible rules, has also been implemented.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.10, No.5, pp. 695-702, 2006.

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