同一问题在不同知识表示下算法难度不同.Rough集理论把知识定义为对对象的分类能力,并提供了一套基于代数系统的知识表达和处理方法.然而在代数表示下,知识的本质以及运算直观性较差,不易于理解.同济大学苗夺谦教授建立了知识与信息之间的关系,在此基础上给出了Rough集理论中概念和运算的信息表示,并给出了知识约简在代数和信息两种表示下的等价性证明.现进一步将知识及其运算表示成粒矩阵形式,继而给出了知识约简在代数、信息和粒矩阵3种表示下的等价性证明.%Different repre sentation for knowledge brings different difficulties in comprehension and programming.Knowledge is regarded as the classification ability according to available knowledge in Rough Set Theory, based on which, a set of algebraic definition for knowledge representation and operation was systematically proposed. However, it is relative difficult to help understand the essence of knowledge in view of algebraic description. Professor Miao in Tongji University built up relations between knowledge and information, he redefined Rough Set algebraic system by information concepts. Furthermore, he also provided equivalent proof for both definitions. In this paper, knowledge and its operation were expressed in form of granular matrix. The equivalent proofs for all three definitions mentioned above were given in this paper.
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