CAJ | 학술논문

该文着力于研究粒计算的基本理论。粒计算作为一种粒数数系被研究，在这种数系中研究粒运算的基本定律、粒与粒之间的不可区分关系；研究这种粒数系中描述型的形式语言等。采用的方法是基于非标准分析中的超实数理论研究实值粒运算应遵循的规则，也研究了伴随二元关系的信息粒的合成、加粗、加细、并和交运算等；在分析前人工作的基础上、基于超实数理论进一步为粒计算研究定义了一种新的不可区分关系，得到了几个相关性质，并且证明了相关结果。随后定义了描述这种粒数数系的描述型形式语言———一种带不可区分关系词的二阶粒逻辑；粒常量、粒变量、粒函数项的相关运算定律也被定义了。最后，以示例演示了这种粒逻辑适应于描述粒数学定理、粒公式化简等。
해문착력우연구립계산적기본이론。립계산작위일충립수수계피연구，재저충수계중연구립운산적기본정률、립여립지간적불가구분관계；연구저충립수계중묘술형적형식어언등。채용적방법시기우비표준분석중적초실수이론연구실치립운산응준순적규칙，야연구료반수이원관계적신식립적합성、가조、가세、병화교운산등；재분석전인공작적기출상、기우초실수이론진일보위립계산연구정의료일충신적불가구분관계，득도료궤개상관성질，병차증명료상관결과。수후정의료묘술저충립수수계적묘술형형식어언———일충대불가구분관계사적이계립라집；립상량、립변량、립함수항적상관운산정률야피정의료。최후，이시례연시료저충립라집괄응우묘술립수학정리、립공식화간등。
In the article,we focus on studying fundamental theory of granular computing.Granular computing is studied as a granular number systems.Operation laws of granulations,the indis-cernibility relation of granulations in the granular number systems are also studied.The formal language for describing the granular number systems needs also to be studied.We study the operation rules of real granulations to adopt the theory of hyperreal numbers in nonstandard analysis.The operations of compound,coarsening and refining,union and intersection of information granularity with binary relations are also studied in the article.We define further a new indiscernibility relation by hyperreal theory and get several related properties based on current relative researches.And related results are proved.Subsequently,the formal language for describing granular computing —a granular language with indiscernibility relation is defined.It is called a second order granular logic in the article.The related operations of granular constants,granular variables and granular function items used in the second-order granular logic are handled necessarily in the article.Finally, the significance of describing granular mathematical theorems defined in the granular number systems is illustrated with real examples.