摘要
首先,本文讨论了弱MTL-代数的性质,并给出弱MTL-代数的等价刻画;其次,将蕴涵演绎系统的概念引入到弱MTL-代数中,并研究了演绎系统与蕴涵演绎系统的关系,且给出蕴涵演绎系统的几个等价条件;最后,讨论了弱MTL-代数中的演绎系统和同余关系之间的相互决定的关系,并证明了在弱MTL-代数中一个蕴涵演绎系统是素的当且仅当由其诱导的商代数是全序的弱MTL-代数。
Firstly, in the present paper, some properties of weak MTL algebras are discussed, and several characterizations of weak MTL algebras are revealed. Secondly, the concept of implicative deductive systems is introduced into weak MTL algebras, and the relationships between deductive systems and implicative deductive systems are investigated, and some equivalent conditions of implicative deductive systems are given. Finally, the connection between deductive systems and congruence relations is discussed, it is proved that in a weak MTL algebra a implicative deductive system is prime if and only if the quotient algebra determined by itself is a liner weak MTL algebra.
出处
《模糊系统与数学》
CSCD
北大核心
2016年第5期42-49,共8页
Fuzzy Systems and Mathematics
基金
国家自然科学基金重点项目(11531009)
国家自然科学基金面上项目(61572016)
中央高校基本科研业务费专项资金项目(GK201501001)
关键词
逻辑代数
弱MTL-代数
演绎系统
蕴涵演绎系统
同余关系
商代数
fuzzy logic
weak MTL-algebras
deductive system
implicative deductive system
congruence relation
quotient algebra
