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| IMTL逻辑系统的一种新扩张形式 | |
| 引用本文： | 周建仁,吴洪博. IMTL逻辑系统的一种新扩张形式[J]. 山东大学学报(理学版), 2015, 50(12): 28-34. DOI: 10.6040/j.issn.1671-9352.0.2014.458 |
| 作者姓名： | 周建仁 吴洪博 |
| 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 |
| 基金项目： | 国家自然科学基金资助项目(11171196);中央高校基本科研业务费专项基金项目(GK201501001) |
| 摘 要： | 提出了一种新的模糊逻辑系统 IMTL*,这种逻辑系统的特点是只使用蕴涵这一种逻辑联接词。证明了这种逻辑系统是IMTL逻辑系统的模型扩张,并且 ?ukasiewicz 逻辑系统和逻辑系统ℵ*都是它的模型扩张,应用这些结论给出了?ukasiewicz 逻辑系统和逻辑系统ℵ*的蕴涵表示形式。只使用蕴涵这一种逻辑联接词的模糊逻辑系统将为模糊逻辑的应用提供方便。 |
| 关 键 词： | IMTL逻辑系统 ukasiewicz 逻辑系统 模糊逻辑 蕴涵表示 IMTL*逻辑系统 ? 逻辑系统L* |
| 收稿时间： | 2014-10-20 |
A schematic extension of IMTL logic system |
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| ZHOU Jian-ren,WU Hong-bo. A schematic extension of IMTL logic system[J]. Journal of Shandong University, 2015, 50(12): 28-34. DOI: 10.6040/j.issn.1671-9352.0.2014.458 | |
| Authors: | ZHOU Jian-ren WU Hong-bo |
| Affiliation: | 1. College of Mathematics and Statistics, Hexi University, Zhangye 734000, Gansu, China; 2. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaanxi, China |
| Abstract: | A new fuzzy logic system IMTL* logic is introduced. The feature of this logic system is only one logic connective concerned. It is proved that IMTL* logic is a schematic extension of IMTL logic and ?ukasiewicz logic and logic system ℵ* are both schematic extension of IMTL* Logic. Finally the pure implication representation of ?ukasiewicz logic and logic ℵ* are obtained. The fuzzy logic systems which is only one logic connective implication concerned will bring convenience to use of fuzzy logic. |
| Keywords: | IMTL logic logic ℵ IMTL* logic ukasiewicz logic ? fuzzy logic * implication representation |
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