EQ-代数上M-算子研究  

Study of Multiplier Operators on EQ-algebras

作　　者：高晓莉 王军涛 程晓云 GAO Xiaoli;WANG Juntao;CHENG Xiaoyun(School of Mathematics and Statistics,Xianyang Normal University,Xianyang 712000,Shaanxi,China;School of Science,Xi’an Shiyou University,Xi’an 710065,Shaanxi,China;School of Science,Xi’an Aeronautical University,Xi’an 710077,Shaanxi,China)

机构地区：[1]咸阳师范学院数学与统计学院,陕西咸阳712000 [2]西安石油大学理学院,陕西西安710065 [3]西安航空学院理学院,陕西西安710077

出　　处：《咸阳师范学院学报》2023年第4期4-10,共7页Journal of Xianyang Normal University

基　　金：陕西省自然科学基础研究计划项目(2022JM-014,2022JQ-068);陕西省教育厅科研计划项目(21JK0963);咸阳师范学院博士科研启动资金项目。

摘　　要：EQ-代数是高阶模糊逻辑所对应的一类重要逻辑代数,将其作为模糊逻辑理论的主要研究领域,对推动人工智能的发展有重要意义。文中主要在EQ-代数上引入Multiplier算子(M-算子)、单M-算子、幂等M-算子等算子的概念,并研究其相关性质,得到了M-算子的复合依然是M-算子,并给出了保序M-算子的等价刻画,证明了在n元好的EQ-代数上,至少可以定义n个互异的M-算子;其次,讨论了M-算子与一些特殊映射(闭包算子、同态映射、幂等映射、恒等映射)之间的关系,给出了M-算子是恒等映射的等价刻画;最后,研究了EQ-代数E上关于M-算子f的不动点集(即Fixf(E))的相关性质,得到在给定条件下,M-算子的不动点集可以构成EQ-代数。EQ-algebras are an important class of logic algebras corresponding to higher-order fuzzy logic.As the main research field of fuzzy logic theory,it is of great significance to promote the development of artificial intelligence.The main purpose of this paper is to introduce the concepts of multiplier operators(m-operators),simple m-operators and idempotent m-operators on EQ-algebras and study their related properties.We obtain that the composition of m-operators is still an m-operator and give an equivalent characterization of order-preserving m-operators.We then prove that at least n different m-operators can be defined on good EQ-algebra with n variables.Furthermore,we discuss the relations between m-operators and some special mappings(closure operator,homomorphism mapping,idempotent mapping,identity mapping)and give the equivalent characterization of m-operators for identical mappings.Finally,we study some related properties of fixed point set of m-operator on EQ-algebra,and get that fixed point set of m-operator is an EQ-algebra under some conditions.

关 键 词：高阶模糊逻辑 EQ-代数 Multiplier算子 不动点集 

分 类 号：O141[理学—数学]