集对逻辑及其运算定律

Set pair logic and its operation theorems

解决现行的集对联系函数四则运算中存在的不确定性问题与逻辑谬误.分析联系函数与模糊隶属函数在表达事物之间联系的相似性,借鉴模糊逻辑的基本方法,定义了以联系度为真值形式的集对命题,进而给出集对逻辑的析取、合取、取否运算法则,建立了集对逻辑的基本框架.在此基础之上,分析了集对逻辑运算的七大运算定律:对合律、幂等律、交换律、结合律、分配律、吸收律和摩根律,由此证明集对逻辑运算构成的代数(S,,,)为软代数.

To solve the uncertainty problem and logical error in the arithmetic of connection function, the similarity between connection function and fuzzy membership function when they express the links among objects was investigated in this study. Based on the basic methods of fuzzy logic, the set pair proposition which has the value form of connection degree was also defined. Thus, the operation rules, such as disjunction, conjunction, negation, were obtained and the basic frame of set pair Logic is established. Furthermore, the seven rules including involution, idempotent, exchange, combination, distribution, absorption, and Morgan were discussed. It proves that （S,∨,∧,-） is soft algebra.