| IMTL逻辑代数的一种新强化形式 |
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| 引用本文： | 周建仁,吴洪博. IMTL逻辑代数的一种新强化形式[J]. 山东大学学报(自然科学版), 2014, 0(4): 84-89,94 |
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| 作者姓名： | 周建仁 吴洪博 |
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| 作者单位： | [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 |
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| 基金项目： | 国家自然科学基金资助项目（11171196） |
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| 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。
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| 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 |
A schematic extension of IMTL-logic algebras |
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| ZHOU Jian-ren,WU Hong-bo. A schematic extension of IMTL-logic algebras[J]. Journal of Shandong University(Natural Science Edition), 2014, 0(4): 84-89,94 |
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| Authors: | ZHOU Jian-ren WU Hong-bo |
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| Affiliation: | ZHOU Jian-ren, WU Hong-bo |
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| Abstract: | 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. |
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| Keywords: | fuzzy logic logic algebra IMTL-algebras IMTL＊-algebras characteristic implication representation the-orem |
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