Simplification and independence of axioms of fuzzy logic systems IMTL and NM

被引：10
作者：
Pei, DW [1 ]
机构：
[1] Xi An Jiao Tong Univ, Ctr Sci Res, Xian 710049, Peoples R China
[2] Yancheng Teachers Coll, Dept Math, Yancheng 224002, Peoples R China
来源：
FUZZY SETS AND SYSTEMS | 2005年 / 152卷 / 02期
关键词：
fuzzy logic; involutive monoidal t-norm-based logic; nilpotent minimum logic; simplification; independence;
D O I：
10.1016/j.fss.2004.12.002
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Monoidal t-norm-based logic MTL is the common formalization of all fuzzy logic of left continuous t-norms and their residua. This system has two important schematic extensions: involutive monoidal t-norm-based logic IMTL and nilpotent minimum logic NM. In this paper, we discuss simplification and independence of axioms of IMTL and NM, the shorter axioms of both logics, and an independent axioms of the system IMTL are given. (c) 2005 Elsevier B.V. All rights reserved.
引用
收藏
页码：303 / 320
页数：18
相关论文
共 25 条
[1]   Basic Fuzzy Logic is the logic of continuous t-norms and their residua [J].
R. Cignoli ;
F. Esteva ;
L. Godo ;
A. Torrens .
Soft Computing, 2000, 4 (2) :106-112
[2]   FUZZY-SETS IN APPROXIMATE REASONING .1. INFERENCE WITH POSSIBILITY DISTRIBUTIONS [J].
DUBOIS, D ;
PRADE, H .
FUZZY SETS AND SYSTEMS, 1991, 40 (01) :143-202
[3]   On the standard and rational completeness of some axiomatic extensions of the monoidal t-norm logic [J].
Esteva F. ;
Gispert J. ;
Godo L. ;
Montagna F. .
Studia Logica, 2002, 71 (2) :199-226
[4]   Monoidal t-norm based logic: towards a logic for left-continuous t-norms [J].
Esteva, F ;
Godo, L .
FUZZY SETS AND SYSTEMS, 2001, 124 (03) :271-288
[5]  
ESTEVA F, P ISMVL 2001 WARS, P81
[6]   CONTRAPOSITIVE SYMMETRY OF FUZZY IMPLICATIONS [J].
FODOR, JC .
FUZZY SETS AND SYSTEMS, 1995, 69 (02) :141-156
[7]   A new axiomatization for involutive monoidal t-norm-based logic [J].
Gottwald, S ;
Jenei, S .
FUZZY SETS AND SYSTEMS, 2001, 124 (03) :303-307
[8]  
Gottwald S., 2001, TREATISE MANY VALUED
[9]  
Hajek P, 1998, Trends in Logic
[10]   On the fundamentals of fuzzy set theory [J].
Hohle, U .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 201 (03) :786-826
123