Rough function model and rough membership function

作     者：Wang Yun Guan Yanyong Huang Zhiqin 

作者机构：School of Science Univ. of Jinan Jinan 250022 P. R. China 

出 版 物：《Journal of Systems Engineering and Electronics》 (系统工程与电子技术（英文版）)

年 卷 期：2008年第19卷第3期

页      面：522-528页

核心收录：

学科分类：08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：the Scientific Research and Development Project of Shandong Provincial Education Department(J06P01) the Science and Technology Fundation of University of Jinan (XKY0703) 

主　　题：rough set theory rough function model indiscernibility relation rough membership function roughnumber rough interval. 

摘      要：Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.