IMTL逻辑代数的一种新强化形式  

A schematic extension of IM TL-logic algebras

作　　者：周建仁[1,2] 吴洪博[2] 

机构地区：[1]河西学院数学与统计学院,甘肃张掖734000 [2]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《山东大学学报（理学版）》2014年第4期84-89,94,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11171196)

摘　　要：对IMTL-代数及其相关逻辑代数进行了进一步的研究,通过加强IMTL-代数条件的方法建立了IMTL*-代数,并通过实例证明了IMTL*-代数结构的存在性;其次,构造了一个非IMTL*-代数的IMTL-代数,说明了IMTL*-代数是IMTL-代数的真的强化形式,并基于IMTL-代数给出了IMTL*-代数的一些等价刻画;最后,给出了IMTL*-代数的蕴涵表示形式。本文的结果是对逻辑代数的研究内容和方法的有益补充。IMTL and its related logic algebras are investigated in depth again and some new useful results are obtained. Firstly, the IMTL-algebras are introduced by strengthening the conditions of IMTL-algebra, and the existence of IMTL-algebras is explained by establishing structures of IMTL＊-algebra.Secondly, an algebra structure is established that is IMTL-algebra and not IMTL＊-algebra, which explains that IMTL＊-algebras are truely strengthened form of IMTL-algebras, and based on IMTL-algebras some equivalent characterization of IMTL＊-algebras are given.At last, the pure implication representation of IMTL＊-algebras is obtained.The results of this paper are necessary complemen-tarity to the methods and contents of logic algebras.

关 键 词：模糊逻辑 逻辑代数 IMTL-代数 IMTL＊-代数 特征 蕴涵表示定理 

分 类 号：O141.1[理学—数学]