基于完备剩余格值逻辑的伪BCI-代数的不分明化理想  

Fuzzyifying Ideals of Pseudo BCI-algebras Based on Complete Residuated Lattice-valued Logic

作　　者：彭家寅[1] PENG Jia-yin(School of Mathematics and Information Science,Neijiang Normal University,Neijiang 641199,China)

机构地区：[1]内江师范学院数学与信息科学学院

出　　处：《模糊系统与数学》2019年第5期10-29,共20页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11071178);教育部数学与应用数学专业综合改革试点项目(01249)

摘　　要：通过完备剩余格值逻辑中一元模糊谓词演算,将伪BCI-代数中的经典模糊理想、模糊p-理想、模糊结合理想、模糊q-理想和模糊a-理想进行重新刻画,引入了BCI-代数的l-值模糊理想、l-值模糊p-理想、l-值模糊结合理想、l-值模糊q-理想和l-值模糊a-理想的概念。利用完备剩余格值逻辑的语义方法,研究这几种l-值模糊理想的性质及关系。提供了l-值模糊理想成为l-值模糊p-理想(l-值模糊q-理想)的条件,研究了这些l-值模糊理想在交、同态映射和笛卡尔积运算下的不变性,推广了经典模糊情形下相应的现有结论。By a unary fuzzy predicate calculus on complete residuated lattice-valued logic, the classic fuzzy ideal, classic fuzzy p-ideal, classic fuzzy associative ideal, classic fuzzy q-ideal and classic fuzzy a-ideal in pseudo BCI-algebra are reportrayed. The concepts of l-valued fuzzy ideals, l-valued fuzzy p-ideals, l-valued fuzzy associative ideas, l-valued fuzzy q-ideals and l-valued fuzzy a-ideals in pseudo BCI-algebra are introduced. Using the semantic method of complete residuated lattice-valued logic, the properties and relations of these l-valued fuzzy ideals are studied. Conditions for an l-valued fuzzy ideal to be an l-valued fuzzy p-ideal(resp. l-valued fuzzy q-ideal) are provided. The invariances of these l-valued fuzzy ideals under the intersection, homomorphic mapping and Descartes product operations are investigated, and the corresponding and existing conclusions in classical fuzzy cases are generalized.

关 键 词：伪BCI-代数 完备剩余格值逻辑 l-值模糊理想 l-值模糊p-理想 l-值模糊结合理想 l-值模糊q-理想 l-值模糊α-理想 

分 类 号：O141[理学—数学]