三种基于不同模糊否定的模糊拒取式推理及其算法<sup>*</sup>

doi:10.16451/j.cnki.issn1003-6059.201502001

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摘要

模糊拒取式推理(FMT)是模糊推理中最基本的推理形式之一，FMT的一个前提——模糊否定在推理中较重要.文中基于区分矛盾否定、对立否定和中介否定的模糊命题逻辑形式系统(FLCOM)，证明矛盾否定、对立否定和中介否定是3种不同的模糊否定，提出与FMT不同的，分别基于矛盾否定、对立否定和中介否定的3种模糊拒取式推理FMT₁、FMT₂和FMT₃.此外，基于R-蕴涵算子I_R定义一种与I_R关联的NR-蕴涵算子I_NR，并依据FMT的算法给出FMT₁、FMT₂和FMT₃的算法，证明FMT₁、FMT₂和FMT₃的算法在I ≤I_NR条件下是还原算法.

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	潘正华
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关键词 ：模糊拒取式推理(FMT), 矛盾否定, 对立否定, 中介否定, 模糊拒取式推理算法

Abstract：

Fuzzy modus tollens (FMT) is one of the most basic inference forms in fuzzy reasoning. As a premise of FMT, fuzzy negation plays a major role in inference. In this paper, based on the fuzzy propositional logic with contradictory negation, opposite negation and medium negation (FLCOM), contradictory negation, opposite negation and medium negation are proved to be different fuzzy negations, and thus three kinds of fuzzy modus tollens, FMT₁, FMT₂ and FMT₃, are proposed,which are different from FMT respectively based on contradictory negation, opposite negation and medium negation. Furthermore, based on the R-implication operator I_R, a fuzzy NR-implication operator I_NR is defined which is associated with I_R. The algorithms of FMT₁, FMT₂ and FMT₃ are proposed according to the algorithm of FMT, and it is proved that algorithms of FMT₁, FMT₂ and FMT₃ are reducible algorithms when I ≤I_NR.

Key words： Fuzzy Modus Tollens(FMT) Contradictory Negation Opposite Negation Medium Negation Algorithm of Fuzzy Modus Tollens

收稿日期: 2013-09-27

ZTFLH:

TP181

基金资助:

国家自然科学基金项目(No.60973156,61375004)、中央高校基本科研业务费专项资金项目(No.JUSRP51317B)资助

作者简介: 潘正华(通讯作者)，男，1957年生，教授，主要研究方向为非经典逻辑理论、知识表示与知识推理.E-mail:panzh@jiangnan.edu.cn.赵洁心，女，1989年生，硕士研究生，主要研究方向为非经典逻辑理论与推理.王姗姗，女，1989年生，硕士研究生，主要研究方向为非经典逻辑理论与推理.

引用本文:

潘正华，赵洁心，王姗姗. 三种基于不同模糊否定的模糊拒取式推理及其算法^*[J]. 模式识别与人工智能, 2015, 28(2): 97-104. PAN Zheng-Hua, ZHAO Jie-Xin, WANG Shan-Shan. Three Kinds of Fuzzy Modus Tollens and Algorithms Based on Different Fuzzy Negations. , 2015, 28(2): 97-104.

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