(T,N)-蕴涵及其基本性质

doi:10.6040/j.issn.1671-9352.0.2017.164

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (11): 71-81.doi: 10.6040/j.issn.1671-9352.0.2017.164

(T,N)-蕴涵及其基本性质

于俊红,周红军^*

陕西师范大学数学与信息科学学院, 陕西西安 710119

收稿日期:2017-04-17 出版日期:2017-11-20 发布日期:2017-11-17
通讯作者: 周红军(1980— ),男,教授,硕士生导师,研究方向为不确定性推理. E-mail:hjzhou@snnu.edu.cn E-mail:18392534761@163.com
作者简介:于俊红(1989— ),女,硕士研究生,研究方向为不确定性推理. E-mail:18392534761@163.com
基金资助:
国家自然科学基金资助项目(61473336);陕西省青年科技新星计划项目(2016KJXX-24);中央高校基本科研业务费专项基金特别支持项目(GK201403001)

(T,N)-implication and its basic properties

YU Jun-hong, ZHOU Hong-jun^*

College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China

Received:2017-04-17 Online:2017-11-20 Published:2017-11-17

摘要/Abstract

摘要： 模糊蕴涵在模糊逻辑和近似推理领域中发挥着非常重要的作用。不同的构造方法可以生成不同的模糊蕴涵, 其中常见的模糊蕴涵类有(S,N)-蕴涵、 R-蕴涵、 QL-蕴涵和Yager蕴涵等。从经典逻辑中的重言式p→q≡(p∧q)出发, 在模糊逻辑中研究由三角模T和模糊否定N按上述方式生成的模糊蕴涵, 称为(T,N)-蕴涵, 进而研究(T,N)-蕴涵的一些基本性质, 包括输入律与分配性等。最后讨论(T,N)-蕴涵与 f-蕴涵、 g-蕴涵、(S,N)-蕴涵和R-蕴涵间的关系。

关键词: 模糊否定, f-蕴涵, R-蕴涵, N)-蕴涵, 三角余模, (T, 分配律, (S, 模糊蕴涵, g-蕴涵, 三角模, N)-蕴涵

Abstract: Fuzzy implications play a fundamental role in fuzzy logic and approximate reasoning. According to construction methods, there are mainly four classes of fuzzy implications, namely,(S,N)-implications, R-implications, QL-implications and Yagers generated implications. We introduce a new class of implications, called(T,N)-implications, generated from t-norms T and fuzzy negations N inspired by the classical tautology p→q≡(p∧q). We discuss the properties of(T,N)-implications and study some classical logic tautologies(e.g., law of importation and distributivity over t-norms or t-conorms)for (T,N)-implications. And the relationships of (T,N)-implications to f-implications, g-implications,(S,N)-implications and R-implications are investigated.

Key words: triangular norm, triangular conorm, (T,N)-implication, R-implication, g-implication, fuzzy implication, f-implication, (S,N)-implication, distributivity equation, fuzzy negation

中图分类号:

O142

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于俊红,周红军. (T,N)-蕴涵及其基本性质[J]. 山东大学学报（理学版）, 2017, 52(11): 71-81.

YU Jun-hong, ZHOU Hong-jun. (T,N)-implication and its basic properties[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 71-81.

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[1]	彭家寅. 剩余格上的落影模糊滤子[J]. 山东大学学报（理学版）, 2018, 53(2): 52-64.
[2]	韩亮,刘华文. 有限链上逻辑算子的分配性方程求解[J]. 山东大学学报（理学版）, 2014, 49(2): 29-35.
[3]	巩增泰,齐颖. 基于Archimedean三角模的广义直觉模糊不确定语言变量集成方法[J]. J4, 2013, 48(3): 53-63.
[4]	李莎莎，巩本学. 量子辛型群@(Sp_q(6))的一种实现[J]. J4, 2010, 45(8): 53-56.
[5]	郭聿琦1,宫春梅2,任学明2. 关于半群上格林关系的一个来龙去脉的综述[J]. J4, 2010, 45(8): 1-18.
[6]	郝加兴,吴洪博. 基于非交换剩余格的模糊蕴涵滤子及其性质[J]. J4, 2010, 45(10): 61-65.
[7]	宋佳,罗敏楠,李永明. 区间值三角模左连续的充要条件[J]. J4, 2009, 44(3): 67-70 .
[8]	刘培德,张新 . 建筑企业融资方案模糊多目标评价研究[J]. J4, 2008, 43(11): 22-26 .
[9]	巩本学,李莎莎 . O(Spq(4))经由Uq(sp(4))的Jantzen途径实现[J]. J4, 2007, 42(8): 91-94 .
[10]	许波,李刚,王振华,林洪,郑秋生 . 20(S)-原人参二醇衍生物对HT1080细胞侵袭转移的影响[J]. J4, 2007, 42(3): 84-88 .

(T,N)-蕴涵及其基本性质

(T,N)-implication and its basic properties

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