Fully implicational methods for approximate reasoning based on interval-valued fuzzy sets

被引：13
作者：
Liu, Huawen [1 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China
来源：
JOURNAL OF SYSTEMS ENGINEERING AND ELECTRONICS | 2010年 / 21卷 / 02期
基金：
中国国家自然科学基金;
关键词：
approximate reasoning; interval-valued fuzzy set; interval-valued fuzzy implication; fully implicational method; reversibility; TRIPLE-I METHOD; INTUITIONISTIC FUZZY; UNIFIED FORMS; T-NORMS; CONNECTIVES;
D O I：
10.3969/j.issn.1004-4132.2010.02.009
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The aim of this paper is to discuss the approximate reasoning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of implications and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens (IFMP) and interval-valued fuzzy modus tollens (IFMT) problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of a-triple I (the abbreviation of triple implications) methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.
引用
收藏
页码：224 / 232
页数：9
相关论文
共 37 条
[1]   INTUITIONISTIC FUZZY-SETS [J].
ATANASSOV, KT .
FUZZY SETS AND SYSTEMS, 1986, 20 (01) :87-96
[2]   Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets [J].
Bustince, H .
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2000, 23 (03) :137-209
[3]   Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application [J].
Cornelis, C ;
Deschrijver, G ;
Kerre, EE .
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2004, 35 (01) :55-95
[4]   Smets-Magrez axioms for R-implicators in interval-valued and intuitionistic fuzzy set theory [J].
Deschrijver, G ;
Kerre, EE .
INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 2005, 13 (04) :453-464
[5]   Classes of intuitionistic fuzzy t-norms satisfying the residuation principle [J].
Deschrijver, G ;
Kerre, EE .
INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 2003, 11 (06) :691-709
[6]   On the representation of intuitionistic fuzzy t-norms and t-conorms [J].
Deschrijver, G ;
Cornelis, C ;
Kerre, EE .
IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2004, 12 (01) :45-61
[7]   On the relationship between some extensions of fuzzy set theory [J].
Deschrijver, G ;
Kerre, EE .
FUZZY SETS AND SYSTEMS, 2003, 133 (02) :227-235
[8]   Implicators based on binary aggregation operators in interval-valued fuzzy set theory [J].
Deschrijver, G ;
Kerre, EE .
FUZZY SETS AND SYSTEMS, 2005, 153 (02) :229-248
[9]   Representability in interval-valued fuzzy set theory [J].
Deschrijver, Glad ;
Cornelis, Chris .
INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 2007, 15 (03) :345-361
[10]  
DZEICH D, 1983, INTERVAL FUZZY MATH, P77
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